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anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let 's see , we have methyl group on the number two carbon , it is a pentene , and that is double-bond between the number two and number three carbons , so this is two-methyl-pent-2-ene . so that 's what we start with , we 're in the presence , we 're in an acidic environment , we 've got what 's gon na be catalyzed by our hydronium here , and we end up with this , and how is our product different from what we started with ? well the double bond is now gone , the number three carbon gains this hydrogen , and now the number two carbon gains a hydroxyl group . so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule , but if you take the hydrogen we added , and the hydroxyl we added , if you combine them , that 's what you need to make a water . so let 's think about how we can , how this actually happens in the presence of our hydronium . so let me redraw this molecule right over here . so we copy and paste it , so that 's not exactly it yet , that is just with the single bond . so let me draw , woops , wrong tool . let me draw the double bond there . and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the entire molecule positive , because the hydrogen proton is positive . so there you go , this now has a positive charge . and this can be pretty reactive , 'cause we know that oxygen is quite electronegative , it lives to keep its electrons . so what is there was a way , what if there 's a way for the oxygen to take back the electrons in this bond right over here , the two electrons in this bond . well what if one of these carbons , especially the ones that have the double bonds , what if some of the electrons from this double bond could be used to snab , to take that hydrogen proton , and then oxygen can hog its electrons again . and you might say , `` oh that 's reasonable , but which of these carbons would actually do it ? '' and to think about which of those carbons would do it , we have to turn to markovnikov 's rule . markovnikov 's rule tells us that , look , if you have a reaction like this , and alkene reaction , the carbon that already has , that 's already attached to more hydrogens is more likely to gain more hydrogens , the carbon that 's attached to more functional groups is more likely to gain more functional groups . another way to think about it is think about , well that is the order of the carbons ? because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbon on the other side of the double bond is only bonded to one , two carbons . so this is a secondary carbon . so the tertiary carbon is going to be more stable as a carbocation , you can think of it as it can spread the charge a little bit . so it would be more likely to lose the electrons in one of these , in one of these bonds , and so the way that we can think about this mechanism , and it might be a little bit clearer when we form the carbocation , is let 's have , going to do this in blue . let 's have these two electrons that form this bond , well now they form a bond with that hydrogen , and now the oxygen can take back these two electrons , and what are we going , what is going to result ? and i 'm drawing it in equilibrium , remember all of these things are going back and forth depending on how things bump into each other , but what are we left with ? so let me copy and paste this again and i 'm copying and pasting in a way that , just so i , this is the backbone , and i 'll add what i need to add . so once this happens , we have this carbon , the number three carbon , now , woops i keep using the wrong tool . the number three carbon now forms a bond with this hydrogen just like that . this carbon , our number two carbon , has lost an electron , it 's no longer sharing this bond . and so now it is going to have a positive charge , it is a carbocation and once again is a tertiary carbocation , it is bonded to one , two , three carbons . that is stable , more stable than if we did it the other way around , if this one grabbed the hydrogen somehow , then this would be a secondary carbocation , it 'd be harder for it to spread that positive charge around . and what about our , what about our molecule up here ? let 's see what it looks like now . we have our oxygen bonded to the two hydrogens , it had one of those lone pairs , and now the electrons in this bond are now going to form another lone pair . so it took back an electron , or you can think of it , it gave away a hydrogen proton . and so this is now just neutral water , and we see that we have a conservation of charge here , this was positive in charge , now our original molecule is positively charged . and what feels good about this is we 're getting , we 're getting close to our end product , at least on our number three carbon , we now have , we now have this hydrogen . now we need to think about , well how do we get a hydroxyl group added right over here ? well we have all this water , we have all this water floating around , let me , i could use this water molecule but the odds of it being the exact same water molecule , we do n't know . but there 's all sorts of water molecules , we 're in an aqueous solution , so let me draw another water molecule here . so the water molecules are all equivalent , but let me draw another water molecule here . and you can imagine , if they just pump into each other in just the right way , this is , water is a polar molecule , it has a partially negative end near the oxygen because the oxygen likes to hog the electrons , and then you have a partial positive end near the hydrogens 'cause they get their electrons hogged , so you can imagine the oxygen end might be attracted to this tertiary carbocation , and so just bumping it in just the right way , it might form a bond . so let me say these two electrons right over here , let 's say they form a bond with this , with that number two carbon , and then what is going to result ? so let me draw , so what is , what is going to result , let me scroll down a little bit , and let me paste , whoops , let me copy and paste our original molecule again . so , here we go . so what could happen ? this is the one we constructed actually , so we have the hydrogen there . we have the hydrogen , now this character , so we have the water molecule , so oxygen bonded to two hydrogens , you have this one lone pair that is n't reacting , but then you have the lone pair that does do the reacting . and so it now forms a bond . woops , let me do it in that orange color . it now , it now forms an actual bond . and we 're really close to our final product , we have our hydrogen on the number three carbon , we have more than we want on our number two carbon , we just want a hydroxyl group , now we have a whole water bonded to the carbon . so somehow we have to get one of these other hydrogens swiped off of it , well that could happen with just another water molecule . so let 's draw that . so another water molecule someplace , i 'll do the different color just to differentiate , although as we know water , well it 's hard to see what color is water if you 're looking at the molecular scale . so here we go , and we 're really in the home stretch at this point . you have another water molecule , let 's say , let me pick a color . so let 's say these electrons right over here , maybe they form a bond with that hydrogen proton , and then these , the electrons in that bond can go back to form a lone pair on that oxygen , and then what are we left with ? and this really is the home stretch . so we are in equilibrium with , so let me draw my five carbons , so let 's see , i have ... h3c , carbon , carbon , ch2 , ch3 , i have a ch3 , i say h3c instead of ch3 , i wrote it that way just so it 's clear that the carbons are bonded to the carbons , you have the original hydrogen right over there , you have the one that we just added as part of this mechanism , you have this orange bond to now , this hydroxyl group , the hydroxyl group , and it had one lone pair before , it had one lone pair before , but bound to both of the electrons from this bond to form another lone pair . to form another lone pair , which i am depicting in pink , and then this water is now , this water molecule is now a hydronium molecule . so let me draw that , so this is now , oxygen , hydrogen , had one lone pair that did n't react , and it had one lone pair that i put in blue that is reacting with this hydrogen proton . with that hydrogen , just like this , and so since it got the hydrogen proton it 's giving its , sharing its electrons now , now this has a positive , this has a positive charge , just like that . i have to be very careful , in the last step i forgot to draw the positive charge ! we always wan na make sure that your charge is being conserved , we started off with the positive charge on the hydronium , then we have the positive charge on the tertiary carbocation right over here on our number two carbon , and now we have the positive charge , would be right over here , because that oxygen , what we saw before that oxygen , which this water molecule was neutral , but you could say , you could view it is `` well now it 's going to be , it 's now sharing these two electrons instead of keeping them , '' so you can view it is maybe it 's giving away an electron , and so now it becomes positive . and then , and then the positive charge finally gets transferred to that other water molecule when it becomes hydronium . but just like that we are done . we have added a hydroxyl group and a hydrogen combined , that 's a water , so that 's why we call it addition of water , and it was catalyzed by acid , so it 's an acid-catalyzed addition of water .
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because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbon on the other side of the double bond is only bonded to one , two carbons .
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and by the same logic , is the right carbon not a tertiary carbon ?
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anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let 's see , we have methyl group on the number two carbon , it is a pentene , and that is double-bond between the number two and number three carbons , so this is two-methyl-pent-2-ene . so that 's what we start with , we 're in the presence , we 're in an acidic environment , we 've got what 's gon na be catalyzed by our hydronium here , and we end up with this , and how is our product different from what we started with ? well the double bond is now gone , the number three carbon gains this hydrogen , and now the number two carbon gains a hydroxyl group . so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule , but if you take the hydrogen we added , and the hydroxyl we added , if you combine them , that 's what you need to make a water . so let 's think about how we can , how this actually happens in the presence of our hydronium . so let me redraw this molecule right over here . so we copy and paste it , so that 's not exactly it yet , that is just with the single bond . so let me draw , woops , wrong tool . let me draw the double bond there . and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the entire molecule positive , because the hydrogen proton is positive . so there you go , this now has a positive charge . and this can be pretty reactive , 'cause we know that oxygen is quite electronegative , it lives to keep its electrons . so what is there was a way , what if there 's a way for the oxygen to take back the electrons in this bond right over here , the two electrons in this bond . well what if one of these carbons , especially the ones that have the double bonds , what if some of the electrons from this double bond could be used to snab , to take that hydrogen proton , and then oxygen can hog its electrons again . and you might say , `` oh that 's reasonable , but which of these carbons would actually do it ? '' and to think about which of those carbons would do it , we have to turn to markovnikov 's rule . markovnikov 's rule tells us that , look , if you have a reaction like this , and alkene reaction , the carbon that already has , that 's already attached to more hydrogens is more likely to gain more hydrogens , the carbon that 's attached to more functional groups is more likely to gain more functional groups . another way to think about it is think about , well that is the order of the carbons ? because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbon on the other side of the double bond is only bonded to one , two carbons . so this is a secondary carbon . so the tertiary carbon is going to be more stable as a carbocation , you can think of it as it can spread the charge a little bit . so it would be more likely to lose the electrons in one of these , in one of these bonds , and so the way that we can think about this mechanism , and it might be a little bit clearer when we form the carbocation , is let 's have , going to do this in blue . let 's have these two electrons that form this bond , well now they form a bond with that hydrogen , and now the oxygen can take back these two electrons , and what are we going , what is going to result ? and i 'm drawing it in equilibrium , remember all of these things are going back and forth depending on how things bump into each other , but what are we left with ? so let me copy and paste this again and i 'm copying and pasting in a way that , just so i , this is the backbone , and i 'll add what i need to add . so once this happens , we have this carbon , the number three carbon , now , woops i keep using the wrong tool . the number three carbon now forms a bond with this hydrogen just like that . this carbon , our number two carbon , has lost an electron , it 's no longer sharing this bond . and so now it is going to have a positive charge , it is a carbocation and once again is a tertiary carbocation , it is bonded to one , two , three carbons . that is stable , more stable than if we did it the other way around , if this one grabbed the hydrogen somehow , then this would be a secondary carbocation , it 'd be harder for it to spread that positive charge around . and what about our , what about our molecule up here ? let 's see what it looks like now . we have our oxygen bonded to the two hydrogens , it had one of those lone pairs , and now the electrons in this bond are now going to form another lone pair . so it took back an electron , or you can think of it , it gave away a hydrogen proton . and so this is now just neutral water , and we see that we have a conservation of charge here , this was positive in charge , now our original molecule is positively charged . and what feels good about this is we 're getting , we 're getting close to our end product , at least on our number three carbon , we now have , we now have this hydrogen . now we need to think about , well how do we get a hydroxyl group added right over here ? well we have all this water , we have all this water floating around , let me , i could use this water molecule but the odds of it being the exact same water molecule , we do n't know . but there 's all sorts of water molecules , we 're in an aqueous solution , so let me draw another water molecule here . so the water molecules are all equivalent , but let me draw another water molecule here . and you can imagine , if they just pump into each other in just the right way , this is , water is a polar molecule , it has a partially negative end near the oxygen because the oxygen likes to hog the electrons , and then you have a partial positive end near the hydrogens 'cause they get their electrons hogged , so you can imagine the oxygen end might be attracted to this tertiary carbocation , and so just bumping it in just the right way , it might form a bond . so let me say these two electrons right over here , let 's say they form a bond with this , with that number two carbon , and then what is going to result ? so let me draw , so what is , what is going to result , let me scroll down a little bit , and let me paste , whoops , let me copy and paste our original molecule again . so , here we go . so what could happen ? this is the one we constructed actually , so we have the hydrogen there . we have the hydrogen , now this character , so we have the water molecule , so oxygen bonded to two hydrogens , you have this one lone pair that is n't reacting , but then you have the lone pair that does do the reacting . and so it now forms a bond . woops , let me do it in that orange color . it now , it now forms an actual bond . and we 're really close to our final product , we have our hydrogen on the number three carbon , we have more than we want on our number two carbon , we just want a hydroxyl group , now we have a whole water bonded to the carbon . so somehow we have to get one of these other hydrogens swiped off of it , well that could happen with just another water molecule . so let 's draw that . so another water molecule someplace , i 'll do the different color just to differentiate , although as we know water , well it 's hard to see what color is water if you 're looking at the molecular scale . so here we go , and we 're really in the home stretch at this point . you have another water molecule , let 's say , let me pick a color . so let 's say these electrons right over here , maybe they form a bond with that hydrogen proton , and then these , the electrons in that bond can go back to form a lone pair on that oxygen , and then what are we left with ? and this really is the home stretch . so we are in equilibrium with , so let me draw my five carbons , so let 's see , i have ... h3c , carbon , carbon , ch2 , ch3 , i have a ch3 , i say h3c instead of ch3 , i wrote it that way just so it 's clear that the carbons are bonded to the carbons , you have the original hydrogen right over there , you have the one that we just added as part of this mechanism , you have this orange bond to now , this hydroxyl group , the hydroxyl group , and it had one lone pair before , it had one lone pair before , but bound to both of the electrons from this bond to form another lone pair . to form another lone pair , which i am depicting in pink , and then this water is now , this water molecule is now a hydronium molecule . so let me draw that , so this is now , oxygen , hydrogen , had one lone pair that did n't react , and it had one lone pair that i put in blue that is reacting with this hydrogen proton . with that hydrogen , just like this , and so since it got the hydrogen proton it 's giving its , sharing its electrons now , now this has a positive , this has a positive charge , just like that . i have to be very careful , in the last step i forgot to draw the positive charge ! we always wan na make sure that your charge is being conserved , we started off with the positive charge on the hydronium , then we have the positive charge on the tertiary carbocation right over here on our number two carbon , and now we have the positive charge , would be right over here , because that oxygen , what we saw before that oxygen , which this water molecule was neutral , but you could say , you could view it is `` well now it 's going to be , it 's now sharing these two electrons instead of keeping them , '' so you can view it is maybe it 's giving away an electron , and so now it becomes positive . and then , and then the positive charge finally gets transferred to that other water molecule when it becomes hydronium . but just like that we are done . we have added a hydroxyl group and a hydrogen combined , that 's a water , so that 's why we call it addition of water , and it was catalyzed by acid , so it 's an acid-catalyzed addition of water .
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so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule , but if you take the hydrogen we added , and the hydroxyl we added , if you combine them , that 's what you need to make a water .
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an electophilic addition or a neucleophilic addition ?
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anytime you 're trying to come up with a mechanism for a reaction , it 's worthwhile to study a little bit of what you are starting with and then thinking about what you finish with and think about what is different . so what we 're starting with , we could call this one , two , three , four , five , so this is , let 's see , we have methyl group on the number two carbon , it is a pentene , and that is double-bond between the number two and number three carbons , so this is two-methyl-pent-2-ene . so that 's what we start with , we 're in the presence , we 're in an acidic environment , we 've got what 's gon na be catalyzed by our hydronium here , and we end up with this , and how is our product different from what we started with ? well the double bond is now gone , the number three carbon gains this hydrogen , and now the number two carbon gains a hydroxyl group . so one way to think about this is , in the presence of an acid , it 's acid-catalyzed , we have gained two hydrogens and an oxygen , which is what we 've gained , what could be used to make a water . and this is actually called an acid-catalyzed addition of water . the water is n't sitting on one part of the molecule , but if you take the hydrogen we added , and the hydroxyl we added , if you combine them , that 's what you need to make a water . so let 's think about how we can , how this actually happens in the presence of our hydronium . so let me redraw this molecule right over here . so we copy and paste it , so that 's not exactly it yet , that is just with the single bond . so let me draw , woops , wrong tool . let me draw the double bond there . and now let me put it in the presence of some hydronium . alright , so we have an oxygen bonded , two . so this would just be water , as oxygen has two lone pairs , but hydronium is a situation where oxygen is sharing one of those lone pairs with a hydrogen proton , thus making the entire molecule positive , because the hydrogen proton is positive . so there you go , this now has a positive charge . and this can be pretty reactive , 'cause we know that oxygen is quite electronegative , it lives to keep its electrons . so what is there was a way , what if there 's a way for the oxygen to take back the electrons in this bond right over here , the two electrons in this bond . well what if one of these carbons , especially the ones that have the double bonds , what if some of the electrons from this double bond could be used to snab , to take that hydrogen proton , and then oxygen can hog its electrons again . and you might say , `` oh that 's reasonable , but which of these carbons would actually do it ? '' and to think about which of those carbons would do it , we have to turn to markovnikov 's rule . markovnikov 's rule tells us that , look , if you have a reaction like this , and alkene reaction , the carbon that already has , that 's already attached to more hydrogens is more likely to gain more hydrogens , the carbon that 's attached to more functional groups is more likely to gain more functional groups . another way to think about it is think about , well that is the order of the carbons ? because the higher order of carbon , the more stable it will be if it forms some type of cation . so if you look at this carbon right over here , our number two carbon , let me circle it , our number two carbon is bonded to one , two , three carbons . so this is a tertiary carbon . this one right over here , this carbon on the other side of the double bond is only bonded to one , two carbons . so this is a secondary carbon . so the tertiary carbon is going to be more stable as a carbocation , you can think of it as it can spread the charge a little bit . so it would be more likely to lose the electrons in one of these , in one of these bonds , and so the way that we can think about this mechanism , and it might be a little bit clearer when we form the carbocation , is let 's have , going to do this in blue . let 's have these two electrons that form this bond , well now they form a bond with that hydrogen , and now the oxygen can take back these two electrons , and what are we going , what is going to result ? and i 'm drawing it in equilibrium , remember all of these things are going back and forth depending on how things bump into each other , but what are we left with ? so let me copy and paste this again and i 'm copying and pasting in a way that , just so i , this is the backbone , and i 'll add what i need to add . so once this happens , we have this carbon , the number three carbon , now , woops i keep using the wrong tool . the number three carbon now forms a bond with this hydrogen just like that . this carbon , our number two carbon , has lost an electron , it 's no longer sharing this bond . and so now it is going to have a positive charge , it is a carbocation and once again is a tertiary carbocation , it is bonded to one , two , three carbons . that is stable , more stable than if we did it the other way around , if this one grabbed the hydrogen somehow , then this would be a secondary carbocation , it 'd be harder for it to spread that positive charge around . and what about our , what about our molecule up here ? let 's see what it looks like now . we have our oxygen bonded to the two hydrogens , it had one of those lone pairs , and now the electrons in this bond are now going to form another lone pair . so it took back an electron , or you can think of it , it gave away a hydrogen proton . and so this is now just neutral water , and we see that we have a conservation of charge here , this was positive in charge , now our original molecule is positively charged . and what feels good about this is we 're getting , we 're getting close to our end product , at least on our number three carbon , we now have , we now have this hydrogen . now we need to think about , well how do we get a hydroxyl group added right over here ? well we have all this water , we have all this water floating around , let me , i could use this water molecule but the odds of it being the exact same water molecule , we do n't know . but there 's all sorts of water molecules , we 're in an aqueous solution , so let me draw another water molecule here . so the water molecules are all equivalent , but let me draw another water molecule here . and you can imagine , if they just pump into each other in just the right way , this is , water is a polar molecule , it has a partially negative end near the oxygen because the oxygen likes to hog the electrons , and then you have a partial positive end near the hydrogens 'cause they get their electrons hogged , so you can imagine the oxygen end might be attracted to this tertiary carbocation , and so just bumping it in just the right way , it might form a bond . so let me say these two electrons right over here , let 's say they form a bond with this , with that number two carbon , and then what is going to result ? so let me draw , so what is , what is going to result , let me scroll down a little bit , and let me paste , whoops , let me copy and paste our original molecule again . so , here we go . so what could happen ? this is the one we constructed actually , so we have the hydrogen there . we have the hydrogen , now this character , so we have the water molecule , so oxygen bonded to two hydrogens , you have this one lone pair that is n't reacting , but then you have the lone pair that does do the reacting . and so it now forms a bond . woops , let me do it in that orange color . it now , it now forms an actual bond . and we 're really close to our final product , we have our hydrogen on the number three carbon , we have more than we want on our number two carbon , we just want a hydroxyl group , now we have a whole water bonded to the carbon . so somehow we have to get one of these other hydrogens swiped off of it , well that could happen with just another water molecule . so let 's draw that . so another water molecule someplace , i 'll do the different color just to differentiate , although as we know water , well it 's hard to see what color is water if you 're looking at the molecular scale . so here we go , and we 're really in the home stretch at this point . you have another water molecule , let 's say , let me pick a color . so let 's say these electrons right over here , maybe they form a bond with that hydrogen proton , and then these , the electrons in that bond can go back to form a lone pair on that oxygen , and then what are we left with ? and this really is the home stretch . so we are in equilibrium with , so let me draw my five carbons , so let 's see , i have ... h3c , carbon , carbon , ch2 , ch3 , i have a ch3 , i say h3c instead of ch3 , i wrote it that way just so it 's clear that the carbons are bonded to the carbons , you have the original hydrogen right over there , you have the one that we just added as part of this mechanism , you have this orange bond to now , this hydroxyl group , the hydroxyl group , and it had one lone pair before , it had one lone pair before , but bound to both of the electrons from this bond to form another lone pair . to form another lone pair , which i am depicting in pink , and then this water is now , this water molecule is now a hydronium molecule . so let me draw that , so this is now , oxygen , hydrogen , had one lone pair that did n't react , and it had one lone pair that i put in blue that is reacting with this hydrogen proton . with that hydrogen , just like this , and so since it got the hydrogen proton it 's giving its , sharing its electrons now , now this has a positive , this has a positive charge , just like that . i have to be very careful , in the last step i forgot to draw the positive charge ! we always wan na make sure that your charge is being conserved , we started off with the positive charge on the hydronium , then we have the positive charge on the tertiary carbocation right over here on our number two carbon , and now we have the positive charge , would be right over here , because that oxygen , what we saw before that oxygen , which this water molecule was neutral , but you could say , you could view it is `` well now it 's going to be , it 's now sharing these two electrons instead of keeping them , '' so you can view it is maybe it 's giving away an electron , and so now it becomes positive . and then , and then the positive charge finally gets transferred to that other water molecule when it becomes hydronium . but just like that we are done . we have added a hydroxyl group and a hydrogen combined , that 's a water , so that 's why we call it addition of water , and it was catalyzed by acid , so it 's an acid-catalyzed addition of water .
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it now , it now forms an actual bond . and we 're really close to our final product , we have our hydrogen on the number three carbon , we have more than we want on our number two carbon , we just want a hydroxyl group , now we have a whole water bonded to the carbon . so somehow we have to get one of these other hydrogens swiped off of it , well that could happen with just another water molecule .
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what 's the name of the final product 2 methil , 2 penthanol ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them .
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what do the loose ends around the lower resistor mean ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have .
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conceptually , in this oversimplified case , why not just use 1 resistor ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression .
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why we only take r2 for v out ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors .
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why is the voltage on the node between the resistors assumed to be very small or 0 ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts .
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it looks to me as if vout is equivalent to the voltage that `` exists '' on the r2 resistor , and therefore could be figured out using a voltmeter ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' .
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also can this also be theoretically ( or practically ) used as a new `` battery or voltage source '' for `` new circuits '' that require lesser voltage input that vi ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors .
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why do the headlights on a car dim when the starter motor is operated ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero .
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so the voltage in the voltage divider , is that basically what a voltmeter would read if you connected it to the circuit at the second resistor ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' .
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if the current in the first wire is to be accounted for as mentioned in how would the calculation continue and how would the current affect the output voltage ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero .
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what is a voltage divider , why is it important and what are some of its applications ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' .
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since both r1 and r2 are in series , why do n't we use simple ohms law to find the vo ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' .
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does that mean that the output voltage ( vout ) in this case is the voltage going out after r2 only ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this .
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the current in the extending wire is 0 amps as told , just like when a voltmeter is connected , which has high resistance and so current instead of going in voltmeter ( like it does in parallel resistors ) goes through resistors only ... right ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero .
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what exactly is the purpose of a voltage divider ?
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now i 'm gon na show you what a circuit , that 's called a voltage divider . this is the name we give to a simple circuit of two series resistors . so , i 'm just gon na draw two series resistors here . and it 's a nickname , in the sense of , it 's just a pattern that we see when we look at circuits . and , i 'll show you what the pattern is . the pattern is , we have two resistors in series . it 's no more than that . and we assume that there 's a voltage over here . we hook up a voltage over here like this . so , that 's called an input voltage . we 'll call it 'vi ' , for 'v in ' . and then , the midpoint of the two resistors , and typically the bottom , that 's called the 'out ' . so , we basically just have a pattern here with the series resistor , driven by some voltage from the ends of the two resistors . and we 're curious about the voltage across one of them . so now we 're gon na develop an expression for this . let 's also label our resistors . this will be 'r1 ' . and this will be 'r2 ' . that 's how we tell our resistors apart . and we 're gon na develop an expression for this . so , let 's first put a current through here . we 'll call that current 'i ' . we 'll make an assumption that this current here , is zero . there 's no current going out of our little circuit here . and that means , of course , that this current here is also 'i ' . so , it 's continuous all the way down . and now we want to develop an expression that tells us what 'v out ' is , in terms of these two resistors and the input voltage . so let 's go over here and do that . first thing we 're gon na write is , we know that , using ohm 's law , we can write an expression for these series resistors on this side here . ohm 's law , we 'll put over here . 'v ' equals 'ir ' . in a specific case here , 'v in ' equals 'i ' times what ? times the series combination of 'r1 ' and 'r2 ' . and the series combination is the sum : 'r1 ' plus 'r2 ' . i 'm gon na solve this for 'i ' . 'i ' equals 'v in ' divided by 'r1 ' plus 'r2 ' . alright , next step is gon na be , let 's solve for -- let 's write an expression that 's related to 'v out ' . and 'v out ' only depends on 'r2 ' and this current here . so we can write 'v out ' equals 'i ' times 'r2 ' . and i 'll solve this equation for 'i ' the same way . equals 'v zero ' over 'r2 ' and now we have two expressions for 'i ' in our circuit , because we made this assumption of zero current going out , those two 'i 's ' are the same . so , let 's set those equal to each other and see what we get . 'i ' is 'v zero ' over 'r2 ' , equals 'v1 ' over 'r1 ' plus 'r2 ' . so now i 'm gon na take 'r2 ' and move it over to the other side of the equation . and we get 'v out ' equals 'v1 ' . sorry , 'v in ' times 'r2 ' over 'r1 ' plus 'r2 ' . and this is called , this is called the voltage divider expression . right here . it gives us an expression for 'v out ' , in terms of 'v in ' , and the ratio of resistors . resistors are always positive numbers . and so this fraction is always less than one . which means that 'v out ' is always somewhat less than 'v in ' . and it 's adjustable , by adjusting the resistor values . it 's a really handy circuit to have . let 's do some examples . we 'll put that up in the corner so we can see it . then real quick , i 'm gon na build a voltage divider that we can practice on . let 's make this '2k ' ohms , two thousand ohms . we 'll make this 6000 ohms , or '6k ' ohms . and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this . right here , is where the output of our voltage divider is . and we 'll say that that is 'v out ' . so let 's solve this using the voltage divider expression . 'v out ' equals 'v in ' , which is 6 volts . times the ratio of resistors . 'r2 ' is '6k ' ohms , divided by '2k ' ohms , plus '6k ' ohms . and notice this always happens , the 'k 's ' all cancel out . that 's nice . and that equals six times , six over , two plus six is eight . and if i do my calculations right , 'v out ' is 4.5 volts . so that 's what a voltage divider is . and if you remember at the beginning , if you remember at the beginning , we made an assumption that this current going out here , was appr -- about zero . if that current is really small , you can use this voltage divider expression . which as , we see up here , is the ratio of the bottom resistor to both resistors . that 's how i remember it . it 's the bottom resistor , over the two resistors added together . if you think the current is not very small , what you do is you go back and you do this analysis . you do the same analysis again but you account for the current that 's in here . so that 's the story on voltage dividers
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and we 'll hook it up to an input source that looks like , let 's say it 's 6 volts . like that . and we 'll take an output off of this .
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in the end of the video sal poses a scenario where the current is not 0 like maybe it is connected to a bulb or something , how would the calculation proceed in that scenario ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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should n't the negative be put on the base ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing .
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how do you rewrite the root if its a negitive decimal with a fraction as an exponent ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now .
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how does work , when x has a positive exponent , turn into a negative ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent .
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at about 0.50 , why do you multiply the two numbers for v to the 3rd to the 1/7 ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now .
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am i wrong in believing that x^1/7 * x^7 = x^1/7 * x^7/1 which is equal to x^7/7=x ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now .
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how do you raise a number to a fraction like 3/7 ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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if you raise a number to 1/7 , it 's the same as taking the 7th root , but how does it work with a faction with a numerator other than 1 ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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is it possible to change order which exponents multiplication takes place , since multiplication is commutative ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six .
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for example , taken from practice rational exponents challenge : ( d^1/8 ) ^5 is equivalent to ( d^5 ) ^1/8 ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now .
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on number 3 , how come whenever you take the reciprocal of the left side , the right side does n't become a reciprocal ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ?
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what does , `` g greater than or equal to zero '' mean ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ?
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and what is a constant ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six .
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why do you make n to the 6th into n to the 1/6 ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now .
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what is 15 ( ab/b^-3 ) ^-4 ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now .
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why dose 3 go on the top and not the bottom ?
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we 're asked to determine whether each expression is equivalent to the seventh root of v to the third power . and , like always , pause the video and see if you can figure out which of these are equivalent to the seventh root of v to the third power . well , a good way to figure out if things are equivalent is to just try to get them all in the same form . so , the seventh root of v to the third power , v to the third power , the seventh root of something is the same thing as raising it to the 1/7 power . so , this is equivalent to v to the third power , raised to the 1/7 power . and if i raise something to an exponent and then raise that to an exponent , well then , that 's the same thing as raising it to the product of these two exponents . so , this is going to be the same thing as v to the three times 1/7 power , which , of course , is 3/7 . 3/7 . so , we 've written it in multiple forms now . let 's see which of these match . so , v to the third to the 1/7 power , well , that was the form that we have right over here , so that is equivalent . v to the 3/7 . that 's what we have right over here , so that one is definitely equivalent . now , let 's think about this one . this is the cube root of v to the seventh . is this going to be equivalent ? well , one way to think about it , this is going to be the same thing as v to the 1/3 power ... actually , no , this was n't the cube root of v to the seventh , this was the cube root of v , and that to the seventh power . so , that 's the same thing as v to the 1/3 power , and then , that to the seventh power . so , that is the same thing as v to the 7/3 power , which is clearly different to v to the 3/7 power . so , this is not going to be equivalent for all v 's , all v 's for which this expression is defined . let 's do a few more of these , or similar types of problems dealing with roots and fractional exponents . the following equation is true for g greater than or equal to zero , and d is a constant . what is the value of d ? well , if i 'm taking the sixth root of something , that 's the same thing as raising it to the 1/6 power . so , the sixth root of g to the fifth , is the same thing as g to the fifth , raised to the 1/6 power . and , just like we just saw in the last example , that 's the same thing as g to the five times 1/6 power . this is just our exponent properties . i raise something to an exponent and then raise that whole thing to another exponent , i can just multiply the exponents . so , that 's the same thing as g to the 5/6 power . and so d is 5/6 . five over six . the sixth root of g to the fifth is the same thing as g to the 5/6 power . let 's do one more of these . the following equation is true for x greater than zero , and d is a constant . what is the value of d ? alright , this is interesting . and i forgot to tell you in the last one , but pause this video as well and see if you can work it out on ... or pause for this question as well and see if you can work it out . well , here , let 's just start rewriting the root as an exponent . so , i can rewrite the whole thing . this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 . so , the key here is when you 're taking the reciprocal of something , that 's the same thing as raising it to the negative of that exponent . another way of thinking about it is you could view this as , you could view it as , x to the 1/7 to the negative one power . and then , if you multiply these exponents , you get what we have right over there . but , either way , d is equal to negative 1/7 .
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this is the same thing as one over , instead of writing the seventh root of x , i 'll write x to the 1/7 power is equal to x to the d. and if i have one over something to a power , that 's the same thing as that something raised to the negative of that power . so , that is the same thing as x to the negative 1/7 power . and so , that is going to be equal to x to the d. and so , d must be equal to , d must be equal to negative 1/7 .
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3rd example question : if 1 / x ^ 1/7 is `` the same as '' x ^ -1/7 , why could n't the answer just be x ^ 1/7 ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that .
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what does y=f ( x ) mean ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y .
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why is it that the range of the l is 0.5 and the range around c was 0.25 , my point is that will the range for the x-axis always be less than that for the range for the y-axis ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that .
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are limits used only in situations when x approaches the value for which the function f ( x ) is undefined , and not for other values ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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why were epsilon delta forms created ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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in what kind of circumstances would people use this epsilon-delta definition out of the studies of mathematics ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine .
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your graph is between l-0.5 and l+0.5 at all times but what if at l-0.25 it all of the sudden dramatically spikes out of l-0.5 just for a quick dip and comes back ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire .
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how does this affect the `` close as you want '' concept ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y .
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is it possible for the range around c that x must be in ( for y to equal l ) to not be centered/symmetrical around c ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y .
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do the upper and lower boundaries of the range have to be equidistant from the given l or the given c ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it .
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why limits were made in the first place ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range .
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why can we make coordinate planes where the `` origin '' is n't at ( 0,0 ) ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that .
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for example- will this definition fail for ( lim x tending to 0 , then f ( x ) = sin1/x ) ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that .
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would such a second discontinuity render sal 's limit incorrect ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit .
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in sal says that we need to be able to do `` this '' for any range from c. what if requested range maps to the part of the function that also is not defined ( for example if there is no `` x '' that would equal l + 12 ) ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y .
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after | so , basically when someone gives me a certain range around the limit , do i have to find the range of the function ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit .
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so ... is the range inclusive ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine .
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are l-0.5 and l+0.5 also attainable if we define a range for c ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise .
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i mean to find instantaneous velocity , why should th limit of f ( x ) aproach 0 ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y .
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why is the range around c , c - .25 and c + .25 and the ranges around l are l + .5 and l - .5 ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that .
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you can only take a real , defined limit of something if it is a point/removable discontinuity or a continuous function , right ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that .
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so what if you had two point/removable discontinuities `` in a row '' on your graph ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ?
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how do you decide what to chose as c- x to be ?
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let 's try to come up with a mathematically rigorous definition for what this statement means . the statement that the limit of f of x as x approaches c is equal to l. so let 's say that this means that you can get f of x as close to l as you want . i 'll put that in quotes right over here , because it 's kind of a little loosey goosey as how close is that . but as close as you want by getting x sufficiently close to c. so another way of saying this is , if you tell me , hey , i want to get my f of x to be within 0.5 of this limit . then you 're telling me if this limit is actually true , you should be able to hand me a value around c. that if x is within that range , then f of x is definitely going to be as close to l as i desire . so let me draw that out to make it a little bit clearer . and i 'm going to zoom in . i 'm going to draw another diagram . so let 's say that this right over here is my y-axis . and i 'm going to zoom in . i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y . let 's say that this is c. and let 's just zoom in on our function . so let 's say our function looks , is doing something like , let 's say it does something like , let 's see , i do n't want it to be defined at c. at least just for the -- it could be . you can always find a limit even where is defined . but let 's say our function looks something like that . and it can have a little kink in it , the way i drew it . so it looks something like this . it 's undefined . let me draw it a little bit different . so it is undefined when x is equal to c. so this is the point where there 's a hole . it is undefined when x is equal to c. so it even has a little kink in it , just like that . and what we want to do is prove that the limit , as x , the limit of f of x -- and let me make it clear , this is the graph of y is equal to f of x -- we want to get an idea for what this definition is saying . if we 're claiming that the limit of f of x , as x approaches c , is l. so conceptually , we get the gist already . we already get the gist that this right over here is l. but what is this definition saying ? well , it 's saying that you can get f of x as close to l as you want . so if you tell someone , i want to get f of x within a certain range of l , then if this limit is actually true , if the limit of f of x as x approaches c really is equal to l , then they should be able to find a range around c. that as long as x is around that range , your f of x is going to be in the range that you want . so let me actually go through that exercise . it really is a little bit like a game . so someone comes up to you and says , well , ok . i do n't necessarily believe that you 're claiming the limit of f of x as x approaches c is equal to l. i 'm not really sure if that 's the case . but i agree with this definition . so i want to get within 0.5 . i want to get f of x within 0.5 of l. so this right over here would be l plus 0.5 . and this right over here is l minus 0.5 . and then you say , fine . i 'm going to give you a range around c , that if you take any x within that range , your f of x is always going to fall in this range that you care about . and so you look at this -- and obviously we have n't explicitly defined this function . but you can even eyeball it , the way this function is defined . it wo n't be that easy for all functions . but you look at it like this . and you say that this value , just the way it 's drawn right over here , let 's say that this is c minus 0.25 . and let 's say that this value right over here is c plus 0.25 . and so you tell them , look , as long as you get x within 0.25 of c , so as long as your x 's are sitting someplace over here , the corresponding f of x is going to sit in the range that you care about . and you say , ok , fine . you won that round . let me make it even tighter . maybe instead of saying within the 0.5 , i want to get within is 0.05 . and then you 'd have to do this exercise again and find another range . and in order for this to be true , you would have to be able to do this for any range that they give you . for any range around l that they give you , you have to be able to get f of x within that range by finding a range around c. that as long as x is that range around c , f of x is going to sit within that range . so i 'll let you think about that a little bit . there 's a lot to think about . but hopefully this made sense . we did it for the particular example of someone hands you the 0.5 , i want f of x within the 0.5 of l , and you say , well , as long as x is within 0.25 of c , you 're going to match it . you need to be able to do that for any range they give you around l. and then this limit will definitely be true . so in the next video , we will now generalize that . and that will really bring us to the famous epsilon delta definition of limits .
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i 'm going to draw a slightly different function , just so we can really focus on what 's going on around here . the range is around c , and the range is around l. so that 's x . this right over here is y .
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for physical systems does the behavior of the l range versus the c range tell us anything meaningful about the system ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it .
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7 is the body able to repair an aneurysm or is surgery required to repair it ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles .
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can people get aneurysms in the veins and if so are they called something different ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end .
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are the aneurysms in the the small arteries just as life threatening as the ones in the large arteries over time ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ?
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what are the symptoms of hypertension ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall .
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can you have hemorrhage from an artery that is arteriosclerotic ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness .
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in the sense of an aneurism but i imagine it like a crack in a pipe ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels .
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if constant high blood pressure in the arteries weakens them , would n't exercise be somewhat dangerous ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ?
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how does htn cause a headache ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ?
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what does hypertension do to the blood vassals and the body ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it .
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if you get an aneurysm and it is untreated what can happen ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles .
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is arteriosclerosis and atherosclerosis the same thing ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels .
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i thought arteriosclerosis was the buildup of plaque in the arteries..does the term include both plaque buildup and he hardening/stiffening of arteries ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it .
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can you feel aneurysm happening ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis .
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how do you cure retinopathy ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly .
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does arteriosclerosis happens in small vessels first or in the bigger vessels first ?
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ? why is it a problem to have high blood pressure ? and i like to think about high blood pressure from two different perspectives -- one would be the perspective of the heart , and the other is the perspective of the blood vessels . and so here you can almost divide it up as the thing that 's making the pressure or generating the pressure , which is the heart , and the thing that 's receiving the pressure . so generating versus receiving pressure , and each of these two areas has some serious consequences for the body . so let 's just divide it up here . let 's just draw a dashed line , divide up our screen , and we 'll talk about both areas . so let 's start with the receiving pressure side . so we have the large and middle sized arteries -- and specifically i mean arteries that are between , let 's say , 25 millimeters in diameter all the way down to about one millimeter in diameter . so primarily these are the vessels that are going to get blood from the heart to the different organs that it needs to get to . and then you of course have the small arteries and arterioles . and these are going to be at the high end . they 're going to be one millimeter . but they 're going to go all the way down and get smaller and smaller to about 0.01 millimeters , so about 1/100 of the size . they 're very tiny . and these are receiving pressure . both of them are receiving pressure . these i 'll draw as -- i 'll leave the drawing up above , and these are kind of very , very narrow ones , right ? so both of them are receiving the pressure , and they 're going to have problems . so for example , if you have , let 's say , a large or middle artery that is -- let me draw it in a different color . let 's say here it 's very elastic -- over time if you keep exposing this elastic vessel or tube to high pressures , over time what would happen is this becomes very firm , like a pipe . so that 's one change . and in fact , that change from being elastic to firm , we call that arteriosclerosis . i 'll write that in white -- arteriosclerosis . and in fact , a very similar thing happens on the other side with the small arteries and arterioles . they also have very similar kind of change . they can go from being very elastic -- i 'm trying to draw it so it 's got some springiness . that 's obviously kind of tricky to draw . these become very firm as well over time , and they lose that elasticity . and when it happens in the small arteries or arterioles , we call that arteriolosclerosis -- a very similar word , but slightly different -- arteriolo -- an extra l and an o -- sclerosis . so this is the difference , right ? they 're very similar things , kind of similar processes , but one is in the smaller arteries and one is in the larger and middle sized arteries . so this is one of the things that can happen when you have lots of high blood pressure constantly exposed to the vessels . they can become firm . ok , going back to the large and middle arteries , you also can have a situation -- i 'll draw it here -- where you have an artery , let 's say -- actually , let me write what it is first . you can have an aneurysm . and an aneurysm is where you have a vessel -- let 's say this is my vessel , and it 's taking blood through it . so blood is going through it . and because of the constant blood pressure that 's going through this vessel , the wall starts to get weak . so at one spot , it starts to get weak . let 's say right here instead of being like that , it starts to look like this . and you get this little area of weakness . i 'll try to draw it like that . and because it 's weak , the blood will start going , and hitting , and bouncing off the walls , and making it a little bit bigger . so it looks like that . and over time , it might do this . it might become a big sack . and that 's an aneurysm . and actually that aneurysm , if it 's a sack of blood , can actually burst and break . and that blood can spill out , and we call that hemorrhage . so you can actually have an aneurysm because of a weak vessel wall . now , looking at the small arteries or arterioles , you can also have , not necessarily aneurysms in the same way , but you can have breaking or hemorrhage . and here i want to show you or remind you that these vessels , these tiny ones anyway , they 're usually not sitting out there on their own . they 're usually within an organ . so this tiny vessel -- remember , it 's one millimeter to a hundredth of a millimeter . so it 's actually sitting inside of a kidney or sitting inside of an eye . and so these organs have inside of them these arterioles and small arteries . and so when they 're in that situation , if you have a break , let 's say -- actually , let me rewrite this slightly differently . if you have a break in the vessel , we actually get organ damage . so this could be because the vessel literally breaks right here and blood spills out . and it could also be because these tiny vessels are necessary to make the organ work . for example , the kidneys require that these small arteries and arterioles are working properly . and if they 're not , you start getting some problems with being able to do the job of the kidney . and so you can get kidney damage . or if it 's in your eye , you can get what we call retinopathy , basically meaning that the retina is not working properly . so you can have kidney damage or retinopathy . you can have aneurysms , arteriosclerosis , or arteriolosclerosis . and these are all related to the fact that the blood vessels are breaking or they 're becoming more firm . and this is all on the side of receiving pressure .
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now , we 've talked about hypertension , and you know that it means that you have high blood pressure . so the next logical thing to think about is why is that bad ?
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how does htn cause headaches ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other .
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where can you find the fifth form of matter which is bose-einstein condensate ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen .
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could you explain me why the oxygen atoms in the molecular formula of water have 4 extra electrons on their outermost shell ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is .
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what makes liquid water have more density than ice ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens .
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how will we come to know the state of matter in a chemical equation ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o .
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so does that mean that there is some ice that can be colder or warmer that other ice ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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or a gas . so let 's just draw a water molecule . so you have oxygen there .
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what is the difference between an atom and a molecule ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule .
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how come oxygen is a gas and hydrogen is a gas but water is a liquid ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q .
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is there any other types of states ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth .
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what is the bose-einstein condensate ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid .
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is temperature a vector or scalar quantity ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth .
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why is it vector/scalar ( which ever 's the answer ) ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds .
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why does ice float on water ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens .
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but if you search it up at science websites , and many other places such as google and bing , they say there is a 4th state of matter ( plasma ) .so is plasma really a state of matter ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil .
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can anyone explain what happens at about 1 000 000 000 000 kelvin/celsius ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here .
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does applying more heat not change the average kinetic energy or something while in its liquid state ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens .
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what state of matter would fire be in ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds .
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in what degrees does water turns to ice ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is .
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how is the gases converted to liquid ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid .
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is ketchup a solid or a liquid ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds .
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why is ice less dense than water ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q .
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how do we identify the states of the products which are formed from a reaction ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating .
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what would be the state of sodium sulfate ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and energy is the ability to do work . and what 's the unit for work ? well , it 's joules .
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what is the smallest unit of matter ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other .
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well , since water can be solid , liquid and gas , does that mean that solid can be gas when its liquid form is heated to a certain temperature ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content .
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how are entropy and enthalpy related , if they even are ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ?
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what is a volatile and non-volatile substance ?
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i think we 're all reasonably familiar with the three states of matter in our everyday world . at very high temperatures you get a fourth . but the three ones that we normally deal with are , things could be a solid , a liquid , or it could be a gas . and we have this general notion , and i think water is the example that always comes to at least my mind . is that solid happens when things are colder , relatively colder . and then as you warm up , you go into a liquid state . and as your warm up even more you go into a gaseous state . so you go from colder to hotter . and in the case of water , when you 're a solid , you 're ice . when you 're a liquid , some people would call ice water , but let 's call it liquid water . i think we know what that is . and then when it 's in the gas state , you 're essentially vapor or steam . so let 's think a little bit about what , at least in the case of water , and the analogy will extend to other types of molecules . but what is it about water that makes it solid , and when it 's colder , what allows it to be liquid . and i 'll be frank , liquids are kind of fascinating because you can never nail them down , i guess is the best way to view them . or a gas . so let 's just draw a water molecule . so you have oxygen there . you have some bonds to hydrogen . and then you have two extra pairs of valence electrons in the oxygen . and a couple of videos ago , we said oxygen is a lot more electronegative than the hydrogen . it likes to hog the electrons . so even though this shows that they 're sharing electrons here and here . at both sides of those lines , you can kind of view that hydrogen is contributing an electron and oxygen is contributing an electron on both sides of that line . but we know because of the electronegativity , or the relative electronegativity of oxygen , that it 's hogging these electrons . and so the electrons spend a lot more time around the oxygen than they do around the hydrogen . and what that results is that on the oxygen side of the molecule , you end up with a partial negative charge . and we talked about that a little bit . and on the hydrogen side of the molecules , you end up with a slightly positive charge . now , if these molecules have very little kinetic energy , they 're not moving around a whole lot , then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules . let me draw some more molecules . when we talk about the whole state of the whole matter , we actually think about how the molecules are interacting with each other . not just how the atoms are interacting with each other within a molecule . i just drew one oxygen , let me copy and paste that . but i could do multiple oxygens . and let 's say that that hydrogen is going to want to be near this oxygen . because this has partial negative charge , this has a partial positive charge . and then i could do another one right there . and then maybe we 'll have , and just to make the point clear , you have two hydrogens here , maybe an oxygen wants to hang out there . so maybe you have an oxygen that wants to be here because it 's got its partial negative here . and it 's connected to two hydrogens right there that have their partial positives . but you can kind of see a lattice structure . let me draw these bonds , these polar bonds that start forming between the particles . these bonds , they 're called polar bonds because the molecules themselves are polar . and you can see it forms this lattice structure . and if each of these molecules do n't have a lot of kinetic energy . or we could say the average kinetic energy of this matter is fairly low . and what do we know is average kinetic energy ? well , that 's temperature . then this lattice structure will be solid . these molecules will not move relative to each other . i could draw a gazillion more , but i think you get the point that we 're forming this kind of fixed structure . and while we 're in the solid state , as we add kinetic energy , as we add heat , what it does to molecules is , it just makes them vibrate around a little bit . if i was a cartoonist , they way you 'd draw a vibration is to put quotation marks there . that 's not very scientific . but they would vibrate around , they would buzz around a little bit . i 'm drawing arrows to show that they are vibrating . it does n't have to be just left-right it could be up-down . but as you add more and more heat in a solid , these molecules are going to keep their structure . so they 're not going to move around relative to each other . but they will convert that heat , and heat is just a form of energy , into kinetic energy which is expressed as the vibration of these molecules . now , if you make these molecules start to vibrate enough , and if you put enough kinetic energy into these molecules , what do you think is going to happen ? well this guy is vibrating pretty hard , and he 's vibrating harder and harder as you add more and more heat . this guy is doing the same thing . at some point , these polar bonds that they have to each other are going to start not being strong enough to contain the vibrations . and once that happens , the molecules -- let me draw a couple more . once that happens , the molecules are going to start moving past each other . so now all of a sudden , the molecule will start shifting . but they 're still attracted . maybe this side is moving here , that 's moving there . you have other molecules moving around that way . but they 're still attracted to each other . even though we 've gotten the kinetic energy to the point that the vibrations can kind of break the bonds between the polar sides of the molecules . our vibration , or our kinetic energy for each molecule , still is n't strong enough to completely separate them . they 're starting to slide past each other . and this is essentially what happens when you 're in a liquid state . you have a lot of atoms that want be touching each other but they 're sliding . they have enough kinetic energy to slide past each other and break that solid lattice structure here . and then if you add even more kinetic energy , even more heat , at this point it 's a solution now . they 're not even going to be able to stay together . they 're not going to be able to stay near each other . if you add enough kinetic energy they 're going to start looking like this . they 're going to completely separate and then kind of bounce around independently . especially independently if they 're an ideal gas . but in general , in gases , they 're no longer touching each other . they might bump into each other . but they have so much kinetic energy on their own that they 're all doing their own thing and they 're not touching . i think that makes intuitive sense if you just think about what a gas is . for example , it 's hard to see a gas . why is it hard to see a gas ? because the molecules are much further apart . so they 're not acting on the light in the way that a liquid or a solid would . and if we keep making that extended further , a solid -- well , i probably should n't use the example with ice . because ice or water is one of the few situations where the solid is less dense than the liquid . that 's why ice floats . and that 's why icebergs do n't just all fall to the bottom of the ocean . and ponds do n't completely freeze solid . but you can imagine that , because a liquid is in most cases other than water , less dense . that 's another reason why you can see through it a little bit better . or it 's not diffracting -- well i wo n't go into that too much , than maybe even a solid . but the gas is the most obvious . and it is true with water . the liquid form is definitely more dense than the gas form . in the gas form , the molecules are going to jump around , not touch each other . and because of that , more light can get through the substance . now the question is , how do we measure the amount of heat that it takes to do this to water ? and to explain that , i 'll actually draw a phase change diagram . which is a fancy way of describing something fairly straightforward . let me say that this is the amount of heat i 'm adding . and this is the temperature . we 'll talk about the states of matter in a second . so heat is often denoted by q . sometimes people will talk about change in heat . they 'll use h , lowercase and uppercase h. they 'll put a delta in front of the h. delta just means change in . and sometimes you 'll hear the word enthalpy . let me write that . because i used to say what is enthalpy ? it sounds like empathy , but it 's quite a different concept . at least , as far as my neural connections could make it . but enthalpy is closely related to heat . it 's heat content . for our purposes , when you hear someone say change in enthalpy , you should really just be thinking of change in heat . i think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary . the best way to think about it is heat content . change in enthalpy is really just change in heat . and just remember , all of these things , whether we 're talking about heat , kinetic energy , potential energy , enthalpy . you 'll hear them in different contexts , and you 're like , i thought i should be using heat and they 're talking about enthalpy . these are all forms of energy . and these are all measured in joules . and they might be measured in other ways , but the traditional way is in joules . and energy is the ability to do work . and what 's the unit for work ? well , it 's joules . force times distance . but anyway , that 's a side-note . but it 's good to know this word enthalpy . especially in a chemistry context , because it 's used all the time and it can be very confusing and non-intuitive . because you 're like , i do n't know what enthalpy is in my everyday life . just think of it as heat contact , because that 's really what it is . but anyway , on this axis , i have heat . so this is when i have very little heat and i 'm increasing my heat . and this is temperature . now let 's say at low temperatures i 'm here and as i add heat my temperature will go up . temperature is average kinetic energy . let 's say i 'm in the solid state here . and i 'll do the solid state in purple . no i already was using purple . i 'll use magenta . so as i add heat , my temperature will go up . heat is a form of energy . and when i add it to these molecules , as i did in this example , what did it do ? it made them vibrate more . or it made them have higher kinetic energy , or higher average kinetic engery , and that 's what temperature is a measure of ; average kinetic energy . so as i add heat in the solid phase , my average kinetic energy will go up . and let me write this down . this is in the solid phase , or the solid state of matter . now something very interesting happens . let 's say this is water . so what happens at zero degrees ? which is also 273.15 kelvin . let 's say that 's that line . what happens to a solid ? well , it turns into a liquid . ice melts . not all solids , we 're talking in particular about water , about h2o . so this is ice in our example . all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is . i could take that analogy a bunch of different ways . but the interesting thing that happens at zero degrees . depending on what direction you 're going , either the freezing point of water or the melting point of ice , something interesting happens . as i add more heat , the temperature does not to go up . as i add more heat , the temperature does not go up for a little period . let me draw that . for a little period , the temperature stays constant . and then while the temperature is constant , it stays a solid . we 're still a solid . and then , we finally turn into a liquid . let 's say right there . so we added a certain amount of heat and it just stayed a solid . but it got us to the point that the ice turned into a liquid . it was kind of melting the entire time . that 's the best way to think about it . and then , once we keep adding more and more heat , then the liquid warms up too . now , we get to , what temperature becomes interesting again for water ? well , obviously 100 degrees celsius or 373 degrees kelvin . i 'll do it in celsius because that 's what we 're familiar with . what happens ? that 's the temperature at which water will vaporize or which water will boil . but something happens . and they 're really getting kinetically active . but just like when you went from solid to liquid , there 's a certain amount of energy that you have to contribute to the system . and actually , it 's a good amount at this point . where the water is turning into vapor , but it 's not getting any hotter . so we have to keep adding heat , but notice that the temperature did n't go up . we 'll talk about it in a second what was happening then . and then finally , after that point , we 're completely vaporized , or we 're completely steam . then we can start getting hot , the steam can then get hotter as we add more and more heat to the system . so the interesting question , i think it 's intuitive , that as you add heat here , our temperature is going to go up . but the interesting thing is , what was going on here ? we were adding heat . so over here we were turning our heat into kinetic energy . temperature is average kinetic energy . but over here , what was our heat doing ? well , our heat was was not adding kinetic energy to the system . the temperature was not increasing . but the ice was going from ice to water . so what was happening at that state , is that the kinetic energy , the heat , was being used to essentially break these bonds . and essentially bring the molecules into a higher energy state . so you 're saying , sal , what does that mean , higher energy state ? well , if there was n't all of this heat and all this kinetic energy , these molecules want to be very close to each other . for example , i want to be close to the surface of the earth . when you put me in a plane you have put me in a higher energy state . i have a lot more potential energy . i have the potential to fall towards the earth . likewise , when you move these molecules apart , and you go from a solid to a liquid , they want to fall towards each other . but because they have so much kinetic energy , they never quite are able to do it . but their energy goes up . their potential energy is higher because they want to fall towards each other . by falling towards each other , in theory , they could do some work . so what 's happening here is , when we 're contributing heat -- and this amount of heat we 're contributing , it 's called the heat of fusion . because it 's the same amount of heat regardless how much direction we go in . when we go from solid to liquid , you view it as the heat of melting . it 's the head that you need to put in to melt the ice into liquid . when you 're going in this direction , it 's the heat you have to take out of the zero degree water to turn it into ice . so you 're taking that potential energy and you 're bringing the molecules closer and closer to each other . so the way to think about it is , right here this heat is being converted to kinetic energy . then , when we 're at this phase change from solid to liquid , that heat is being used to add potential energy into the system . to pull the molecules apart , to give them more potential energy . if you pull me apart from the earth , you 're giving me potential energy . because gravity wants to pull me back to the earth . and i could do work when i 'm falling back to the earth . a waterfall does work . it can move a turbine . you could have a bunch of falling sals move a turbine as well . and then , once you are fully a liquid , then you just become a warmer and warmer liquid . now the heat is , once again , being used for kinetic energy . you 're making the water molecules move past each other faster , and faster , and faster . to some point where they want to completely disassociate from each other . they want to not even slide past each other , just completely jump away from each other . and that 's right here . this is the heat of vaporization . and the same idea is happening . before we were sliding next to each other , now we 're pulling apart altogether . so they could definitely fall closer together . and then once we 've added this much heat , now we 're just heating up the steam . we 're just heating up the gaseous water . and it 's just getting hotter and hotter and hotter . but the interesting thing there , and i mean at least the interesting thing to me when i first learned this , whenever i think of zero degrees water i 'll say , oh it must be ice . but that 's not necessarily the case . if you start with water and you make it colder and colder and colder to zero degrees , you 're essentially taking heat out of the water . you can have zero degree water and it has n't turned into ice yet . and likewise , you could have 100 degree water that has n't turned into steam yeat . you have to add more energy . you can also have 100 degree steam . you can also have zero degree water . anyway , hopefully that gives you a little bit of intuition of what the different states of matter are . and in the next problem , we 'll talk about how much heat exactly it does take to move along this line . and maybe we can solve some problems on how much ice we might need to make our drink cool .
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all solids are n't ice . although , you could think of a rock as solid magma . because that 's what it is .
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could a rock become a gas ?
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