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van der Waals equation of state : equation, typically approximate, which relates the pressure and volume of a gas to the number of gas molecules or number of moles of gas and the temperature of the gas
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vapor pressure : partial pressure of a vapor at which it is in equilibrium with the liquid (or solid, in the case of sublimation) phase of the same substance
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The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
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A mole of any substance has a number of molecules equal to the number of atoms in a 12-g sample of carbon-12. The number of molecules in a mole is called Avogadro’s numberNA,NA,NA=6.02×1023mol−1.NA=6.02×1023mol−1.
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A mole of any substance has a mass in grams numerically equal to its molecular mass in unified mass units, which can be determined from the periodic table of elements. The ideal gas law can also be written and solved in terms of the number of moles of gas:pV=nRT,pV=nRT,wherenis the number of moles andRis the universal ...
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The ideal gas law is generally valid at temperatures well above the boiling temperature.
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The van der Waals equation of state for gases is valid closer to the boiling point than the ideal gas law.
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Above the critical temperature and pressure for a given substance, the liquid phase does not exist, and the sample is “supercritical.”
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Kinetic theory is the atomic description of gases as well as liquids and solids. It models the properties of matter in terms of continuous random motion of molecules.
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The ideal gas law can be expressed in terms of the mass of the gas’s molecules andv2–,v2–,the average of the molecular speed squared, instead of the temperature.
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The temperature of gases is proportional to the average translational kinetic energy of molecules. Hence, the typical speed of gas moleculesvrmsvrmsis proportional to the square root of the temperature and inversely proportional to the square root of the molecular mass.
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In a mixture of gases, each gas exerts a pressure equal to the total pressure times the fraction of the mixture that the gas makes up.
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The mean free path (the average distance between collisions) and the mean free time of gas molecules are proportional to the temperature and inversely proportional to the molar density and the molecules’ cross-sectional area.
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Every degree of freedom of an ideal gas contributes12kBT12kBTper atom or molecule to its changes in internal energy.
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Every degree of freedom contributes12R12Rto its molar heat capacity at constant volumeCV.CV.
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Degrees of freedom do not contribute if the temperature is too low to excite the minimum energy of the degree of freedom as given by quantum mechanics. Therefore, at ordinary temperatures,d=3d=3for monatomic gases,d=5d=5for diatomic gases, andd≈6d≈6for polyatomic gases.
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The motion of individual molecules in a gas is random in magnitude and direction. However, a gas of many molecules has a predictable distribution of molecular speeds, known as the Maxwell-Boltzmann distribution.
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The average and most probable velocities of molecules having the Maxwell-Boltzmann speed distribution, as well as the rms velocity, can be calculated from the temperature and molecular mass.
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f ( p , V , T ) = 0 f ( p , V , T ) = 0
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W = ∫ V 1 V 2 p d V W = ∫ V 1 V 2 p d V
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E int = ∑ i ( K ¯ i + U ¯ i ) , E int = ∑ i ( K ¯ i + U ¯ i ) ,
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E int = n N A ( 3 2 k B T ) = 3 2 n R T E int = n N A ( 3 2 k B T ) = 3 2 n R T
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Δ E int = Q − W Δ E int = Q − W
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C p = C V + R C p = C V + R
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γ = C p / C V γ = C p / C V
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p V γ = constant p V γ = constant
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adiabatic process : process during which no heat is transferred to or from the system
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boundary : imagined walls that separate the system and its surroundings
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closed system : system that is mechanically and thermally isolated from its environment
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cyclic process : process in which the state of the system at the end is same as the state at the beginning
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environment : outside of the system being studied
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equation of state : describes properties of matter under given physical conditions
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equilibrium : thermal balance established between two objects or parts within a system
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extensive variable : variable that is proportional to the amount of matter in the system
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first law of thermodynamics : the change in internal energy for any transition between two equilibrium states isΔEint=Q−WΔEint=Q−W
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intensive variable : variable that is independent of the amount of matter in the system
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internal energy : average of the total mechanical energy of all the molecules or entities in the system
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isobaric process : process during which the system’s pressure does not change
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isochoric process : process during which the system’s volume does not change
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isothermal process : process during which the system’s temperature remains constant
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molar heat capacity at constant pressure : quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant pressure
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molar heat capacity at constant volume : quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant volume
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open system : system that can exchange energy and/or matter with its surroundings
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quasi-static process : evolution of a system that goes so slowly that the system involved is always in thermodynamic equilibrium
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reversible process : process that can be reverted to restore both the system and its environment back to their original states together
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surroundings : environment that interacts with an open system
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thermodynamic process : manner in which a state of a system can change from initial state to final state
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thermodynamic system : object and focus of thermodynamic study
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A thermodynamic system, its boundary, and its surroundings must be defined with all the roles of the components fully explained before we can analyze a situation.
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Thermal equilibrium is reached with two objects if a third object is in thermal equilibrium with the other two separately.
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A general equation of state for a closed system has the formf(p,V,T)=0,f(p,V,T)=0,with an ideal gas as an illustrative example.
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Positive (negative) work is done by a thermodynamic system when it expands (contracts) under an external pressure.
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Heat is the energy transferred between two objects (or two parts of a system) because of a temperature difference.
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Internal energy of a thermodynamic system is its total mechanical energy.
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The internal energy of a thermodynamic system is a function of state and thus is unique for every equilibrium state of the system.
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The increase in the internal energy of the thermodynamic system is given by the heat added to the system less the work done by the system in any thermodynamics process.
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The thermal behavior of a system is described in terms of thermodynamic variables. For an ideal gas, these variables are pressure, volume, temperature, and number of molecules or moles of the gas.
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For systems in thermodynamic equilibrium, the thermodynamic variables are related by an equation of state.
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A heat reservoir is so large that when it exchanges heat with other systems, its temperature does not change.
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A quasi-static process takes place so slowly that the system involved is always in thermodynamic equilibrium.
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A reversible process is one that can be made to retrace its path and both the temperature and pressure are uniform throughout the system.
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There are several types of thermodynamic processes, including (a) isothermal, where the system’s temperature is constant; (b) adiabatic, where no heat is exchanged by the system; (c) isobaric, where the system’s pressure is constant; and (d) isochoric, where the system’s volume is constant.
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As a consequence of the first law of thermodymanics, here is a summary of the thermodymaic processes: (a) isothermal:ΔEint=0,Q=W;ΔEint=0,Q=W;(b) adiabatic:Q=0,ΔEint=−W;Q=0,ΔEint=−W;(c) isobaric:ΔEint=Q−W;ΔEint=Q−W;and (d) isochoric:W=0,ΔEint=Q.W=0,ΔEint=Q.
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For an ideal gas, the molar capacity at constant pressureCpCpis given byCp=CV+R=dR/2+RCp=CV+R=dR/2+R, where d is the number of degrees of freedom of each molecule/entity in the system.
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A real gas has a specific heat close to but a little bit higher than that of the corresponding ideal gas withCp≃CV+R.Cp≃CV+R.
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A quasi-static adiabatic expansion of an ideal gas produces a steeper pV curve than that of the corresponding isotherm.
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A realistic expansion can be adiabatic but rarely quasi-static.
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W = Q h − Q c W = Q h − Q c
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e = W Q h = 1 − Q c Q h e = W Q h = 1 − Q c Q h
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K R = Q c W = Q c Q h − Q c K R = Q c W = Q c Q h − Q c
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K P = Q h W = Q h Q h − Q c K P = Q h W = Q h Q h − Q c
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e = 1 − T c T h e = 1 − T c T h
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K R = T c T h − T c K R = T c T h − T c
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K P = T h T h − T c K P = T h T h − T c
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Δ S = Q T Δ S = Q T
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Δ S = S B − S A = ∫ A B d Q / T Δ S = S B − S A = ∫ A B d Q / T
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∮ d S = ∮ d Q T = 0 ∮ d S = ∮ d Q T = 0
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lim T → 0 ( Δ S ) T = 0 lim T → 0 ( Δ S ) T = 0
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Carnot cycle : cycle that consists of two isotherms at the temperatures of two reservoirs and two adiabatic processes connecting the isotherms
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Carnot engine : Carnot heat engine, refrigerator, or heat pump that operates on a Carnot cycle
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Carnot principle : principle governing the efficiency or performance of a heat device operating on a Carnot cycle: any reversible heat device working between two reservoirs must have the same efficiency or performance coefficient, greater than that of an irreversible heat device operating between the same two reservoir...
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Clausius statement of the second law of thermodynamics : heat never flows spontaneously from a colder object to a hotter object
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coefficient of performance : measure of effectiveness of a refrigerator or heat pump
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cold reservoir : sink of heat used by a heat engine
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disorder : measure of order in a system; the greater the disorder is, the higher the entropy
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efficiency (e) : output work from the engine over the input heat to the engine from the hot reservoir
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entropy : state function of the system that changes when heat is transferred between the system and the environment
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entropy statement of the second law of thermodynamics : entropy of a closed system or the entire universe never decreases
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heat engine : device that converts heat into work
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heat pump : device that delivers heat to a hot reservoir
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hot reservoir : source of heat used by a heat engine
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irreversibility : phenomenon associated with a natural process
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irreversible process : process in which neither the system nor its environment can be restored to their original states at the same time
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isentropic : reversible adiabatic process where the process is frictionless and no heat is transferred
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Kelvin statement of the second law of thermodynamics : it is impossible to convert the heat from a single source into work without any other effect
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perfect engine : engine that can convert heat into work with100%100%efficiency
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perfect refrigerator (heat pump) : refrigerator (heat pump) that can remove (dump) heat without any input of work
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refrigerator : device that removes heat from a cold reservoir
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reversible process : process in which both the system and the external environment theoretically can be returned to their original states
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third law of thermodynamics : absolute zero temperature cannot be reached through any finite number of cooling steps
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