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5tgz85W1DXyZYJOMhGT85 | physics | heat-and-thermodynamics | heat-transfer | Two materials having coefficients of thermal
conductivity '3K' and 'K' and thickness 'd' and
'3d', respectively, are joined to form a slab as
shown in the figure. The temperatures of the
outer surfaces are '$$\theta $$<sub>2</sub>' and '$$\theta $$<sub>1</sub>' respectively,
($$\theta $$<sub>2</sub> > $$\theta $$<su... | [{"identifier": "A", "content": "$${{{\\theta _1}} \\over {10}} + {{9{\\theta _2}} \\over {10}}$$"}, {"identifier": "B", "content": "$${{{\\theta _2} + {\\theta _1}} \\over 2}$$"}, {"identifier": "C", "content": "$${{{\\theta _1}} \\over {6}} + {{5{\\theta _2}} \\over {6}}$$"}, {"identifier": "D", "content": "$${{{\\th... | ["A"] | null | Let interface temperature in steady state conduction is $\theta$, then assuming no heat loss through sides;<br/><br/>
$$
\left(\begin{array}{l}
\text { Rate of heat } \\
\text { flow through } \\
\text { first slab }
\end{array}\right)=\left(\begin{array}{l}
\text { Rate of heat } \\
\text { flow through } \\
\text { s... | mcq | jee-main-2019-online-9th-april-evening-slot | 11,309 |
R8QRAQ5jGlUe0bd4QxoiT | physics | heat-and-thermodynamics | heat-transfer | Two identical beakers A and B contain equal
volumes of two different liquids at 60°C each
and left to cool down. Liquid in A has density
of 8 × 10<sup>2</sup> kg/m<sup>3</sup> and specific heat of
2000 J kg<sup>–1</sup> K<sup>–1</sup> while liquid in B has density
of 10<sup>3</sup> kg m<sup>–3</sup> and specific heat o... | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734265253/exam_images/y1jxn2oedvrztauzszul.webp\" style=\"max-width: 100%; height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2019 (Online) 8th April Morning Slot Physics - Heat and Thermodynamics... | ["B"] | null | <p>We know, m = V . $$\rho$$</p>
<p>where, V = volume and $$\rho$$ = density.</p>
<p>So, we have</p>
<p>$${{dQ} \over {dt}} = {h \over {ms}}(T - {T_0}) = {{h(T - {T_0})} \over {V\,.\,\rho s}}$$</p>
<p>Since, h, (T $$-$$ T<sub>0</sub>) and V are constant for both beaker.</p>
<p>$$\therefore$$ $${{dQ} \over {dt}} \propto... | mcq | jee-main-2019-online-8th-april-morning-slot | 11,310 |
X7kmGjQQHpdY0IcEAluV9 | physics | heat-and-thermodynamics | heat-transfer | A heat source at T = 10<sup>3</sup> K is connected to another heat reservoir at T = 10<sup>2</sup> K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK<sup>–1</sup>m<sup>–1</sup>, the energy flux through it in the steady state is - | [{"identifier": "A", "content": "200 Wm<sup>$$-$$2</sup>"}, {"identifier": "B", "content": "65 Wm<sup>$$-$$2</sup>"}, {"identifier": "C", "content": "120 Wm<sup>$$-$$2</sup>"}, {"identifier": "D", "content": "90 Wm<sup>$$-$$2</sup>"}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266867/exam_images/t2yrsghxaizut6a0btui.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 10th January Morning Slot Physics - Heat and Thermodynamics Question 311 English Explanation">
<... | mcq | jee-main-2019-online-10th-january-morning-slot | 11,311 |
IePFxWpif4iMvXIYdhYDr | physics | heat-and-thermodynamics | heat-transfer | A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K<sub>1</sub> and the of the outer cylinder is K<sub>2</sub>. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing a... | [{"identifier": "A", "content": "K<sub>1</sub> + K<sub>2</sub> "}, {"identifier": "B", "content": "$${{{K_1} + 3{K_2}} \\over 4}$$"}, {"identifier": "C", "content": "$${{{K_1} + {K_2}} \\over 2}$$"}, {"identifier": "D", "content": "$${{2{K_1} + 3{K_2}} \\over 5}$$"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267499/exam_images/gnp5hb8lja91ukvbaycf.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th January Morning Slot Physics - Heat and Thermodynamics Question 297 English Explanation">
<... | mcq | jee-main-2019-online-12th-january-morning-slot | 11,312 |
AZjNuv18b7swWvjg2kjgy2xukg0c52vn | physics | heat-and-thermodynamics | heat-transfer | Three rods of identical cross-section and lengths are made of three different materials of thermal
conductivity K<sub>1</sub>
, K<sub>2</sub>
and K<sub>3</sub>
, respecrtively. They are joined together at their ends to make a long rod
(see figure). One end of the long rod is maintained at 100<sup>o</sup>C and the othe... | [{"identifier": "A", "content": "K<sub>1</sub> : K<sub>3</sub> = 2 : 3,\n<br>K<sub>2</sub> : K<sub>3</sub> = 2 : 5"}, {"identifier": "B", "content": "K<sub>1</sub> < K<sub>2</sub> < K<sub>3</sub>"}, {"identifier": "C", "content": "K<sub>1</sub> : K<sub>2</sub> = 5 : 2,\n<br>K<sub>1</sub> : K<sub>3</sub> = 3 : 5"}... | ["A"] | null | All three rods have same length($$l$$) and area of cross-section(A).
<br><br>They are in series combination so heat current is same for all rods.
<br><br>$$ \therefore $$ $${\left( {{{\Delta Q} \over {\Delta t}}} \right)_1} = {\left( {{{\Delta Q} \over {\Delta t}}} \right)_2} = {\left( {{{\Delta Q} \over {\Delta t}}} \... | mcq | jee-main-2020-online-6th-september-evening-slot | 11,313 |
GwI0nGXTjxK9X8rSfc1kltitszl | physics | heat-and-thermodynamics | heat-transfer | The temperature $$\theta$$ at the junction of two insulating sheets, having thermal resistances R<sub>1</sub> and R<sub>2</sub> as well as top and bottom temperatures $$\theta$$<sub>1</sub> and $$\theta$$<sub>2</sub> (as shown in figure) is given by :<br/><br/><img src="data:image/png;base64,UklGRhAJAABXRUJQVlA4IAQJAAA... | [{"identifier": "A", "content": "$${{{\\theta _1}{R_2} + {\\theta _2}{R_1}} \\over {{R_1} + {R_2}}}$$"}, {"identifier": "B", "content": "$${{{\\theta _1}{R_1} + {\\theta _2}{R_2}} \\over {{R_1} + {R_2}}}$$"}, {"identifier": "C", "content": "$${{{\\theta _1}{R_2} - {\\theta _2}{R_1}} \\over {{R_2} - {R_1}}}$$"}, {"ident... | ["A"] | null | Temperature at the junction is $$\theta$$.<br><br>so using the formula<br><br>$${{{T_2} - T} \over {{R_1}}} = {{T - {T_1}} \over {{R_2}}}$$<br><br>$${{{\theta _2} - \theta } \over {{R_2}}} = {{\theta - {\theta _1}} \over {{R_1}}}$$$${R_1}({\theta _2} - \theta ) = {R_2}(\theta - {\theta _1})$$<br><br>$${R_1}{\theta _2... | mcq | jee-main-2021-online-26th-february-morning-slot | 11,314 |
E9NkG1T0M7tTbjjWl01kmj1h6nh | physics | heat-and-thermodynamics | heat-transfer | Two identical metal wires of thermal conductivities K<sub>1</sub> and K<sub>2</sub> respectively are connected in series. The effective thermal conductivity of the combination is : | [{"identifier": "A", "content": "$${{2{K_1}{K_2}} \\over {{K_1} + {K_2}}}$$"}, {"identifier": "B", "content": "$${{{K_1} + {K_2}} \\over {{K_1}{K_2}}}$$"}, {"identifier": "C", "content": "$${{{K_1} + {K_2}} \\over {2{K_1}{K_2}}}$$"}, {"identifier": "D", "content": "$${{{K_1}{K_2}} \\over {{K_1} + {K_2}}}$$"}] | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266424/exam_images/dr66pnswcucxhvvj4bpg.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 17th March Morning Shift Physics - Heat and Thermodynamics Question 205 English Explanation">
<br>... | mcq | jee-main-2021-online-17th-march-morning-shift | 11,315 |
1ktjnr4zg | physics | heat-and-thermodynamics | heat-transfer | Two thin metallic spherical shells of radii r<sub>1</sub> and r<sub>2</sub> (r<sub>1</sub> < r<sub>2</sub>) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$$<sub>1</sub> and the outer shell... | [{"identifier": "A", "content": "$${{4\\pi K{r_1}{r_2}({\\theta _2} - {\\theta _1})} \\over {{r_2} - {r_1}}}$$"}, {"identifier": "B", "content": "$${{\\pi {r_1}{r_2}({\\theta _2} - {\\theta _1})} \\over {{r_2} - {r_1}}}$$"}, {"identifier": "C", "content": "$${{K({\\theta _2} - {\\theta _1})} \\over {{r_2} - {r_1}}}$$"}... | ["A"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265668/exam_images/pmaver8f2epncecp1lfb.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264892/exam_images/e5rriyzwe6nxuvgsbjlw.webp"><img src="https://res.c... | mcq | jee-main-2021-online-31st-august-evening-shift | 11,317 |
1l547v4hz | physics | heat-and-thermodynamics | heat-transfer | <p>Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ___________ min.</p> | [] | null | 15 | <p>$$H = {{{V^2}} \over R}\,.\,\Delta t$$</p>
<p>$$ \Rightarrow H = {{{V^2}} \over {{R_1}}}\,.\,20 = {{{V^2}} \over {{R_2}}}\,.\,60$$ ..... (i)</p>
<p>Also, $$H = {{{V^2}} \over {\left[ {{{{R_1}{R_2}} \over {{R_1} + {R_2}}}} \right]}}\,.\,\Delta t$$</p>
<p>$$ = {4 \over 3}\,.\,{{{V^2}} \over {{R_1}}}\,.\,\Delta t$$ [$$... | integer | jee-main-2022-online-29th-june-morning-shift | 11,318 |
1l547zpzh | physics | heat-and-thermodynamics | heat-transfer | <p>As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm<sup>2</sup> for each plate. The equivalent thermal conductivity of the compound plate is $$\le... | [] | null | 21 | <p>$${{{L_1}} \over {{K_1}{A_1}}} + {{{L_2}} \over {{K_2}{A_2}}} = {{{L_1} + {L_2}} \over {{K_{eff}}{A_{eff}}}}$$</p>
<p>$$ \Rightarrow {4 \over K} + {{2.5} \over {2K}} = {{6.5} \over {{K_{eff}}}}$$</p>
<p>$$ \Rightarrow {{10.5} \over {2K}} = {{6.5} \over {{K_{eff}}}}$$</p>
<p>$$ \Rightarrow {K_{eff}} = {{13K} \over {1... | integer | jee-main-2022-online-29th-june-morning-shift | 11,319 |
1l5c4db07 | physics | heat-and-thermodynamics | heat-transfer | <p>Two metallic blocks M<sub>1</sub> and M<sub>2</sub> of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M<sub>2</sub> is K then the thermal conductivity of M<sub>1</sub> will be :</p>
<p>[Assume steady state heat conduction]</p>
<p><img src="data:image/png;b... | [{"identifier": "A", "content": "10 K"}, {"identifier": "B", "content": "8 K"}, {"identifier": "C", "content": "12.5 K"}, {"identifier": "D", "content": "2 K"}] | ["B"] | null | <p>Thermal current is same so</p>
<p>$${{dQ} \over {dt}} = {{\Delta {T_1}} \over {{{{I_1}} \over {{K_1}A}}}} = {{\Delta {T_2}} \over {{{{I_2}} \over {{K_2}A}}}}$$</p>
<p>or $${{20} \over {16}} \times K' = {{80} \over 8} \times K$$</p>
<p>$$ \Rightarrow K' = 8\,K$$</p> | mcq | jee-main-2022-online-24th-june-morning-shift | 11,320 |
1l6i1373g | physics | heat-and-thermodynamics | heat-transfer | <p>An ice cube of dimensions $$60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm}$$ is placed in an insulation box of wall thickness $$1 \mathrm{~cm}$$. The box keeping the ice cube at $$0^{\circ} \mathrm{C}$$ of temperature is brought to a room of temperature $$40^{\circ} \mathrm{C}$$. The rate of melting o... | [{"identifier": "A", "content": "$$61 \\times 10^{-3} \\mathrm{~kg} \\mathrm{~s}^{-1}$$"}, {"identifier": "B", "content": "$$61 \\times 10^{-5} \\mathrm{~kg} \\mathrm{~s}^{-1}$$"}, {"identifier": "C", "content": "$$208 \\mathrm{~kg} \\mathrm{~s}^{-1}$$"}, {"identifier": "D", "content": "$$30 \\times 10^{-5} \\mathrm{~k... | ["B"] | null | <p>$${{\Delta Q} \over {\Delta t}} = {{kA({T_1} - {T_2})} \over l}$$</p>
<p>$$ \Rightarrow {{mL} \over {\Delta t}} = {{kA({T_1} - {T_2})} \over l}$$</p>
<p>$$ \Rightarrow {m \over {\Delta t}} = {{kA({T_1} - {T_2})} \over {Ll}}$$</p>
<p>$$ \simeq 61.1 \times {10^{ - 5}}$$ kg/s</p> | mcq | jee-main-2022-online-26th-july-evening-shift | 11,321 |
1l6jhb1jz | physics | heat-and-thermodynamics | heat-transfer | <p>If $$K_{1}$$ and $$K_{2}$$ are the thermal conductivities, $$L_{1}$$ and $$L_{2}$$ are the lengths and $$A_{1}$$ and $$A_{2}$$ are the cross sectional areas of steel and copper rods respectively such that $$\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2$$. Then, for the arrangement as shown in t... | [{"identifier": "A", "content": "$$18^{\\circ} \\mathrm{C}$$"}, {"identifier": "B", "content": "$$14^{\\circ} \\mathrm{C}$$"}, {"identifier": "C", "content": "$$45^{\\circ} \\mathrm{C}$$"}, {"identifier": "D", "content": "$$150^{\\circ} \\mathrm{C}$$"}] | ["C"] | null | <p>$$450 - T = {{dQ} \over {dt}} \times {{{l_1}} \over {{K_1}{A_1}}}$$</p>
<p>$$T - 0 = {{dQ} \over {dt}} \times {{{l_2}} \over {{K_2}{A_2}}}$$</p>
<p>So, $${{450 - T} \over T} = {{{K_2}{A_2}{l_1}} \over {{K_1}{A_1}{l_2}}} = 9 \times {1 \over 2} \times 2 = 9$$</p>
<p>$$450 - T = 9T$$</p>
<p>$$ \Rightarrow T = 45^\circ ... | mcq | jee-main-2022-online-27th-july-morning-shift | 11,322 |
1l6jhh8jx | physics | heat-and-thermodynamics | heat-transfer | <p>Read the following statements :</p>
<p>A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.</p>
<p>B. Two bodies $$P$$ and $$Q$$ having equal surface areas are maintained at temperature $$10^{\circ} \mathrm{C}$$ and $$20^{\circ} \... | [{"identifier": "A", "content": "A, B, C only"}, {"identifier": "B", "content": "A, B only"}, {"identifier": "C", "content": "A, C only"}, {"identifier": "D", "content": "B, C, D only"}] | ["A"] | null | <p>From Newton's cooling law $${{dQ} \over {dt}} = - k(T - {T_s})$$ the statement A is correct.</p>
<p>For B</p>
<p>$$U = \sigma eA{T^4}$$</p>
<p>So, $${{{U_1}} \over {{U_2}}} = {\left( {{{283} \over {293}}} \right)^4} \simeq {1 \over {1.15}}$$</p>
<p>Statement B is correct</p>
<p>For C</p>
<p>$$\eta = 1 - {{{T_1}} \... | mcq | jee-main-2022-online-27th-july-morning-shift | 11,323 |
1lgp107f6 | physics | heat-and-thermodynamics | heat-transfer | <p>Two plates $$\mathrm{A}$$ and $$\mathrm{B}$$ have thermal conductivities $$84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ and $$126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of... | [] | null | 40 | Let's denote the temperature at the surface of contact as T. We can find this temperature by considering the heat transfer through each plate when the system reaches steady state. At steady state, the rate of heat transfer through both plates A and B is the same.
<br/><br/>
We can use the formula for heat transfer rate... | integer | jee-main-2023-online-13th-april-evening-shift | 11,324 |
1lh303j46 | physics | heat-and-thermodynamics | heat-transfer | <p>A body cools in 7 minutes from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$. The temperature of the surrounding is $$10^{\circ} \mathrm{C}$$. The temperature of the body after the next 7 minutes will be:</p> | [{"identifier": "A", "content": "$$34^{\\circ} \\mathrm{C}$$"}, {"identifier": "B", "content": "$$28^{\\circ} \\mathrm{C}$$"}, {"identifier": "C", "content": "$$32^{\\circ} \\mathrm{C}$$"}, {"identifier": "D", "content": "$$30^{\\circ} \\mathrm{C}$$"}] | ["B"] | null | <p>Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. The average rate of cooling can be represented as:</p>
<p>$$\frac{T_1-T_2}{t} = K \left(\frac{T_1+T_2}{2} - T_s\right)$$</p>
<p>where:</p>
<ul>... | mcq | jee-main-2023-online-6th-april-evening-shift | 11,325 |
1lsg5s187 | physics | heat-and-thermodynamics | heat-transfer | <p>A block of ice at $$-10^{\circ} \mathrm{C}$$ is slowly heated and converted to steam at $$100^{\circ} \mathrm{C}$$. Which of the following curves represent the phenomenon qualitatively:</p> | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lshj8dut/4e8a7ee4-3db7-464c-a053-7074b1ea2c1b/363cd550-c8e0-11ee-8501-bb04786aa212/file-6y3zli1lshj8duu.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/6y3zli1lshj8dut/4e8a7ee4-3db7-464c-a05... | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsoio7ig/b6b04b1f-10e9-44e5-b610-c1f1fac15efa/81b35880-ccb7-11ee-8ef5-472d1767d2da/file-6y3zli1lsoio7ih.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsoio7ig/b6b04b1f-10e9-44e5-b610-c1f1fac15efa/81b35880-ccb7-11ee-8e... | mcq | jee-main-2024-online-30th-january-evening-shift | 11,326 |
lv0vy00d | physics | heat-and-thermodynamics | heat-transfer | <p>On celcius scale the temperature of body increases by $$40^{\circ} \mathrm{C}$$. The increase in temperature on Fahrenheit scale is :</p> | [{"identifier": "A", "content": "$$75^{\\circ} \\mathrm{F}$$\n"}, {"identifier": "B", "content": "$$70^{\\circ} \\mathrm{F}$$\n"}, {"identifier": "C", "content": "$$72^{\\circ} \\mathrm{F}$$\n"}, {"identifier": "D", "content": "$$68^{\\circ} \\mathrm{F}$$"}] | ["C"] | null | <p>To find the increase in temperature on the Fahrenheit scale, we use the relationship between the Celsius and Fahrenheit temperature scales. The formula to convert Celsius to Fahrenheit is:</p>
<p>$$F = \frac{9}{5}C + 32$$</p>
<p>However, since we are interested in the <strong>increase</strong> in temperature, we c... | mcq | jee-main-2024-online-4th-april-morning-shift | 11,327 |
XRCRiBlsQV1VCE8s | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | At what temperature is the $$r.m.s$$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $${47^ \circ }C?$$ | [{"identifier": "A", "content": "$$80K$$ "}, {"identifier": "B", "content": "$$-73$$ $$K$$ "}, {"identifier": "C", "content": "$$3$$ $$K$$ "}, {"identifier": "D", "content": "$$20$$ $$K$$ "}] | ["D"] | null | $${v_{rms}} = $$$$\sqrt {{{RT} \over M}} $$
<br><br>For $${v_{rms}}$$ to be equal $${{{T_{{H_2}}}} \over {{M_{{H_2}}}}} = {{{T_{{O_2}}}} \over {{M_{{O_2}}}}}$$
<br><br>Here $${M_{{H_2}}} = 2;\,\,{M_{{O_2}}} = 32;$$
<br><br>$${T_{{O_2}}} = 47 + 273 = 320K$$
<br><br>$$\therefore$$ $${{{T_{{H_2}}}} \over 2} = {{320} \over... | mcq | aieee-2002 | 11,328 |
m4xLDHoo8t3QStkL | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will | [{"identifier": "A", "content": "increase "}, {"identifier": "B", "content": "decrease "}, {"identifier": "C", "content": "remain same "}, {"identifier": "D", "content": "decrease for some, while increase for others "}] | ["C"] | null | Since pressure and volume are not changing, so temperature remains same. | mcq | aieee-2002 | 11,329 |
P4Acm3A1OxAjOz8l | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gamma = 7/5} \right)$$. What is $$\gamma $$ for the mixture? $$\gamma $$ Denotes the ratio of specific heat at constant pressure, to that at constant volume | [{"identifier": "A", "content": "$$35/23$$ "}, {"identifier": "B", "content": "$$23/15$$ "}, {"identifier": "C", "content": "$$3/2$$ "}, {"identifier": "D", "content": "$$4/3$$ "}] | ["C"] | null | $${{{n_1} + {n_2}} \over {\gamma - 1}} = {{{n_1}} \over {{\gamma _1} - 1}} + {{{n_2}} \over {{\gamma _2} - 1}}$$
<br>$$ \Rightarrow {{1 + 1} \over {\gamma - 1}}$$
<br>$$ = {1 \over {{5 \over 3} - 1}} + {1 \over {{7 \over 5} - 1}}$$
<br>$$ \Rightarrow \gamma = {3 \over 2}$$ | mcq | aieee-2004 | 11,331 |
CvgU46G7abcmnd4S | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A gaseous mixture consists of $$16$$ $$g$$ of helium and $$16$$ $$g$$ of oxygen. The ratio $${{Cp} \over {{C_v}}}$$ of the mixture is | [{"identifier": "A", "content": "$$1.62$$ "}, {"identifier": "B", "content": "$$1.59$$ "}, {"identifier": "C", "content": "$$1.54$$ "}, {"identifier": "D", "content": "$$1.4$$ "}] | ["A"] | null | $${{{n_1} + {n_2}} \over {r - 1}} = {{{n_1}} \over {{r_1} - 1}} + {{{n_2}} \over {{r_2} - 1}}$$
<br>$${{{{16} \over 4} + {{16} \over {32}}} \over {r - 1}} = {{16/4} \over {{5 \over 3} - 1}} + {{16/32} \over {1.4 - 1}}$$
<br>$$\therefore$$ $$\gamma = 1.62$$ | mcq | aieee-2005 | 11,332 |
lUwj8MqZ20HXY9Sj | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $${T_0},$$ while Box contains one mole of helium at temperature $$\left( {{7 \over 3}} \right){T_0}.$$ The boxes are then put into thermal contact with each other, and heat flows between them until... | [{"identifier": "A", "content": "$${T_f} = {3 \\over 7}{T_0}$$ "}, {"identifier": "B", "content": "$${T_f} = {7 \\over 3}{T_0}$$ "}, {"identifier": "C", "content": "$${T_f} = {3 \\over 2}{T_0}$$ "}, {"identifier": "D", "content": "$${T_f} = {5 \\over 2}{T_0}$$ "}] | ["C"] | null | Heat lost by He $$=$$ Heat gained by $${N_2}$$
<br>$${n_1}C{v_1}\Delta {T_1} = {n_2}C{v_2}\Delta {T_2}$$
<br>$${3 \over 2}R\left[ {{7 \over 3}{T_0} - {T_f}} \right]$$
<br>$$ = {5 \over 2}R\left[ {{T_f} - {T_0}} \right] \Rightarrow {T_f}$$
<br>$$ = {3 \over 2}{T_0}$$ | mcq | aieee-2006 | 11,333 |
vkKkodUJbwcBvU05 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $${V^q},$$ where $$V$$ is the volume of the gas. The value of $$q$$ is: $$\left( {\gamma = {{{C_p}} \over {{C_v}}}} \right)$$ | [{"identifier": "A", "content": "$${{\\gamma + 1} \\over 2}$$ "}, {"identifier": "B", "content": "$${{\\gamma - 1} \\over 2}$$ "}, {"identifier": "C", "content": "$${{3\\gamma + 5} \\over 6}$$ "}, {"identifier": "D", "content": "$${{3\\gamma - 5} \\over 6}$$ "}] | ["A"] | null | $$\tau = {1 \over {\sqrt 2 \pi {d^2}\left( {{N \over V}} \right)\sqrt {{{3RT} \over M}} }}$$
<br>$$\tau \propto {V \over {\sqrt T }}$$
<br>As, $$\,\,\,\,T{V^{\gamma - 1}} = K$$
<br>So, $$\,\,\,\,\tau \propto {V^{\gamma + 1/2}}$$
<br>Therefore, $$q = {{\gamma + 1} \over 2}$$ | mcq | jee-main-2015-offline | 11,336 |
n2n8IDQQwOZwWfQOS8p3j | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Which of the following shows the correct relationship between the pressure ‘P’ and density $$\rho $$ of an ideal gas at constant temperature ? | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1l82xc3xv/2fb8c94d-5c69-456a-8a24-b0e01b38d50b/484dc430-34e3-11ed-b84c-a3c7c2456516/file-1l82xc3xw.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1l82xc3xv/2fb8c94d-5c69-456a-8a24-b0e01b38d50b/484... | ["D"] | null | We know, ideal gas equation,
<br><br>PV = nRT
<br><br>Here T = constant.
<br><br>$$ \therefore $$ PV = constant
<br><br>$$ \Rightarrow $$ P $${m \over \rho }$$ = constant
<br><br>$$ \Rightarrow $$ P $$ \propto $$ $$\rho $$ | mcq | jee-main-2016-online-10th-april-morning-slot | 11,337 |
GG5jnHCbuhvtaHRT | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | C<sub>P</sub> and C<sub>v</sub> are specific heats at constant pressure and constant volume respectively. It is observed that <br/>C<sub>P</sub> – C<sub>v</sub> = a for hydrogen gas<br/> C<sub>P</sub> – C<sub>v</sub> = b for nitrogen gas<br/> The correct relation between a and b is | [{"identifier": "A", "content": "a = 28 b"}, {"identifier": "B", "content": "a = 1/14 b"}, {"identifier": "C", "content": "a = b"}, {"identifier": "D", "content": "a = 14 b"}] | ["D"] | null | As we know, for 1 g mole of a gas,
<br><br> C<sub>p</sub> – C<sub>v</sub> = R where C<sub>p</sub> and C<sub>v</sub> are molar
specific heat capacities.
<br><br>So, when n gram moles are given,
<br><br>C<sub>p</sub> – C<sub>v</sub> = $${R \over n}$$
<br><br>For hydrogen (n = 2), C<sub>p</sub> – C<sub>v</sub> = $${R \ove... | mcq | jee-main-2017-offline | 11,339 |
SiUiqscAgq9DjtfucRX02 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20<sup>o</sup>C to 90<sup>o</sup>C. Work done
by gas is close to – (Gas constant R = 8.31 J/mol.K) | [{"identifier": "A", "content": "581 J"}, {"identifier": "B", "content": "73 J"}, {"identifier": "C", "content": "146 J"}, {"identifier": "D", "content": "291 J"}] | ["D"] | null | WD = P$$\Delta $$V = nR$$\Delta $$T = $${1 \over 2} \times 8.31 \times 70$$ | mcq | jee-main-2019-online-10th-january-evening-slot | 11,342 |
aAVEJjHVxfZv6fLGg53rsa0w2w9jx7f8ml3 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be
the heat energy absorbed by the gas, in this process ? | [{"identifier": "A", "content": "35 J"}, {"identifier": "B", "content": "30 J"}, {"identifier": "C", "content": "25 J"}, {"identifier": "D", "content": "40 J"}] | ["A"] | null | At constant pressure,
<br><br>W = P$$\Delta $$V = nR$$\Delta $$T
<br><br>At constant pressure, heat supplied
<br><br>Q = nC<sub>p</sub>$$\Delta $$T
<br><br>$${W \over Q} = {R \over {{C_p}}}$$
<br><br>For diatomic gas, C<sub>p</sub> = $${7 \over 2}R$$
<br><br>$$ \therefore $$ $${{10} \over Q} = {R \over {{7 \over 2}R}}$... | mcq | jee-main-2019-online-12th-april-evening-slot | 11,343 |
UIYDiPk7re8pX8vYHm3rsa0w2w9jx3ostqk | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the
molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K) | [{"identifier": "A", "content": "21.6 J/mol K"}, {"identifier": "B", "content": "17.4 J/mol K"}, {"identifier": "C", "content": "15.7 J/mol K"}, {"identifier": "D", "content": "19.7 J/mol K"}] | ["B"] | null | $${f_{mix}} = {{{n_1}{f_1} + {n_2}{f_2}} \over {{n_1} + {n_2}}}$$<br>
$$ \Rightarrow {{2 \times 3 + 3 \times 5} \over 5} = {{21} \over 5}$$<br><br>
$${C_v} = {{fR} \over 5} = {{21} \over 5} \times {R \over 2} = 17.4$$ J/mol K | mcq | jee-main-2019-online-12th-april-morning-slot | 11,344 |
v9sBRRddI5wqEP93Lg3rsa0w2w9jwzmkaqj | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by
$$\Delta $$T. the heat required to produce the same change in temperature, at a constant pressure is : | [{"identifier": "A", "content": "$${7 \\over 5}Q$$"}, {"identifier": "B", "content": "$${3 \\over 2}Q$$"}, {"identifier": "C", "content": "$${2 \\over 3}Q$$"}, {"identifier": "D", "content": "$${5 \\over 3}Q$$"}] | ["A"] | null | Heat supplied at constant volume<br>
Q = nC<sub>V</sub>$$\Delta $$T<br><br>
and heat supplied at constant pressure<br>
Q' = nC<sub>P</sub>$$\Delta $$T<br><br>
$$Q' = {{{C_P}} \over {{C_V}}}Q = \left( {1 + {2 \over 5}} \right)Q = {7 \over 5}Q$$
| mcq | jee-main-2019-online-10th-april-evening-slot | 11,345 |
ujpmVbAmuT0MZd2xaM9Wv | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | For a given gas at 1 atm pressure, rms speed
of the molecule is 200 m/s at 127°C. At 2 atm
pressure and at 227°C, the rms speed of the
molecules will be : | [{"identifier": "A", "content": "100 m/s"}, {"identifier": "B", "content": "100 $$\\sqrt 5 $$ m/s"}, {"identifier": "C", "content": "80 $$\\sqrt 5 $$ m/s"}, {"identifier": "D", "content": "80 m/s"}] | ["B"] | null | $${V_{rms}} = \sqrt {{{3RT} \over {{M_w}}}} $$<br><br>
$$ \Rightarrow {V_{rms}} \propto \sqrt T $$<br><br>
Now, $${v \over {200}} = \sqrt {{{500} \over {400}}} $$<br><br>
$$ \Rightarrow {v \over {200}} = {{\sqrt 5 } \over 2}$$<br><br>
$$ \Rightarrow v = 100\sqrt 5 $$ m/s | mcq | jee-main-2019-online-9th-april-morning-slot | 11,347 |
kZBDPe1Cq1cODFtZq19AY | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The temperature, at which the root mean square
velocity of hydrogen molecules equals their
escape velocity from the earth, is closest to :<br/>
[Boltzmann Constant k<sub>B</sub> = 1.38 × 10<sup>–23</sup> J/K
Avogadro Number N<sub>A</sub> = 6.02 × 10<sup>26</sup> /kg
Radius of Earth : 6.4 × 10<sup>6</sup> m
Gravitationa... | [{"identifier": "A", "content": "3 \u00d7 10<sup>5</sup> K"}, {"identifier": "B", "content": "10<sup>4</sup> K"}, {"identifier": "C", "content": "650 K"}, {"identifier": "D", "content": "800 K"}] | ["B"] | null | $${V_{rms}} = \sqrt {{{3RT} \over M}} = 11.2 \times {10^3}m/s$$<br><br>
$$ \Rightarrow $$ $$T = {M \over {3R}} \times {\left( {11.2 \times {{10}^3}} \right)^2}$$<br><br>
= $${{2 \times {{10}^{ - 3}}} \over {3 \times 8.3}} \times 125.44 \times {10^6} = {10^4}K$$ | mcq | jee-main-2019-online-8th-april-evening-slot | 11,348 |
JlIUmv2W7LyEKKFnAIyr5 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $$\ell $$<sub>1</sub>, and that below the piston is $$\ell $$<sub>2</sub>, such that $$\ell $... | [{"identifier": "A", "content": "$${{nRT} \\over g}\\left[ {{{{\\ell _1} - {\\ell _2}} \\over {{\\ell _1}{\\ell _2}}}} \\right]$$"}, {"identifier": "B", "content": "$${{RT} \\over g}\\left[ {{{2{\\ell _1} + {\\ell _2}} \\over {{\\ell _1}{\\ell _2}}}} \\right]$$"}, {"identifier": "C", "content": "$${{nRT} \\over g}\\lef... | ["A"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265926/exam_images/o5bx2exymits5oekl7lw.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th January Evening Slot Physics - Heat and Thermodynamics Question 294 English Explanation">
<... | mcq | jee-main-2019-online-12th-january-evening-slot | 11,349 |
uTilrpd98X6CJSFoVauSV | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27<sup>o</sup>C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole] | [{"identifier": "A", "content": "0.9 kJ"}, {"identifier": "B", "content": "6 kJ "}, {"identifier": "C", "content": "10 kJ "}, {"identifier": "D", "content": "14 kJ"}] | ["C"] | null | We know,
<br><br>V<sub>rms</sub> $$ \propto $$ $$\sqrt T $$
<br><br>So, to make V<sub>rms</sub> double we have to make temperature 4 times.
<br><br>$$ \therefore $$ Final temperature = 300 $$ \times $$ 4 = 1200 K
<br><br>As N<sub>2</sub> gas present in the closed vessel
<br><br>So it is a isochoric p... | mcq | jee-main-2019-online-9th-january-evening-slot | 11,352 |
2jvUqHzYygn5u4guHuQCx | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $$\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],$$ is close to : | [{"identifier": "A", "content": "3.16"}, {"identifier": "B", "content": "0.32"}, {"identifier": "C", "content": "0.45"}, {"identifier": "D", "content": "2.24"}] | ["A"] | null | We know,
<br><br>V<sub>rms</sub> = $$\sqrt {{{3RT} \over M}} $$
<br><br>Where M = molar mass of the gas.
<br><br>Here temperature is 300 K for both the gas. So temperature is constant. R is also a constant.
<br><br>$$ \therefore $$ V<sub>rms</sub> $$ \propto \,\,\sqrt {{1 \over M}} $$
<br><br>$$ \t... | mcq | jee-main-2019-online-9th-january-morning-slot | 11,353 |
ysYAdKtQiaarBXb8ox7k9k2k5hhekk9 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Consider a mixture of n moles of helium gas
and 2n moles of oxygen gas (molecules taken
to be rigid) as an ideal gas. Its C<sub>P</sub>/C<sub>V</sub> value
will be : | [{"identifier": "A", "content": "23/15"}, {"identifier": "B", "content": "67/45"}, {"identifier": "C", "content": "40/27"}, {"identifier": "D", "content": "19/13"}] | ["D"] | null | $${{{C_P}} \over {{C_V}}} = {{{n_1}{C_{{P_1}}} + {n_2}{C_{{P_2}}}} \over {{n_1}{C_{{V_1}}} + {n_2}{C_{{V_2}}}}}$$
<br><br>= $${{n \times {{5R} \over 2} + 2n \times {{7R} \over 2}} \over {n \times {{3R} \over 2} + 2n \times {{5R} \over 2}}}$$
<br><br>= $${{5 + 14} \over {3 + 10}}$$
<br><br>= $${{19} \over {13}}$$ | mcq | jee-main-2020-online-8th-january-evening-slot | 11,354 |
MACCh4nSqypQKyWKt7jgy2xukg0b5qk1 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a
molecule varies with T as : | [{"identifier": "A", "content": "$$\\sqrt T $$"}, {"identifier": "B", "content": "T"}, {"identifier": "C", "content": "$${1 \\over T}$$"}, {"identifier": "D", "content": "$${1 \\over {\\sqrt T }}$$"}] | ["D"] | null | Time (t) = $${V \over {4\pi \sqrt 2 {r^2}vN}}$$ ....(1)
<br><br>Here, v = most probable speed
<br>= $$\sqrt {{{2RT} \over {\pi M}}} $$
<br><br>$$ \Rightarrow $$ v $$ \propto $$ $$\sqrt T $$
<br><br>$$ \therefore $$ From (1),
<br><br>t $$ \propto $$ $${1 \over {\sqrt T }}$$
| mcq | jee-main-2020-online-6th-september-evening-slot | 11,355 |
SJnWiaUzWOmZnSwtBKjgy2xukfrv5ssd | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Initially a gas of diatomic molecules is contained in a cylinder of volume V<sub>1</sub>
at a pressure P<sub>1</sub>
and
temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in
number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a
volume 2V<sub... | [] | null | 5 | We know, PV = nRT
<br>$$ \therefore $$ P<sub>1</sub>V<sub>1</sub> = nR (250)
<br><br>and P<sub>2</sub>(2V<sub>1</sub>) = $${{5n} \over 4}R \times \left( {2000} \right)$$
<br><br>By Dividing
<br><br>$${{{P_1}} \over {2{P_2}}}$$ = $${{4 \times 250} \over {5 \times 2000}}$$
<br><br>$$ \Rightarrow $$ $${{{P_1}} \over {{P_2... | integer | jee-main-2020-online-6th-september-morning-slot | 11,356 |
ibtOK02U1yIoljgqUKjgy2xukfosjz4m | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Nitrogen gas is at 300<sup>o</sup>C temperature. The
temperature (in K) at which the rms speed of a
H<sub>2</sub> molecule would be equal to the rms speed
of a nitrogen molecule, is _______.
<br/>(Molar mass of N<sub>2</sub> gas 28 g). | [] | null | 40TO41 | V<sub>rms</sub> = $$\sqrt {{{3RT} \over M}} $$
<br><br>V<sub>N<sub>2</sub></sub> = $$\sqrt {{{3R(573)} \over 28}} $$
<br><br>V<sub>H<sub>2</sub></sub> = $$\sqrt {{{3RT} \over 2}} $$
<br><br>Given, V<sub>N<sub>2</sub></sub> = V<sub>H<sub>2</sub></sub>
<br><br>$$\sqrt {{{3RT} \over 2}} $$ = $$\sqrt {{{3R(573)} \over 28}}... | integer | jee-main-2020-online-5th-september-evening-slot | 11,357 |
3BcpB0BRnUUtFWQqQ6jgy2xukexs1a92 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | An ideal gas in a closed container is slowly
heated. As its temperature increases, which of
the following statements are true?
<br/>(A) the mean free path of the molecules
decreases.
<br/>(B) the mean collision time between the
molecules decreases.
<br/>(C) the mean free path remains unchanged.
<br/>(D) the mean collis... | [{"identifier": "A", "content": "(C) and (D)\n"}, {"identifier": "B", "content": "(A) and (D)"}, {"identifier": "C", "content": "(B) and (C)"}, {"identifier": "D", "content": "(A) and (B)"}] | ["C"] | null | The mean free path of molecules of an ideal gas is given as:
<br><br>$$\lambda $$ = $${V \over {\sqrt 2 \pi {d^2}N}}$$
<br><br>where : V = Volume of container
<br>N = No of molecules
<br><br>Mean free path is independent of temperature hence with increasing temp since volume of container does not change (closed contain... | mcq | jee-main-2020-online-2nd-september-evening-slot | 11,359 |
ZfN9md8GtxREfOhQBK7k9k2k5l8i62w | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Two gases-argon (atomic radius 0.07 nm,
atomic weight 40) and xenon (atomic radius
0.1 nm, atomic weight 140) have the same
number density and are at the same
temperature. The raito of their respective mean
free times is closest to : | [{"identifier": "A", "content": "2.3"}, {"identifier": "B", "content": "1.83"}, {"identifier": "C", "content": "4.67"}, {"identifier": "D", "content": "3.67"}] | ["B"] | null | $$\lambda = {1 \over {\sqrt 2 \pi {d^2}n}}$$
<br><br>Mean free time, t = $${\lambda \over v}$$
<br><br>Also v $$ \propto $$ $$\sqrt {{T \over M}} $$
<br><br>$$ \therefore $$ t $$ \propto $$ $${{\sqrt M } \over d}$$
<br><br>$${{{t_{Ar}}} \over {{t_{xe}}}}$$ = $${{d_{Xe}^2} \over {d_{Ar}^2}} \times \sqrt {{{{M_{Ar}}} \... | mcq | jee-main-2020-online-9th-january-evening-slot | 11,360 |
hOz1govHnfWpYM2LcA7k9k2k5gvbmth | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The plot that depicts the behavior of the mean
free time t (time between two successive
collisions) for the molecules of an ideal gas, as
a function of temperature (T), qualitatively, is:<br/>
(Graphs are schematic and not drawn to scale)<div></div> | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734263572/exam_images/ujhx4yynml2aigtsfmtx.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2020 (Online) 8th January Morning Slot Physics - Heat and Thermodynamics... | ["B"] | null | Mean free time =
<span style="display: inline-block;vertical-align: middle;">
<div style="text-align: center;border-bottom: 1px solid black;">Mean free path</div>
<div style="text-align: center;">Average speed</div>
</span>
<br><br>= $${{{1 \over {\sqrt 2 \pi {D^2}n}}} \over {\sqrt {{{8RT} \over {\pi M}}} }}... | mcq | jee-main-2020-online-8th-january-morning-slot | 11,361 |
dw958HyEAv1F85NhVH7k9k2k5f77x3m | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean
collision time between the gas molecule changes from $${\tau _1}$$
to $${\tau _2}$$
. If $${{{C_p}} \over {{C_v}}} = \gamma $$ for this gas then a good
estimate for $${{{\tau _2}} \over {{\tau _1}}}$$
is given by : | [{"identifier": "A", "content": "$${\\left( 2 \\right)^{{{1 + \\gamma } \\over 2}}}$$"}, {"identifier": "B", "content": "2"}, {"identifier": "C", "content": "$${\\left( {{1 \\over 2}} \\right)^{{{1 + \\gamma } \\over 2}}}$$"}, {"identifier": "D", "content": "$${\\left( {{1 \\over 2}} \\right)^\\gamma }$$"}] | ["A"] | null | $$\tau $$ $$ \propto $$ $${V \over {\sqrt T }}$$ ....(1)
<br><br>Also we know, PV<sup>$$\gamma $$</sup> = k
<br><br>We know, PV = nRT
<br><br>$$ \Rightarrow $$ P $$ \propto $$ $${T \over V}$$
<br><br>$$ \therefore $$ $$\left( {{T \over V}} \right)$$V<sup>$$\gamma $$</sup> = k
<br><br>$$ \Rightarrow $$TV<sup>$$\gamma $$... | mcq | jee-main-2020-online-7th-january-evening-slot | 11,362 |
1R1dDAQKz8jgrDcPs8jgy2xukfaybjcx | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The change in the magnitude of the volume of an ideal gas when a small additional pressure $$\Delta $$P is
applied at a constant temperature, is the same as the change when the temperature is reduced by
a small quantity $$\Delta $$T at constant pressure. The initial temperature and pressure of the gas were 300
K and 2 ... | [] | null | 150 | We know, $$PV = nRT$$<br><br>$$ \therefore $$ $$P\Delta V + V\Delta P = 0$$ (for constant temp.)<br><br>and $$P\Delta V$$ = $$nR\Delta T$$ (for constant pressure)<br><br>$$\Delta T = {{P\Delta V} \over {nR}}$$<br><br>$$\Delta P = - {{P\Delta V} \over V}$$ ($$\Delta V$$ is same in both cases)<br><br>$${{\Delta T} \over... | integer | jee-main-2020-online-4th-september-evening-slot | 11,363 |
u4N2icvMVOxcFhCpQ51klrocwqf | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | On the basis of kinetic theory of gases, the gas exerts pressure because its molecules : | [{"identifier": "A", "content": "continuously lose their energy till it reaches wall."}, {"identifier": "B", "content": "are attracted by the walls of container."}, {"identifier": "C", "content": "suffer change in momentum when impinge on the walls of container."}, {"identifier": "D", "content": "continuously stick to ... | ["C"] | null | On the basis of kinetic theory of gases, the gas exerts pressure
because its molecules contain uniform speed, random motion and
perform elastic collision with each other, as well as with the walls of
container. As a result of which gaseous molecules suffer change in
momentum when impinge on the walls of container | mcq | jee-main-2021-online-24th-february-evening-slot | 11,364 |
dGnJYy6YSyceBLcYZi1klrowfet | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The root mean square speed of molecules of a given mass of a gas at 27$$^\circ$$C and 1 atmosphere pressure is 200 ms<sup>$$-$$1</sup>. The root mean square speed of molecules of the gas at 127$$^\circ$$C and 2 atmosphere pressure is $${{x \over {\sqrt 3 }}}$$ ms<sup>$$-$$1</sup>. The value of x will be _________. | [] | null | 400 | Given, T<sub>1</sub> = 27$$^\circ$$C = 27 + 273 = 300K, p<sub>1</sub> = 1 atm, v<sub>1</sub> = 200 ms<sup>$$-$$1</sup>, T<sub>2</sub> = 127$$^\circ$$C = 400 K, p<sub>2</sub> = 12 atm, v<sub>2</sub> = ?<br/><br/>As we know that,<br/><br/>Root mean square speed, $${v_{rms}} = \sqrt {{{3RT} \over m}} $$<br/><br/>$$\theref... | integer | jee-main-2021-online-24th-february-evening-slot | 11,365 |
qbgzZqlj9cVKTf67ou1kltk9bzp | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equili... | [] | null | 25 | By energy conservation<br><br>$${3 \over 2}{n_1}R{T_1} + {3 \over 2}{n_2}R{T_2} = {3 \over 2}({n_1} + {n_2})RT$$<br><br>Using PV = nRT<br><br>P<sub>1</sub>V<sub>1</sub> + P<sub>2</sub>V<sub>2</sub> = P(V<sub>1</sub> + V<sub>2</sub>)<br><br>$$P = {{{P_1}{V_1} + {P_2}{V_2}} \over {{V_1} + {V_2}}} = {{2 \times 4.5 + 3 \ti... | integer | jee-main-2021-online-26th-february-morning-slot | 11,366 |
d1Dh1z6cmtypQABGHM1kmhp8r9s | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is : | [{"identifier": "A", "content": "$${{3RT} \\over V}$$"}, {"identifier": "B", "content": "$${{4RT} \\over V}$$"}, {"identifier": "C", "content": "$${{88RT} \\over V}$$"}, {"identifier": "D", "content": "$${5 \\over 2}{{RT} \\over V}$$"}] | ["D"] | null | No. of moles of O<sub>2</sub> :
<br>n<sub>1</sub> = $${{16} \over {32}}$$ = 0.5 mole<br><br>No. of moles of N<sub>2</sub> :
<br>n<sub>2</sub> = $${{28} \over {28}}$$ = 1 mole<br><br>No. of moles of CO<sub>2</sub> :
<br>n<sub>3</sub> = $${{44} \over {44}}$$ = 1 mole<br><br>Total no. of moles in container : n = n<sub>... | mcq | jee-main-2021-online-16th-march-morning-shift | 11,367 |
TCwXd5eQAWlgxYFmEc1kmip5f3b | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Calculate the value of mean free path ($$\lambda$$) for oxygen molecules at temperature 27$$^\circ$$C and pressure 1.01 $$\times$$ 10<sup>5</sup> Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 $$\times$$ 10<sup>$$-$$23</sup> JK<sup>$$-$$1</sup>) | [{"identifier": "A", "content": "32 nm"}, {"identifier": "B", "content": "58 nm"}, {"identifier": "C", "content": "86 nm"}, {"identifier": "D", "content": "102 nm"}] | ["D"] | null | $${I_{mean}} = {{RT} \over {\sqrt 2 \pi {d^2}{N_A}P}}$$<br><br>$$ = {{1.38 \times 300 \times {{10}^{ - 23}}} \over {\sqrt 2 \times 3.14 \times {{(0.3 \times {{10}^{ - 9}})}^2} \times 1.01 \times {{10}^5}}}$$<br><br>$$ = 102 \times {10^{ - 9}}$$ m<br><br>$$ = 102$$ nm | mcq | jee-main-2021-online-16th-march-evening-shift | 11,368 |
N3JuLFKtW3sxfqQhOM1kmlw1724 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be :<br/><br/>(Molecular weight of oxygen is 32g/mol; R = 8.3 J K<sup>$$-$$1</sup> mol<sup>$$-$$1</sup>) | [{"identifier": "A", "content": "$$\\sqrt {{{3\\pi } \\over 8}} $$"}, {"identifier": "B", "content": "$$\\sqrt {{3 \\over 3}} $$"}, {"identifier": "C", "content": "$$\\sqrt {{8 \\over 3}} $$"}, {"identifier": "D", "content": "$$\\sqrt {{{8\\pi } \\over 3}} $$"}] | ["A"] | null | $${V_{rms}} = \sqrt {{{3RT} \over M}} $$<br><br>$${V_{avg}} = \sqrt {{8 \over \pi }{{RT} \over M}} $$<br><br>$${{{V_{rms}}} \over {{V_{avg}}}} = \sqrt {{{3\pi } \over 8}} $$ | mcq | jee-main-2021-online-18th-march-evening-shift | 11,369 |
1krqbuew2 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning. | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734265877/exam_images/ipju1hnqrv1ovm6vhj03.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2021 (Online) 20th July Evening Shift Physics - Heat and Thermodynamics ... | ["C"] | null | PV = nRT<br><br>PV $$\propto$$ T<br><br>Straight line with positive slope (nR) | mcq | jee-main-2021-online-20th-july-evening-shift | 11,371 |
1krudowyj | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | For a gas C<sub>P</sub> $$-$$ C<sub>V</sub> = R in a state P and C<sub>P</sub> $$-$$ C<sub>V</sub> = 1.10 R in a state Q, T<sub>P</sub> and T<sub>Q</sub> are the temperatures in two different states P and Q respectively. Then | [{"identifier": "A", "content": "T<sub>P</sub> = T<sub>Q</sub>"}, {"identifier": "B", "content": "T<sub>P</sub> < T<sub>Q</sub>"}, {"identifier": "C", "content": "T<sub>P</sub> = 0.9 T<sub>Q</sub>"}, {"identifier": "D", "content": "T<sub>P</sub> > T<sub>Q</sub>"}] | ["D"] | null | C<sub>P</sub> $$-$$ C<sub>V</sub> = R for ideal gas and gas behaves as ideal gas at high temperature, so T<sub>P</sub> > T<sub>Q</sub> | mcq | jee-main-2021-online-25th-july-morning-shift | 11,372 |
1krwc2vcy | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A system consists of two types of gas molecules A and B having same number density 2 $$\times$$ 10<sup>25</sup>/m<sup>3</sup>. The diameter of A and B are 10 $$\mathop A\limits^o $$ and 5 $$\mathop A\limits^o $$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecu... | [] | null | 25 | $$\because$$ mean free path<br><br>$$\lambda = {1 \over {\sqrt 2 \pi {d^2}n}}$$<br><br>$${{{\lambda _1}} \over {{\lambda _2}}} = {{d_2^2{n_2}} \over {d_1^2{n_1}}}$$<br><br>$$ = {\left( {{5 \over {10}}} \right)^2} = 0.25 = 25 \times {10^{ - 2}}$$ | integer | jee-main-2021-online-25th-july-evening-shift | 11,373 |
1kryt8uuz | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $$\times$$ 10<sup>$$-$$9</sup> J per molecules is : | [{"identifier": "A", "content": "0.75 $$\\times$$ 10<sup>11</sup>"}, {"identifier": "B", "content": "3 $$\\times$$ 10<sup>11</sup>"}, {"identifier": "C", "content": "1.5 $$\\times$$ 10<sup>11</sup>"}, {"identifier": "D", "content": "6 $$\\times$$ 10<sup>11</sup>"}] | ["C"] | null | KE = $${3 \over 2}kT$$<br><br>PV = $${N \over {{N_A}}}RT$$<br><br>N = $${{PV} \over {kT}}$$<br><br>= N = 1.5 $$\times$$ 10<sup>11</sup> | mcq | jee-main-2021-online-27th-july-morning-shift | 11,374 |
1ktacm6k5 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are V<sub>H</sub>, V<sub>O</sub> and V<sub>C</sub> respectively then : | [{"identifier": "A", "content": "V<sub>H</sub> > V<sub>O</sub> > V<sub>C</sub>"}, {"identifier": "B", "content": "V<sub>C</sub> > V<sub>O</sub> > V<sub>H</sub>"}, {"identifier": "C", "content": "V<sub>H</sub> = V<sub>O</sub> > V<sub>C</sub>"}, {"identifier": "D", "content": "V<sub>H</sub> = V<sub>O</sub>... | ["A"] | null | $${V_{RMS}} = \sqrt {{{3RT} \over {{M_W}}}} $$<br><br>At the same temperature $${V_{RMS}} \propto {1 \over {\sqrt {{M_W}} }}$$<br><br>$$\Rightarrow$$ V<sub>H</sub> > V<sub>O</sub> > V<sub>C</sub><br><br>Option (a) | mcq | jee-main-2021-online-26th-august-morning-shift | 11,375 |
1ktdyy2yp | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A balloon carries a total load of 185 kg at normal pressure and temperature of 27$$^\circ$$C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $$-$$7$$^\circ$$C. Assuming the volume constant? | [{"identifier": "A", "content": "181.46 kg"}, {"identifier": "B", "content": "214.15 kg"}, {"identifier": "C", "content": "219.07 kg"}, {"identifier": "D", "content": "123.54 kg"}] | ["D"] | null | P<sub>m</sub> = $$\rho$$RT<br><br>$$\therefore$$ $${{{P_1}} \over {{P_2}}} = {{{\rho _1}{T_1}} \over {{\rho _1}{T_2}}}$$<br><br>$${{{\rho _1}} \over {{\rho _2}}} \Rightarrow {{{P_1}{T_2}} \over {{P_2}{T_1}}} = \left( {{{76} \over {45}}} \right) \times {{266} \over {300}}$$<br><br>$${{{\rho _1}} \over {{\rho _2}}} \Righ... | mcq | jee-main-2021-online-27th-august-morning-shift | 11,377 |
1kte0lyrk | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | An ideal gas is expanding such that PT<sup>3</sup> = constant. The coefficient of volume expansion of the gas is : | [{"identifier": "A", "content": "$${1 \\over T}$$"}, {"identifier": "B", "content": "$${2 \\over T}$$"}, {"identifier": "C", "content": "$${4 \\over T}$$"}, {"identifier": "D", "content": "$${3 \\over T}$$"}] | ["C"] | null | PT<sup>3</sup> = constant<br><br>$$\left( {{{nRT} \over v}} \right)$$T<sup>3</sup> = constant<br><br>T<sup>4</sup> V<sup>$$-$$1</sup> = constant<br><br>T<sup>4</sup> = kV<br><br>$$ \Rightarrow 4{{\Delta T} \over T} = {{\Delta V} \over V}$$ ....... (1)<br><br>$$\Delta$$V = V$$\gamma$$$$\Delta$$T ........ (2)<br><br>comp... | mcq | jee-main-2021-online-27th-august-morning-shift | 11,378 |
1ktflyluw | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | if the rms speed of oxygen molecules at 0$$^\circ$$C is 160 m/s, find the rms speed of hydrogen molecules at 0$$^\circ$$C. | [{"identifier": "A", "content": "640 m/s"}, {"identifier": "B", "content": "40 m/s"}, {"identifier": "C", "content": "80 m/s"}, {"identifier": "D", "content": "332 m/s"}] | ["A"] | null | $${V_{rms}} = \sqrt {{{3KT} \over M}} $$<br><br>$${{{{({V_{rms}})}_{{O_2}}}} \over {{{({V_{rms}})}_{{H_2}}}}} = \sqrt {{{{M_{{H_2}}}} \over {{M_{{O_2}}}}}} = \sqrt {{2 \over {32}}} $$<br><br>$${({V_{rms}})_{{H_2}}} = 4 \times {({V_{rms}})_{{O_2}}}$$<br><br>$$ = 4 \times 160$$<br><br>$$ = 640$$ m/s | mcq | jee-main-2021-online-27th-august-evening-shift | 11,379 |
1kth4rlyz | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $${{dp} \over {dv}} = - ap$$. If p = p<sub>0</sub> at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant) | [{"identifier": "A", "content": "$${{{p_0}} \\over {aeR}}$$"}, {"identifier": "B", "content": "$${{a{p_0}} \\over {eR}}$$"}, {"identifier": "C", "content": "infinity"}, {"identifier": "D", "content": "0$$^\\circ$$C"}] | ["A"] | null | $$\int\limits_{{p_0}}^p {{{dp} \over P} = - a\int\limits_0^v {dv} } $$<br><br>$$\ln \left( {{p \over {{p_0}}}} \right) = - av$$<br><br>$$p = {p_0}{e^{ - av}}$$<br><br>For temperature maximum p-v product should be maximum<br><br>$$T = {{pv} \over {nR}} = {{{p_0}v{e^{ - av}}} \over R}$$<br><br>$${{dT} \over {dv}} = 0 \... | mcq | jee-main-2021-online-31st-august-morning-shift | 11,380 |
1ktjpk972 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A mixture of hydrogen and oxygen has volume 500 cm<sup>3</sup>, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :- | [{"identifier": "A", "content": "3 : 8"}, {"identifier": "B", "content": "3 : 16"}, {"identifier": "C", "content": "16 : 3"}, {"identifier": "D", "content": "8 : 3"}] | ["C"] | null | PV = nRT<br><br>400 $$\times$$ 10<sup>3</sup> $$\times$$ 500 $$\times$$ 10<sup>$$-$$6</sup> = n$$\left( {{{25} \over 3}} \right)$$ (300)<br><br>n = $${{2 \over {25}}}$$<br><br>n = n<sub>1</sub> + n<sub>2</sub><br><br>$${{2 \over {25}}}$$ = $${{{M_1}} \over 2} + {{{M_2}} \over {32}}$$<br><br>Also, M<sub>1</sub> + M<sub>... | mcq | jee-main-2021-online-31st-august-evening-shift | 11,381 |
1ktmvzpp7 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | The average translational kinetic energy of N<sub>2</sub> gas molecules at .............$$^\circ$$C becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given k<sub>B</sub> = 1.38 $$\times$$ 10<sup>$$-$$23</sup> J/K) (Fill the nearest integer). | [] | null | 500 | Given, the average translational kinetic energy of dinitrogen (N<sub>2</sub>) = Kinetic energy of an electron .... (i)<br/><br/>Translational kinetic energy of dinitrogen (N<sub>2</sub>)<br/><br/>$$KE = {3 \over 2}{K_B}T$$<br/><br/>Here, T = temperature of the gas,<br/><br/>and K<sub>B</sub> = Boltzmann constant.<br/><... | integer | jee-main-2021-online-1st-september-evening-shift | 11,382 |
1l54v5c4q | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm<sup>3</sup> is :</p> | [{"identifier": "A", "content": "72 $$\\times$$ 10<sup>5</sup>"}, {"identifier": "B", "content": "32 $$\\times$$ 10<sup>5</sup>"}, {"identifier": "C", "content": "27 $$\\times$$ 10<sup>4</sup>"}, {"identifier": "D", "content": "54 $$\\times$$ 10<sup>4</sup>"}] | ["C"] | null | <p>Total number of moles are</p>
<p>$$n = {n_{{H_2}}} + {n_{{O_2}}}$$</p>
<p>$$ = {{16} \over 2} + {{128} \over {32}}$$</p>
<p>= 12 moles</p>
<p>Using $$PV = nRT$$</p>
<p>$$V = {{nRT} \over P}$$</p>
<p>$$ = {{12 \times 8.31 \times 273.15} \over {{{10}^5}}}$$ m<sup>3</sup></p>
<p>= 0.27 m<sup>3</sup> = 27 $$\times$$ 10<... | mcq | jee-main-2022-online-29th-june-evening-shift | 11,385 |
1l55k1zzq | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?</p> | [{"identifier": "A", "content": "The velocity of atomic oxygen remains same"}, {"identifier": "B", "content": "The velocity of atomic oxygen doubles"}, {"identifier": "C", "content": "The velocity of atomic oxygen becomes half"}, {"identifier": "D", "content": "The velocity of atomic oxygen becomes four times"}] | ["B"] | null | <p>As $${v_{rms}} = \sqrt {{{3RT} \over {{M_0}}}} $$</p>
<p>T is doubled and oxygen molecule is dissociated into atomic oxygen molar mass is halved.</p>
<p>So, $$v{'_{rms}} = \sqrt {{{3RT \times 2{T_0}} \over {{M_0}/2}}} = 2{v_{rms}}$$</p>
<p>So velocity of atomic oxygen is doubled.</p> | mcq | jee-main-2022-online-28th-june-evening-shift | 11,386 |
1l56uofhs | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>For a perfect gas, two pressures P<sub>1</sub> and P<sub>2</sub> are shown in figure. The graph shows :</p>
<p> <img src="data:image/png;base64,UklGRowQAABXRUJQVlA4IIAQAADwDAGdASrzAgADP4HA3GW2MS2nIbOY8sAwCWlu6enH/xQZXTG4Xx9Af7b1WXDXIb1leZ54+1Hz86Y/f/zBv//o1VWfX/j+hl5Ali+h6MjVBU5tdwHqYqCpza7gPUxUFTm1tR+blMaPzjtQSbWjR... | [{"identifier": "A", "content": "P<sub>1</sub> > P<sub>2</sub>"}, {"identifier": "B", "content": "P<sub>1</sub> < P<sub>2</sub>"}, {"identifier": "C", "content": "P<sub>1</sub> = P<sub>2</sub>"}, {"identifier": "D", "content": "Insufficient data to draw any conclusion"}] | ["A"] | null | <p>As per ideal gas equation, $$V = {{nR} \over P}T$$</p>
<p>$$\Rightarrow$$ Slope of V-T graph is inversely proportional to P.</p>
<p>As m<sub>2</sub> > m<sub>1</sub> $$\Rightarrow$$ P<sub>1</sub> > P<sub>2</sub></p> | mcq | jee-main-2022-online-27th-june-evening-shift | 11,387 |
1l57qkk8f | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>A mixture of hydrogen and oxygen has volume 2000 cm<sup>3</sup>, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:</p>
<p>[Take gas constant R = 8.3 JK<sup>$$-$$1</sup>mol<sup>$$-$$1</sup>]</p> | [{"identifier": "A", "content": "$${1 \\over 3}$$"}, {"identifier": "B", "content": "$${3 \\over 1}$$"}, {"identifier": "C", "content": "$${1 \\over 16}$$"}, {"identifier": "D", "content": "$${16 \\over 1}$$"}] | ["B"] | null | <p>$${P_1}V = {n_1}RT$$</p>
<p>$${P_2}V = {n_2}RT$$</p>
<p>$$\Rightarrow$$ (100 kPa) V = (n<sub>1</sub> + n<sub>2</sub>)RT</p>
<p>$$ \Rightarrow {n_1} + {n_2} = {{(100\,kPa)(2000\,c{m^3})} \over {8.3 \times 300}}$$ ..... (1)</p>
<p>Also, n<sub>1</sub> $$\times$$ 2 + n<sub>2</sub> $$\times$$ 32 = 0.76 ...... (2)</p>
<p>... | mcq | jee-main-2022-online-27th-june-morning-shift | 11,388 |
1l58bmg2b | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :</p>
<p>(R = universal gas constant)</p> | [{"identifier": "A", "content": "$${{M{v^2}} \\over {7R}}$$"}, {"identifier": "B", "content": "$${{M{v^2}} \\over {5R}}$$"}, {"identifier": "C", "content": "2$${{M{v^2}} \\over {7R}}$$"}, {"identifier": "D", "content": "7$${{M{v^2}} \\over {5R}}$$"}] | ["B"] | null | <p>Let there be n moles of gas</p>
<p>E<sub>loss</sub> = E<sub>gain</sub></p>
<p>$${1 \over 2}(nM){v^2} = n{C_v}\Delta T$$</p>
<p>$${1 \over 2}M{v^2} = {C_v}\Delta T$$</p>
<p>here, $$\gamma = 1.4 = {7 \over 5}$$ i.e. diatomic gas</p>
<p>$$\therefore$$ $${C_v} = {{5R} \over 2}$$</p>
<p>Now, $${1 \over 2}M{v^2} = {{5R} ... | mcq | jee-main-2022-online-26th-june-morning-shift | 11,389 |
1l58ho01i | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27$$^\circ$$C. The ratio of their average kinetic energy per molecule respectively will be :</p> | [{"identifier": "A", "content": "3 : 2"}, {"identifier": "B", "content": "9 : 4"}, {"identifier": "C", "content": "2 : 3"}, {"identifier": "D", "content": "1 : 1"}] | ["D"] | null | <p>$$K{E_{avg}} = {3 \over 2}kT$$ (At lower temperature)</p>
<p>As temperature is same for both the gases.</p>
<p>$$\Rightarrow$$ Both gases will have same average kinetic energy.</p>
<p>$$ \Rightarrow {{{{(K{E_{avg}})}_{\arg on}}} \over {{{(K{E_{avg}})}_{oxygen}}}} = {1 \over 1}$$</p> | mcq | jee-main-2022-online-26th-june-evening-shift | 11,390 |
1l59q74cs | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>When a gas filled in a closed vessel is heated by raising the temperature by 1$$^\circ$$C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.</p> | [] | null | 250 | <p>$$PV = nRT$$</p>
<p>So $${{dP} \over P} \times 100 = {{dT} \over T} \times 100$$</p>
<p>$$0.4 = {1 \over T} \times 100$$</p>
<p>$$ \Rightarrow T = 250\,K$$</p> | integer | jee-main-2022-online-25th-june-evening-shift | 11,391 |
1l5akciog | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The relation between root mean square speed (v<sub>rms</sub>) and most probable sped (v<sub>p</sub>) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :</p> | [{"identifier": "A", "content": "$${v_{rms}} = \\sqrt {{2 \\over 3}} {v_p}$$"}, {"identifier": "B", "content": "$${v_{rms}} = \\sqrt {{3 \\over 2}} {v_p}$$"}, {"identifier": "C", "content": "$${v_{rms}} = {v_p}$$"}, {"identifier": "D", "content": "$${v_{rms}} = \\sqrt {{1 \\over 3}} {v_p}$$"}] | ["B"] | null | <p>$${v_{rms}} = \sqrt {{{3RT} \over M}} $$</p>
<p>$${v_p} = \sqrt {{{2RT} \over M}} $$</p>
<p>$$ \Rightarrow {v_{rms}} = \sqrt {{3 \over 2}} {v_p}$$</p> | mcq | jee-main-2022-online-25th-june-morning-shift | 11,392 |
1l5bco4rh | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>A monoatomic gas performs a work of $${Q \over {4}}$$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R during this transformation. Where R is the gas constant.</p> | [] | null | 2 | <p>By 1<sup>st</sup> law,</p>
<p>$$\Delta U = \Delta Q - {{\Delta Q} \over 4} = {3 \over 4}\Delta Q$$</p>
<p>$$ \Rightarrow n{C_v}\Delta T = {3 \over 4}nC\Delta T$$</p>
<p>$$ \Rightarrow C = {{4{C_v}} \over 3} = 2R$$</p> | integer | jee-main-2022-online-24th-june-evening-shift | 11,393 |
1l5c4eol6 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127$$^\circ$$C. Th amount of heat required to double the speed of its molecules is ____________ k cal.</p>
<p>Take R = 2 cal mole<sup>$$-$$1</sup> K<sup>$$-$$1</sup>)</p> | [] | null | 12 | <p>Because the vessel is closed, it will be an isochoric process.</p>
<p>To double the speed, temperature must be 4 times (v $$\alpha$$$$\sqrt{T}$$)</p>
<p>So, T<sub>f</sub> = 1600 K, T<sub>i</sub> = 400 K</p>
<p>number of moles are $${{56} \over {28}} = 2$$</p>
<p>so Q = nCv $$\Delta$$T = 2 $$\times$$ $${5 \over 2}$$ ... | integer | jee-main-2022-online-24th-june-morning-shift | 11,394 |
1l5w2ab6v | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is :</p>
<p>(Given 0$$^\circ$$C = 273 K)</p> | [{"identifier": "A", "content": "300 K"}, {"identifier": "B", "content": "400 K"}, {"identifier": "C", "content": "600 K"}, {"identifier": "D", "content": "491 K"}] | ["D"] | null | <p>Here volume is constant.</p>
<p>$$\therefore$$ $${{{P_1}} \over {{T_1}}} = {{{P_2}} \over {{T_2}}}$$</p>
<p>$$ \Rightarrow {{100} \over {273}} = {{180} \over {{T_2}}}$$</p>
<p>$$ \Rightarrow {T_2} = {{180} \over {100}} \times 273$$</p>
<p>$$ = 1.8 \times 273$$</p>
<p>$$ = 491\,K$$</p> | mcq | jee-main-2022-online-30th-june-morning-shift | 11,395 |
1l6dy94rt | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>Following statements are given :</p>
<p>(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.</p>
<p>(B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.</p>
<p>(C) The average kinetic energy of a gas molecule decreases wi... | [{"identifier": "A", "content": "(A) and (D) only"}, {"identifier": "B", "content": "(A), (B) and (D) only"}, {"identifier": "C", "content": "(B) and (D) only"}, {"identifier": "D", "content": "(A), (B) and (E) only"}] | [] | null | <p>Because KE $$\propto$$ T so A is correct, B is incorrect, statement C cannot be said, statement D is contradicting itself, statement E is incorrect (Isothermal process)</p>
<p>So no answer correct (Bonus)</p>
<p>If the statement of D would have been.</p>
<p>"Pressure of gas increases with increase in temperature at ... | mcq | jee-main-2022-online-25th-july-morning-shift | 11,396 |
1l6gmsotu | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $$40 \mathrm{~K}$$ at constant pressure. The increase in the internal energy of the gas in this process is :</p>
<p>(Given $$\mathrm{R}=8.3 \,\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$ )</p> | [{"identifier": "A", "content": "5810 J"}, {"identifier": "B", "content": "3486 J"}, {"identifier": "C", "content": "11620 J"}, {"identifier": "D", "content": "6972 J"}] | ["B"] | null | <p>$$\Delta U = n{C_v}\Delta T$$</p>
<p>$$ = 7 \times {{3R} \over 2} \times 40$$</p>
<p>$$ = 3486\,J$$</p> | mcq | jee-main-2022-online-26th-july-morning-shift | 11,398 |
1l6jhlhju | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $$1: 4$$, then</p>
<p>A. The r.m.s. velocity of gas molecules in two vessels will be the same.</p>
<p>B. The ratio of pressure in these vessels will be $$1: 4$$.</p>
<p>C. The ratio of pressure wi... | [{"identifier": "A", "content": "A and C only"}, {"identifier": "B", "content": "B and D only"}, {"identifier": "C", "content": "A and B only"}, {"identifier": "D", "content": "C and D only"}] | ["C"] | null | <p>$${v_{rms}} = \sqrt {{{3RT} \over {{M_0}}}} $$ because T is same</p>
<p>v<sub>rms</sub> will be same so, A is correct D is incorrect</p>
<p>$${{{P_1}} \over {{P_2}}} = {{{n_1}R{T_1}/{V_1}} \over {{n_2}R{T_2}/{V_2}}} = {{{n_1}} \over {{n_2}}} = {1 \over 4}$$</p>
<p>B is correct</p>
<p>C is incorrect</p> | mcq | jee-main-2022-online-27th-july-morning-shift | 11,399 |
1l6m9z6gc | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>Given below are two statements :</p>
<p>Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.</p>
<p>Statement II : The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed wi... | [{"identifier": "A", "content": "Both Statement I and Statement II are true"}, {"identifier": "B", "content": "Both Statement I and Statement II are false"}, {"identifier": "C", "content": "Statement I is true but Statement II is false"}, {"identifier": "D", "content": "Statement I is false but Statement II is true"}] | ["D"] | null | <p>Average momentum $$ = \left\langle {\overrightarrow P } \right\rangle = 0$$</p>
<p>$${v_{rms}} = \sqrt {{{3RT} \over M}} $$</p>
<p>If temperature is doubled and oxygen atoms are used then</p>
<p>$$v{'_{rms}} = \sqrt {{{3R(2T)} \over {M/2}}} = 4\,{v_{rms}}$$</p> | mcq | jee-main-2022-online-28th-july-morning-shift | 11,400 |
1l6nri3bg | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>A vessel contains $$14 \mathrm{~g}$$ of nitrogen gas at a temperature of $$27^{\circ} \mathrm{C}$$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :</p>
<p>Take $$\mathrm{R}=8.32 \mathrm{~J} \mathrm{~mol}^{-1} \,\mathrm{k}^{-1}$$.</p> | [{"identifier": "A", "content": "2229 J"}, {"identifier": "B", "content": "5616 J"}, {"identifier": "C", "content": "9360 J"}, {"identifier": "D", "content": "13,104 J"}] | ["C"] | null | <p>n = 0.5</p>
<p>T = 300</p>
<p>For v<sub>rms</sub> to be doubled T' = 4 $$\times$$ 300 = 1200</p>
<p>$$\Rightarrow$$ Heat transferred</p>
<p>$$ = (0.5)\left( {{5 \over 2}} \right)(8.32)(900)$$</p>
<p>$$ = 9360$$ J</p> | mcq | jee-main-2022-online-28th-july-evening-shift | 11,401 |
1l6rhrrge | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The root mean square speed of smoke particles of mass $$5 \times 10^{-17} \mathrm{~kg}$$ in their Brownian motion in air at NTP is approximately. [Given $$\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$$]</p> | [{"identifier": "A", "content": "$$60 \\mathrm{~mm} \\mathrm{~s}^{-1}$$"}, {"identifier": "B", "content": "$$12 \\mathrm{~mm} \\mathrm{~s}^{-1}$$"}, {"identifier": "C", "content": "$$15 \\mathrm{~mm} \\mathrm{~s}^{-1}$$"}, {"identifier": "D", "content": "$$36 \\mathrm{~mm} \\mathrm{~s}^{-1}$$"}] | ["C"] | null | At NTP, $T=298 \mathrm{~K}$
<br/><br/>$$
\begin{aligned}
v_{\mathrm{rms}} &=\sqrt{\frac{3 R T}{M}} \\
&=\sqrt{\frac{3 k N_{A} \times 298}{5 \times 10^{-17} \times N_{A}}}
\end{aligned}
$$
<br/><br/>$\simeq 15 \mathrm{~mm} / \mathrm{s}$ | mcq | jee-main-2022-online-29th-july-evening-shift | 11,402 |
1ldnxuc96 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.</p>
<p><img src="data:image/png;base64,UklGRpYOAABXRUJQVlA4IIoOAABQowCdASoAA10BP4G+1mW2LywpoRPp8sAwCWlu/HyY/etQ2/1o/YD1n/N/5DaOb4/y+2P4B/Hn3/0rfdvMO8y+k5KR603njrTH/93/Aku8... | [{"identifier": "A", "content": "$$-273^{\\circ} \\mathrm{C}$$"}, {"identifier": "B", "content": "$$-373^{\\circ} \\mathrm{C}$$"}, {"identifier": "C", "content": "$$-100^{\\circ} \\mathrm{C}$$"}, {"identifier": "D", "content": "$$-40^{\\circ} \\mathrm{C}$$"}] | ["A"] | null |
<p>In thermodynamics, the pressure-temperature graph for an ideal gas kept at constant volume (isochoric process) is a straight line. This is because for an ideal gas, the pressure is proportional to the temperature (as described by the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number... | mcq | jee-main-2023-online-1st-february-evening-shift | 11,403 |
1ldogfhjn | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>$$\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the temperature and $$a, b, R$$ are the constants. The physical quantity, which has dimensional formula as that of $$\frac{b^{2}}{a}$$, will be:</p> | [{"identifier": "A", "content": "Energy density"}, {"identifier": "B", "content": "Bulk modulus"}, {"identifier": "C", "content": "Modulus of rigidity"}, {"identifier": "D", "content": "Compressibility"}] | ["D"] | null | $[a]=\left[\mathrm{ML}^{5} \mathrm{~T}^{-2}\right]$
<br/><br/>$$
\begin{aligned}
& {[b]=\left[\mathrm{L}^{3}\right] } \\\\
& {\left[\frac{b^{2}}{a}\right]=\left[\frac{\mathrm{L}^{6}}{\mathrm{ML}^{5} \mathrm{~T}^{2}}\right] }=\left[\mathrm{M}^{-1} \mathrm{LT}^{-2}\right] \\\\
&=[\text { Compressibility] }
\end{aligned}... | mcq | jee-main-2023-online-1st-february-morning-shift | 11,404 |
1ldogglba | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The average kinetic energy of a molecule of the gas is</p> | [{"identifier": "A", "content": "proportional to volume"}, {"identifier": "B", "content": "dependent on the nature of the gas"}, {"identifier": "C", "content": "proportional to absolute temperature"}, {"identifier": "D", "content": "proportional to pressure"}] | ["C"] | null | Average kinetic energy of a molecule of gas
<br/><br/>$$
=\frac{f}{2} k_{B} T
$$
<br/><br/>f is degree of freedom. | mcq | jee-main-2023-online-1st-february-morning-shift | 11,405 |
1ldpmjfey | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The correct relation between $$\gamma = {{{c_p}} \over {{c_v}}}$$ and temperature T is :</p> | [{"identifier": "A", "content": "$$\\gamma \\propto T$$"}, {"identifier": "B", "content": "$$\\gamma \\propto {1 \\over {\\sqrt T }}$$"}, {"identifier": "C", "content": "$$\\gamma \\propto {1 \\over T}$$"}, {"identifier": "D", "content": "$$\\gamma \\propto T^\\circ $$"}] | ["D"] | null | $\gamma=\frac{C_{P}}{C_{V}}$
<br/><br/>At low temperature $(T), \gamma$ is independent of $T$. | mcq | jee-main-2023-online-31st-january-morning-shift | 11,406 |
ldqvp4sz | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A flask contains hydrogen and oxygen in the ratio of $2: 1$ by mass at temperature $27^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is: | [{"identifier": "A", "content": "1 : 1"}, {"identifier": "B", "content": "4 : 1"}, {"identifier": "C", "content": "1 : 4"}, {"identifier": "D", "content": "2 : 1"}] | ["A"] | null | <p>K.E. per molecule $$ = \left( {{f \over 2}KT} \right)$$</p>
<p>$${{\mathrm{average{{(K.E)}_{hydrogen}}}} \over {\mathrm{average{{(K.E)}_{oxygen}}}}} = {{{f_{\mathrm{hydrogen}}}} \over {{f_{\mathrm{oxygen}}}}} = 1$$</p> | mcq | jee-main-2023-online-30th-january-evening-shift | 11,407 |
1ldr10ozk | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The pressure $$(\mathrm{P})$$ and temperature ($$\mathrm{T})$$ relationship of an ideal gas obeys the equation
$$\mathrm{PT}^{2}=$$ constant. The volume expansion coefficient of the gas will be :</p> | [{"identifier": "A", "content": "$$3 T^{2}$$"}, {"identifier": "B", "content": "$$\\frac{3}{T^2}$$"}, {"identifier": "C", "content": "$$\\frac{3}{T^3}$$"}, {"identifier": "D", "content": "$$\\frac{3}{T}$$"}] | ["D"] | null | <p>$$PT^2$$ = constant</p>
<p>From $$PV = nRT \Rightarrow {{{T^3}} \over V} = $$ constant</p>
<p>$${T^3} \propto V$$ ..... (1)</p>
<p>$$3{T^2}dT \propto dV$$ ..... (2)</p>
<p>From (1) and (2)</p>
<p>$${{3dT} \over T} = {{dV} \over V}$$</p>
<p>$$\therefore$$ $$\gamma = {1 \over V}{{dV} \over {dT}} = {3 \over T}$$</p> | mcq | jee-main-2023-online-30th-january-morning-shift | 11,408 |
1ldsb4on3 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>At 300 K, the rms speed of oxygen molecules is $$\sqrt {{{\alpha + 5} \over \alpha }} $$ times to that of its average speed in the gas. Then, the value of $$\alpha$$ will be</p>
<p>(used $$\pi = {{22} \over 7}$$)</p> | [{"identifier": "A", "content": "27"}, {"identifier": "B", "content": "28"}, {"identifier": "C", "content": "24"}, {"identifier": "D", "content": "32"}] | ["B"] | null | <p>$${v_{rms}} = \sqrt {{{\alpha + 5} \over \alpha }} {v_{avg}}$$</p>
<p>$$\sqrt {{{3RT} \over m}} = \sqrt {{{\alpha + 5} \over 5}} \sqrt {{{8RT} \over {\pi m}}} $$</p>
<p>$${{3 \times \pi } \over 8} = {{\alpha + 5} \over \alpha }$$</p>
<p>$${{33} \over {28}} = {{\alpha + 5} \over \alpha }$$</p>
<p>$$\alpha = 28$... | mcq | jee-main-2023-online-29th-january-evening-shift | 11,409 |
1ldugujbl | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The root mean square velocity of molecules of gas is</p> | [{"identifier": "A", "content": "Proportional to temperature ($$T$$)"}, {"identifier": "B", "content": "Inversely proportional to square root of temperature $$\\left( {\\sqrt {{1 \\over T}} } \\right)$$"}, {"identifier": "C", "content": "Proportional to square of temperature ($$T^2$$)"}, {"identifier": "D", "content": ... | ["D"] | null | The rms speed of a gas molecule is<br/><br/>
$$
\mathrm{V}_{\mathrm{RMS}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}
$$<br/><br/>
$\mathrm{V}_{\mathrm{RMS}} \propto \sqrt{\mathrm{T}}$ | mcq | jee-main-2023-online-25th-january-morning-shift | 11,410 |
lgnytfbn | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | A flask contains Hydrogen and Argon in the ratio $2: 1$ by mass. The temperature of the mixture is $30^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of the two gases ( $\mathrm{K}$ argon/K hydrogen) is :
<br/><br/>
(Given: Atomic Weight of $\mathrm{Ar}=39.9$ )
| [{"identifier": "A", "content": "$\\frac{39.9}{2}$"}, {"identifier": "B", "content": "2"}, {"identifier": "C", "content": "39.9"}, {"identifier": "D", "content": "1"}] | ["D"] | null | The average kinetic energy per molecule of a gas is given by the expression $\frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the temperature of the gas in kelvins. Since the temperature of the mixture is given in Celsius, we need to convert it to kelvins by adding 273.15 to get $303.15$ K.
<br/><br/>
Let... | mcq | jee-main-2023-online-15th-april-morning-shift | 11,412 |
1lgozkn8g | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The initial pressure and volume of an ideal gas are P$$_0$$ and V$$_0$$. The final pressure of the gas when the gas is suddenly compressed to volume $$\frac{V_0}{4}$$ will be :</p>
<p>(Given $$\gamma$$ = ratio of specific heats at constant pressure and at constant volume)</p> | [{"identifier": "A", "content": "P$$_0$$(4)$$^{\\frac{1}{\\gamma}}$$"}, {"identifier": "B", "content": "P$$_0$$"}, {"identifier": "C", "content": "4P$$_0$$"}, {"identifier": "D", "content": "P$$_0$$(4)$$^{\\gamma}$$"}] | ["D"] | null | When the gas is compressed suddenly, it undergoes an adiabatic process where no heat is exchanged with the surroundings.<br/><br/> Therefore, we can use the adiabatic equation of state to relate the initial and final pressure and volume of the gas: $$P_0V_0^\gamma=P_fV_f^\gamma$$ where $$P_f$$ and $$V_f$$ are the final... | mcq | jee-main-2023-online-13th-april-evening-shift | 11,413 |
1lgvrb5w2 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,</p> | [{"identifier": "A", "content": "4RT"}, {"identifier": "B", "content": "16RT"}, {"identifier": "C", "content": "8RT"}, {"identifier": "D", "content": "11RT"}] | ["D"] | null | <p>The internal energy (U) of a gas depends on its degrees of freedom (f). <br/><br/>For a monatomic gas like neon, the degrees of freedom are f = 3 (translational). For a diatomic gas like oxygen, the degrees of freedom are f = 5 (3 translational + 2 rotational).</p>
<p>The internal energy for each component of the ga... | mcq | jee-main-2023-online-10th-april-evening-shift | 11,416 |
1lh25jt13 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The number of air molecules per cm$$^3$$ increased from $$3\times10^{19}$$ to $$12\times10^{19}$$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:</p> | [{"identifier": "A", "content": "1.25"}, {"identifier": "B", "content": "0.25"}, {"identifier": "C", "content": "0.50"}, {"identifier": "D", "content": "0.75"}] | ["B"] | null | 1. The collision frequency (f) is given by the formula :
<br/><br/>$$ f = \sqrt{2} \pi d^2 v n_v $$
<br/><br/> Where:
<br/><br/>- $d$ is the diameter of the molecule,
<br/><br/>- $v$ is the average velocity of the molecules, and
<br/><br/>- $n_v$ is the number density (number of molecules per unit ... | mcq | jee-main-2023-online-6th-april-morning-shift | 11,418 |
1lh2zqgi8 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The temperature of an ideal gas is increased from $$200 \mathrm{~K}$$ to $$800 \mathrm{~K}$$. If r.m.s. speed of gas at $$200 \mathrm{~K}$$ is $$v_{0}$$. Then, r.m.s. speed of the gas at $$800 \mathrm{~K}$$ will be:</p> | [{"identifier": "A", "content": "$$v_{0}$$"}, {"identifier": "B", "content": "$$2 v_{0}$$"}, {"identifier": "C", "content": "$$4 v_{0}$$"}, {"identifier": "D", "content": "$$\\frac{v_{0}}{4}$$"}] | ["B"] | null | <p>The root-mean-square (r.m.s) speed of an ideal gas is given by the formula:</p>
<p>$$v_\mathrm{rms} = \sqrt{\frac{3RT}{M}}$$</p>
<p>where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.</p>
<p>In this case, we are given that the initial temperature is $$200 \, K$$ and the f... | mcq | jee-main-2023-online-6th-april-evening-shift | 11,419 |
1lh30nbav | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:</p> | [{"identifier": "A", "content": "$$1: 1$$"}, {"identifier": "B", "content": "$$1: 2$$"}, {"identifier": "C", "content": "$$1: 4$$"}, {"identifier": "D", "content": "$$4: 1$$"}] | ["D"] | null | <p>The speed of sound in a gas is given by the formula:</p>
<p>$$v = \sqrt{\frac{\gamma RT}{M}}$$</p>
<p>where $$v$$ is the speed of sound, $$\gamma$$ is the adiabatic index, $$R$$ is the universal gas constant, $$T$$ is the temperature, and $$M$$ is the molar mass of the gas.</p>
<p>For diatomic gases, such as hydroge... | mcq | jee-main-2023-online-6th-april-evening-shift | 11,420 |
lsan06k0 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2 \mathrm{~km} / \mathrm{s}$, the root mean square velocity of oxygen at the same condition in $\mathrm{km} / \mathrm{s}$ is : | [{"identifier": "A", "content": "1.0"}, {"identifier": "B", "content": "1.5"}, {"identifier": "C", "content": "2.0"}, {"identifier": "D", "content": "0.5"}] | ["D"] | null | <p>Here is your text with LaTeX notation and paragraph tags converted as requested:</p>
<p>To calculate the root mean square (rms) velocity of gas molecules, we can use the formula:</p>
<p>$$ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} $$</p>
<p>where:</p>
<ul>
<li>$$ v_{\text{rms}} $$ is the root mean square velocity of the... | mcq | jee-main-2024-online-1st-february-evening-shift | 11,421 |
jaoe38c1lscpgjpr | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The equation of state of a real gas is given by $$\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$$, where $$\mathrm{P}, \mathrm{V}$$ and $$\mathrm{T}$$ are pressure, volume and temperature respectively and $$\mathrm{R}$$ is the universal gas constant. The dimensions of $$\... | [{"identifier": "A", "content": "P"}, {"identifier": "B", "content": "RT"}, {"identifier": "C", "content": "PV"}, {"identifier": "D", "content": "R"}] | ["A"] | null | <p>$$\begin{aligned}
& {[\mathrm{P}]=\left[\frac{\mathrm{a}}{\mathrm{V}^2}\right] \Rightarrow[\mathrm{a}]=\left[\mathrm{PV}^2\right]} \\
& \text { And }[\mathrm{V}]=[\mathrm{b}] \\
& \frac{[\mathrm{a}]}{\left[\mathrm{b}^2\right]}=\frac{\left[\mathrm{PV}^2\right]}{\left[\mathrm{V}^2\right]}=[\mathrm{P}]
\end{aligned}$$<... | mcq | jee-main-2024-online-27th-january-evening-shift | 11,423 |
jaoe38c1lscpmq3f | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The total kinetic energy of 1 mole of oxygen at $$27^{\circ} \mathrm{C}$$ is :
[Use universal gas constant $$(R)=8.31 \mathrm{~J} /$$ mole K]</p> | [{"identifier": "A", "content": "6232.5 J"}, {"identifier": "B", "content": "5670.5 J"}, {"identifier": "C", "content": "6845.5 J"}, {"identifier": "D", "content": "5942.0 J"}] | ["A"] | null | <p>The total kinetic energy of a mole of an ideal gas can be determined by using the equipartition theorem, which states that the energy is equally distributed among degrees of freedom. For a diatomic molecule such as oxygen ($$O_2$$), there are 5 degrees of freedom (3 translational and 2 rotational - assuming the vibr... | mcq | jee-main-2024-online-27th-january-evening-shift | 11,424 |
jaoe38c1lsd5uul8 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The speed of sound in oxygen at S.T.P. will be approximately: (given, $$R=8.3 \mathrm{~JK}^{-1}, \gamma=1.4$$)</p> | [{"identifier": "A", "content": "341 m/s"}, {"identifier": "B", "content": "333 m/s"}, {"identifier": "C", "content": "325 m/s"}, {"identifier": "D", "content": "315 m/s"}] | ["D"] | null | <p>The speed of sound in a gas at standard temperature and pressure (STP) can be calculated using the following formula derived from the ideal gas law and the speed of sound relation in a gas:</p>
<p>$$ v = \sqrt{\gamma \frac{R T}{M}} $$</p>
<p>Where:</p>
<ul>
<li>$$ v $$ = speed of sound in the gas</li>
<li>$$ \gamm... | mcq | jee-main-2024-online-31st-january-evening-shift | 11,425 |
jaoe38c1lse68uaj | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>The parameter that remains the same for molecules of all gases at a given temperature is :</p> | [{"identifier": "A", "content": "kinetic energy\n"}, {"identifier": "B", "content": "mass\n"}, {"identifier": "C", "content": "momentum\n"}, {"identifier": "D", "content": "speed"}] | ["A"] | null | <p>$$\mathrm{KE}=\frac{\mathrm{f}}{2} \mathrm{kT}$$</p> | mcq | jee-main-2024-online-31st-january-morning-shift | 11,426 |
1lsgdgm07 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $$47^{\circ} \mathrm{C}$$ ?</p> | [{"identifier": "A", "content": "20 K"}, {"identifier": "B", "content": "80 K"}, {"identifier": "C", "content": "4 K"}, {"identifier": "D", "content": "$$-73$$ K"}] | ["A"] | null | <p>$$\begin{aligned}
& \sqrt{\frac{3 R T}{2}}=\sqrt{\frac{3 R(320)}{32}} \\
& T=\frac{320}{16}=20 \mathrm{~K}
\end{aligned}$$</p> | mcq | jee-main-2024-online-30th-january-morning-shift | 11,429 |
lv0vyue8 | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>P-T diagram of an ideal gas having three different densities $$\rho_1, \rho_2, \rho_3$$ (in three different cases) is shown in the figure. Which of the following is correct :</p>
<p><img src="data:image/png;base64,UklGRvwPAABXRUJQVlA4IPAPAAAwCAGdASoAA94CP4HA22W2MLsnIbLpG2AwCWlu+/y5FlJNCB4T8PqD/Yf3z2g9LPO/WGFnO2fz39E... | [{"identifier": "A", "content": "$$\\rho_1>\\rho_2$$\n"}, {"identifier": "B", "content": "$$\\rho_2<\\rho_3$$\n"}, {"identifier": "C", "content": "$$\\rho_1=\\rho_2=\\rho_3$$\n"}, {"identifier": "D", "content": "$$\\rho_1<\\rho_2$$"}] | ["A"] | null | <p>$$\begin{aligned}
& P M=\rho R T \\
& \Rightarrow \frac{P}{T}=\left(\frac{R}{m}\right) \rho=\text { slope }
\end{aligned}$$</p>
<p>So from given curve, $$\rho_1>\rho_2>\rho_3$$</p> | mcq | jee-main-2024-online-4th-april-morning-shift | 11,431 |
lv3veaso | physics | heat-and-thermodynamics | kinetic-theory-of-gases-and-gas-laws | <p>Given below are two statements :</p>
<p>Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.</p>
<p>Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.</p>
<p>In the light of the above statements, ... | [{"identifier": "A", "content": "Statement I is false but Statement II is true\n"}, {"identifier": "B", "content": "Both Statement I and Statement II are true\n"}, {"identifier": "C", "content": "Statement I is true but Statement II is false\n"}, {"identifier": "D", "content": "Both Statement I and Statement II are fal... | ["B"] | null | <p>Let's analyze the given statements one by one in detail:</p>
<p><b>Statement (I): The mean free path of gas molecules is inversely proportional to the square of molecular diameter.</b></p>
<p>The mean free path ($ \lambda $) of gas molecules is the average distance a molecule travels before colliding with another ... | mcq | jee-main-2024-online-8th-april-evening-shift | 11,432 |
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