# Solved papers for JEE Main & Advanced Physics Kinetic Theory of Gases JEE PYQ-Kinetic Theory Of Gases

### done JEE PYQ-Kinetic Theory Of Gases Total Questions - 41

• question_answer1) Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will                                                                                                                                                 [AIEEE 2002]

A)
increase

B)
decrease

C)
remain same

D)
decrease for some while increase for others

• question_answer2) At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at ${{47}^{o}}C$?                                                                                                                        [AIEEE 2002]

A)
80 K

B)
- 73 K

C)
3 K

D)
20 K

• question_answer3) 1 mole of a gas with $\gamma =7/5$ is mixed with 1 mole of a gas with $\gamma =5/3$ , then the value of $\gamma$ for the resulting mixture is                                                                             [AIEEE 2002]

A)
$7/5$

B)
$2/5$

C)
$24/16$

D)
$12/7$

• question_answer4) Which of the following parameters does not characterise the thermodynamic state of matter?    [AIEEE 2003]

A)
Temperature

B)
Pressure

C)
Work

D)
Volume

• question_answer5) 5. One mole of ideal monatomic gas$(\gamma =5/3)$is mixed with one mole of diatomic gas$(\gamma =7/5)$What is$\gamma$for the mixture? y denotes the ratio of specific heat at constant pressure, to that at constant volume                           [AIEEE 2004]

A)
3/2

B)
23/15

C)
35/23

D)
4/3

• question_answer6) Two thermally insulated vessels 1 and 2 are filled with air at temperatures$({{T}_{1}},{{T}_{2}}),$volumes $({{V}_{1}},{{V}_{2}}),$and pressures$({{p}_{1}},{{p}_{2}}),$respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be                                           [AIEEE 2004]

A)
${{T}_{1}}+{{T}_{2}}$

B)
$\frac{({{T}_{1}}+{{T}_{2}})}{2}$

C)
$\frac{{{T}_{1}}{{T}_{2}}({{p}_{1}}{{V}_{1}}+{{p}_{2}}{{V}_{2}})}{{{p}_{1}}{{V}_{1}}{{T}_{2}}+{{p}_{2}}{{V}_{2}}{{T}_{1}}}$

D)
$\frac{{{T}_{1}}{{T}_{2}}({{p}_{1}}{{V}_{1}}+{{p}_{2}}{{V}_{2}})}{{{p}_{1}}{{V}_{1}}{{T}_{1}}+{{p}_{2}}{{V}_{2}}{{T}_{2}}}$

• question_answer7) An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${{V}_{1}}$ and contains ideal gas at pressure ${{P}_{1}}$ and temperature ${{T}_{1}}$. The other chamber has volume ${{V}_{2}}$ and contains ideal gas at pressure ${{P}_{2}}$ and temperature ${{T}_{2}}$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be         [AIEEE 2008]

A)
$\frac{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}$

B)
$\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}$

C)
$\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}$

D)
$\frac{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}$

• question_answer8)  One kg of a diatomic gas is at a pressure of $8\times {{10}^{4}}N/{{m}^{2}}.$ The density of the gas is$4\text{ }kg/{{m}^{3}}$. What is the energy of the gas due to its thermal motion? [AIEEE 2009]

A)
$3\times {{10}^{4}}J$

B)
$5\times {{10}^{4}}J$

C)
$6\times {{10}^{4}}J$

D)
$7\times {{10}^{4}}J.$

• question_answer9)  Direction - This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. A perfect gas at 27°C is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to                                                                                                         [JEE ONLINE 07-05-2012]

A)
327°C

B)
200°C

C)
54°C

D)
300°C

• question_answer10)  A thin tube sealed at both is 100 cm long. It lies horizontally, the middle 20 cm contacting mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced?                                                       [JEE ONLINE 23-04-2013] (Given: cross section of the tube can be assumed to be uniform)

A)
2.95 cm

B)
5.18 cm

C)
8.65 cm

D)
0.0 cm

• question_answer11)  The plot given below is the average power delivered to an LRC circuit versus frequency. The quality factor of the circuit is:                                                       [JEE ONLINE 23-04-2013]

A)
5.0

B)
2.0

C)
2.5

D)
0.4

• question_answer12)    This question has statement -1 and statement -2. Of the four choices given after the Statements, choose the one that best describes the two Statements.                                                             [JEE ONLINE 23-04-2013] Statement-1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume. Statement 1: A perfect gas is heated keeping pressure constant pressure is lower than that at constant volume.

A)
Statement-1 is true, Statement-2 is true, and Statement 2 is the count explanation of Statement 1.

B)
Statement -1 is true, Statement-2 is false.

C)
Statement 1 is true, Statement 2 is true but Statement 2 is not the correct explanation of Statement 1.

D)
Statement -1 is false, Statement -2 is true.

• question_answer13) Modern vacuum pumps can evacuate a vessel down to a pressure of $4.0\times {{10}^{-15}}$atm. at room temperature (300 K). Taking $\text{R=8}\text{.0J}{{\text{K}}^{\text{-1}}}\text{mol}{{\text{e}}^{\text{-1}}}\text{,1atm=1}{{\text{0}}^{\text{5}}}\text{Pa}$ and${{\text{N}}_{\text{Avogadro}}}=6\times {{10}^{23}}\text{mol}{{\text{e}}^{-1}},$the mean distance between molecules of gas in an evacuated vessel will be of the order of:                                                   [JEE ONLINE 09-04-2014]

A)
0.2 mm

B)
0.2 mm

C)
0.2 cm

D)
0.2 nm

• question_answer14) At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 $\text{m}{{\text{s}}^{\text{-1}}}$. The gas is: [JEE ONLINE 12-04-2014]

A)
${{H}_{2}}$

B)
$C{{l}_{2}}$

C)
${{O}_{2}}$

D)
${{F}_{2}}$

• question_answer15) A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to 0°C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (${{k}_{B}}$ is Boltzmann constant).                                          [JEE ONLINE 19-04-2014]

A)
0

B)
$\frac{273{{k}_{B}}}{2Mg}$

C)
$\frac{546{{k}_{B}}}{3Mg}$

D)
$\frac{819{{k}_{B}}}{2Mg}$

• question_answer16) 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 : $\left( \gamma =\frac{{{C}_{p}}}{{{C}_{v}}} \right)$                                      [JEE MAIN 2015]

A)
$\frac{\gamma +1}{2}$

B)
$\frac{\gamma -1}{2}$

C)
$\frac{3\gamma +5}{6}$

D)
$\frac{3\gamma -5}{6}$

• question_answer17) In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as ${{T}^{q}}.$ A good estimate for q is:                                                   [JEE ONLINE 10-04-2015]

A)
1

B)
$\frac{1}{4}$

C)
$\frac{1}{2}$

D)
2

• question_answer18)             Using equipartition of energy, the specific heat $(in\text{ }J\text{ }k{{g}^{-1}}{{K}^{-}}^{1})$ of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27)          [JEE MAIN 11-04-2015]

A)
25

B)
410

C)
925

D)
1850

• question_answer19) Which of the following shown the correct relationship between the pressure 'P' and density $\rho$ of an ideal gas at constant temperature?                                                                               [JEE ONLINE 10-04-2016]

A)

B)

C)

D)

• question_answer20) The temperature of an open room of volume $30{{m}^{3}}$increases from $17{{\,}^{o}}C$to$27{{\,}^{o}}C$ due to sunshine. The atmospheric pressure in the room remains $1\times {{10}^{5}}\,Pa.$ If ${{n}_{i}}$and ${{n}_{f}}$ are the number of molecules in the room before and after heating, then ${{n}_{f}}-{{n}_{i}}$will be:-[JEE Main 2017]

A)
$2.5\times {{10}^{25}}$

B)
$-2.5\times {{10}^{25}}$

C)
$-1.61\times {{10}^{23}}$

D)
$1.38\times {{10}^{23}}$

• question_answer21) ${{C}_{p}}$ and ${{C}_{v}}$ are specific heats at constant pressure and constant volume respectively. It is observed that ${{C}_{p}}-{{C}_{v}}=a$ for hydrogen gas ${{C}_{p}}-{{C}_{v}}=b$for nitrogen gas the correct relation between a and b is:               [JEE Main 2017]

A)
$a=14\,b$

B)
$a=28\,b$

C)
$a=\frac{1}{14}b$

D)
$a=b$

• question_answer22) An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure $({{C}_{P}})$ and at constant volume $({{C}_{V}})$is                                                                       [JEE Online 08-04-2017]

A)
$\frac{7}{5}$

B)
6

C)
$\frac{7}{2}$

D)
$\frac{5}{2}$

• question_answer23)  For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram?    [JEE Online 09-04-2017]

A)

B)

C)

D)

• question_answer24)    The value closest to the thermal velocity of a Helium atom at room temperature $(300K)$ in $m{{s}^{-1}}$ is:           [JEE Online 15-04-2018 (II)] $\left[ {{k}_{B}}=1.4\times {{10}^{-23}}J/K;{{m}_{He}}=7\times {{10}^{-27}}kg \right]$

A)
$1.3\times {{10}^{4}}$

B)
$1.3\times {{10}^{5}}$

C)
$1.3\times {{10}^{2}}$

D)
$1.3\times {{10}^{3}}$

• question_answer25) Two moles of helium are mixed with moles of hydrogen. If$\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{3}{2}$ for the mixture, then the value of n is     [JEE Online 15-04-2018 (II)]

A)
3/2

B)
2

C)
1

D)
3

• question_answer26)    A Mixture of 2 moles of helium gas$\left( atomic\text{ }mass=4u \right)$, and 1 mole of argon gas $\left( atomic\text{ }mass=40u \right)$ is kept at 300 K in a container. The ratio of their rms speeds $\left[ \frac{{{V}_{rms}}\,(helium)}{{{V}_{rms}}\,(argon\,)} \right]$ , is close to:                                    [JEE Main 09-Jan-2019 Morning]

A)
0.32

B)
3.16

C)
2.24

D)
0.45

• question_answer27) The force of interaction between two atoms is given by $F=\alpha \beta \exp \left( \frac{{{x}^{2}}}{\alpha kT} \right);$ where x is the distance, k is the Boltzmann constant and Tis temperature and $\alpha$ and $\beta$are two constants. The dimension of $\beta$ is- [JEE Main 11-Jan-2019 Morning]

A)
${{M}^{2}}{{L}^{2}}{{T}^{-2}}$

B)
${{M}^{0}}{{L}^{2}}{{T}^{-4}}$

C)
$ML{{T}^{-2}}$

D)
${{M}^{2}}L{{T}^{-4}}$

• question_answer28) In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process, the temperature of the gas is increased by $\Delta T$. The amount of heat absorbed by gas is (R is gas constant)-                                      [JEE Main 11-Jan-2019 Evening]

A)
$\frac{2K}{3}\Delta T$

B)
$\frac{1}{2}R\Delta T$

C)
$\frac{3}{2}R\Delta T$

D)
$\frac{1}{2}KR\Delta T$

• question_answer29) An ideal gas occupies a volume of $2{{m}^{3}}$ at a pressure of$3\times {{10}^{6}}Pa$. The energy of the gas is- [JEE Main 12-Jan-2019 Morning]

A)
$9\times {{10}^{6}}J$

B)
$3\times {{10}^{2}}J$

C)
$6\times {{10}^{4}}J$

D)
${{10}^{8}}J$

• question_answer30) An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is $6\times {{10}^{-8}}s.$If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to-                               [JEE Main 12-Jan-2019 Evening]

A)
$4\times {{10}^{-8}}s$

B)
$3\times {{10}^{-6}}s$

C)
$0.5\times {{10}^{-8}}s$

D)
$2\times {{10}^{-7}}s$

• question_answer31) If ${{10}^{22}}$gas molecules each of mass ${{10}^{-26}}kg$ collide with a surface (perpendicular to it) elastically per second over an area $1{{m}^{2}}$with a speed ${{10}^{4}}m/s,$the pressure exerted by the gas molecules will be of the order of : [JEE Main 8-4-2019 Morning]

A)
${{10}^{8}}N/{{m}^{2}}$

B)
${{10}^{4}}N/{{m}^{2}}$

C)
${{10}^{3}}N/{{m}^{2}}$

D)
${{10}^{16}}N/{{m}^{2}}$

• question_answer32)    The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to: [Boltzmann Constant ${{k}_{B}}=1.38\times {{10}^{-23}}J/K$ Avogadro Number ${{N}_{A}}=6.02\times {{10}^{26}}/kg$ Radius of Earth : $6.4\times {{10}^{6}}m$ Gravitational acceleration on Earth$=10m{{s}^{-2}}$     [JEE Main 8-4-2019 Afternoon]

A)
650 K

B)
$3\times {{10}^{5}}K$

C)
${{10}^{4}}$ K

D)
800 K

• question_answer33) An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $\overline{\text{v}},m$is its mass and ${{k}_{B}}$is Boltzmann constant, then its temperature will be : [JEE Main 9-4-2019 Morning]

A)
$\frac{m{{\overline{\text{v}}}^{2}}}{6{{k}_{B}}}$

B)
$\frac{m{{\overline{\text{v}}}^{2}}}{5{{k}_{B}}}$

C)
$\frac{m{{\overline{\text{v}}}^{2}}}{3{{k}_{B}}}$

D)
$\frac{m{{\overline{\text{v}}}^{2}}}{7{{k}_{B}}}$

• question_answer34) For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at $127{}^\circ C.$ At 2 atm pressure and at$~227{}^\circ C,$the rms speed of the molecules will be :                                  [JEE Main 9-4-2019 Morning]

A)
$80\text{ }m/s$

B)
100 5 m/s

C)
$80\sqrt{5}m/s$

D)
$100\text{ }m/s$

• question_answer35) A $25\times {{10}^{-3}}{{m}^{3}}$volume cylinder is filled with 1 mol of ${{O}_{2}}$gas at room temperature (300K). The molecular diameter of ${{O}_{2}}$, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an ${{O}_{2}}$ molecule? [JEE Main 10-4-2019 Morning]

A)
$\tilde{\ }{{10}^{11}}$

B)
$\tilde{\ }{{10}^{13}}$

C)
$\tilde{\ }{{10}^{10}}$

D)
$\tilde{\ }{{10}^{12}}$

• question_answer36) The number density of molecules of a gas depends on their distance r from the origin as, $n(r)={{n}_{0}}{{e}^{-\alpha {{r}^{4}}}}.$Then the total number of molecules is proportional to :         [JEE Main 12-4-2019 Afternoon]

A)
${{n}_{0}}{{\alpha }^{1/4}}$

B)
${{n}_{0}}{{\alpha }^{-3}}$

C)
${{n}_{0}}{{\alpha }^{-3/4}}$

D)
$\sqrt{{{n}_{0}}}{{\alpha }^{1/2}}$

• question_answer37) Two moles of an ideal gas with $\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{4}{3}$. The value of $\frac{{{C}_{P}}}{{{C}_{V}}}$ for the mixture is:                                                                        [JEE MAIN Held on 07-01-2020 Morning]

A)
1.47

B)
1.42

C)
1.50

D)
1.45

• question_answer38) The plot that depicts the behavior of the mean Free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is (Graphs are schematic and not drawn to scale) [JEE MAIN Held On 08-01-2020 Morning]

A)

B)

C)

D)

• question_answer39) 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 ${{C}_{p}}\,/\,{{C}_{v}}$ value will be                                    [JEE MAIN Held on 08-01-2020 Evening]

A)
40/27

B)
19/13

C)
67/45

D)
23/15

• question_answer40) Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass$\frac{m}{4}$. The ratio of the specific heats $\left( C_{V}^{A}\,\,\text{and}\,\,C_{V}^{B} \right)$ of gas A and B, respectively is:                               [JEE MAIN Held on 09-01-2020 Morning]

A)
3 : 5

B)
7 : 9

C)
5 : 7

D)
5 : 9

• question_answer41) 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 ratio of their respective mean free times is closest to [JEE MAIN Held on 09-01-2020 Evening]

A)
1.83

B)
4.67

C)
2.3

D)
None of these