How many questions from Kinetic Theory of Gases appear in JEE?

Kinetic Theory of Gases has appeared in 135 of the last 186 JEE Main and JEE Advanced papers — about 73% of them — contributing 146 questions in total across those papers.

Is Kinetic Theory of Gases an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 73% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Kinetic Theory of Gases questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Kinetic Theory of Gases JEE Previous Year Questions with Answers

Q1·PhysicsSingle correctJEE Main 2026

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ________ kPa.

(A)100
(B)120
(C)90
(D)105

Q2·PhysicsSingle correctJEE Main 2026

If 2 mole of an ideal monoatomic gas at temperature

T

, is mixed with 6 mole of another ideal monoatomic gas at temperature

2T

then the temperature of mixture is :

(A) $\frac{5}{2}T$
(B) $\frac{5}{4}T$
(C) $\frac{7}{2}T$
(D) $\frac{7}{4}T$

Q3·PhysicsSingle correctJEE Main 2026

An ideal gas at pressure P and temperature T is expanding such that PT³ = constant. The coefficient of volume expansion of the gas is ________.

(A) $\dfrac{2}{T}$
(B) $\dfrac{1}{T}$
(C) $\dfrac{4}{T}$
(D) $\dfrac{3}{T}$

Q4·PhysicsSingle correctJEE Main 2026

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If the average kinetic energy of

H_{2}

and

O_{2}

molecules, kept in two different sized containers are same, then their temperatures will be same. Reason R: The r.m.s. speed of

H_{2}

and

O_{2}

molecules are same at same temperature. Choose the correct answer from the options given below

(A)Both A and R are true and R is the correct explanation of A
(B)Both A and R are true but R is NOT the correct explanation of A
(C)A is true but R is false
(D)A is false but R is true

Q5·PhysicsSingle correctJEE Main 2026

One gas of

n_1

mole of molecules at temperature

T_1

, volume

V_1

, and pressure

P_1

, and another gas of

n_2

mole of molecules at temperature

T_2

, volume

V_2

, and pressure

P_2

, are mixed resulting in pressure

P

and volume

V

of the mixture. The temperature of the mixture is _____.

(A) $(T_1 + T_2)/2$
(B) $T_1T_2PV/(T_2P_1V_1 + T_1P_2V_2)$
(C) $(T_2P_1V_1 + T_1P_2V_2)/(T_1T_2PV)$
(D) $|T_1 - T_2|/2$

Q6·PhysicsSingle correctJEE Main 2026

A mixture of carbon dioxide and oxygen has volume 8310 cm

^{3}

, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ______. (Assume both carbon dioxide and oxygen gases behave like ideal gases)

[R = 8.31

J/mol.K

]

(A)0.15 and 0.18
(B)0.25 and 0.08
(C)0.21 and 0.12
(D)0.13 and 0.20

Q7·PhysicsSingle correctJEE Main 2026

The mean free path of a molecule of diameter

5 \times 10^{-10}

m at the temperature 41°C and pressure

1.38 \times 10^{5}

Pa, is given as ____m. (Given

k_{B} = 1.38 \times 10^{-23}

J/K).

(A) $2\sqrt{2} \times 10^{-10}$
(B) $10\sqrt{2} \times 10^{-8}$
(C) $2\sqrt{2} \times 10^{-8}$
(D) $2 \times 10^{-8}$

Q8·PhysicsSingle correctJEE Main 2026

An air bubble of volume 2.9 cm

^{3}

rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17 °C. The volume of the bubble when it reaches the surface, where the water temperature is 27 °C, is____ cm

^{3}

. (g = 10 m/s

^{2}

, density of water =

10^{3}

kg/m

^{3}

, and 1 atm pressure is

10^{5}

Pa)

(A)4.2
(B)2.0
(C)3.0
(D)4.5

Q9·PhysicsSingle correctJEE Main 2026

A cylindrical tube

AB

of length

l

, closed at both ends contains an ideal gas of 1 mol having molecular weight

M

. The tube is rotated in a horizontal plane with constant angular velocity

\omega

about an axis perpendicular to

AB

and passing through the edge at end A, as shown in the figure. If

P_{A}

and

P_{B}

are the pressures at

A

and

B

respectively, then (Consider the temperature is same at all points in the tube)

(A) $P_{B} = P_{A} \exp (M\omega^{2}l^{2} / 2RT)$
(B) $P_{B} = P_{A}$
(C) $P_{B} = P_{A} \exp (M\omega^{2}l^{2} / 3RT)$
(D) $P_{B} = P_{A} \exp (M\omega^{2}l^{2} / RT)$

Q10·PhysicsNumericalJEE Main 2026

An insulated cylinder of volume 60 cm

^3

is filled with a gas at 27°C and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 cm

^3

while allowing the temperature to rise to 77°C. The final pressure is ________ atmospheric pressure.

Q11·PhysicsSingle correctJEE Main 2026

The r.m.s speed of oxygen molecules at

47^\circ

C is equal to that of the hydrogen molecules kept at______

^\circ

C. (Mass of oxygen molecule/mass of hydrogen molecule=32/2)

(A)−235
(B)−100
(C)−253
(D)−20

Q12·PhysicsNumericalJEE Advanced 2025

The left and right compartments of a thermally isolated container of length L are separated by a thermally conducting, movable piston of area A. The left and right compartments are filled with

\frac{3}{2}

and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant k and natural length

\frac{2L}{5}

. In thermodynamic equilibrium, the piston is at a distance

\frac{L}{2}

from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is

P = \frac{kL}{A}\alpha

, then the value of

\alpha

is ____

Q13·PhysicsSingle correctJEE Main 2025

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Given: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

(A)1 : 10
(B)10 : 1
(C) $1:\sqrt{10}$
(D)1 : 1

Q14·PhysicsSingle correctJEE Main 2025

Match the List-I (type of gas) with List-II (ratio of specific heats

\dfrac{C_P}{C_V}

). Choose the correct answer from the options given below:

List-I (Type of gas)	List-II ($C_P/C_V$)
A.Triatomic rigid gas	I. $\dfrac{C_P}{C_V}=\dfrac{5}{3}$
B.Diatomic non-rigid gas	II. $\dfrac{C_P}{C_V}=\dfrac{7}{5}$
C.Monoatomic gas	III. $\dfrac{C_P}{C_V}=\dfrac{4}{3}$
D.Diatomic rigid gas	IV. $\dfrac{C_P}{C_V}=\dfrac{9}{7}$

(A)A-III, B-IV, C-I, D-II
(B)A-III, B-II, C-IV, D-I
(C)A-II, B-IV, C-I, D-III
(D)A-IV, B-II, C-III, D-I

Q15·PhysicsSingle correctJEE Main 2025

There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa):

(A)4.4
(B)6
(C)24
(D)18

Q16·PhysicsSingle correctJEE Main 2025

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are

3\times10^{-7}

m and 600 m/s, respectively. Find the frequency of its collisions.

(A) $2\times10^{10}$ /s
(B) $9\times10^{9}$ /s
(C) $2\times10^{9}$ /s
(D) $5\times10^{9}$ /s

Q17·PhysicsSingle correctJEE Main 2025

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by

1^\circ

C. Its initial temperature must be:

(A) $25^\circ$ C
(B)2500 K
(C)250 K
(D) $250^\circ$ C

Q18·PhysicsIntegerJEE Main 2025

The internal energy of air in a

4\,m\times4\,m\times3\,m

sized room at 1 atmospheric pressure will be ______

\times10^6\,J

. (Consider air as a diatomic molecule)

Q19·PhysicsIntegerJEE Main 2025

\gamma_A

is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom.

\gamma_B

is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If

\dfrac{\gamma_A}{\gamma_B}=\left(1+\dfrac{1}{n}\right)

, then the value of

n

is ______.

Q20·PhysicsIntegerJEE Main 2025

A container of fixed volume contains a gas at

27^\circ

C. To double the pressure of the gas, the temperature of gas should be raised to ______

^\circ

C.

Q21·PhysicsSingle correctJEE Main 2025

The kinetic energy of translation of the molecules in 50 g of CO

_2

gas at

17^\circ

C is:

(A)3986.3 J
(B)4102.8 J
(C)4205.5 J
(D)3582.7 J

Q22·PhysicsSingle correctJEE Main 2025

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q23·PhysicsSingle correctJEE Main 2025

The ratio of vapour densities of two gases at the same temperature is

\frac{4}{25}

, then the ratio of r.m.s. velocities will be:

(A) $\frac{25}{4}$
(B) $\frac{2}{5}$
(C) $\frac{5}{2}$
(D) $\frac{4}{25}$

Q24·PhysicsIntegerJEE Main 2025

The temperature of 1 mole of an ideal monoatomic gas is increased by 50°C at constant pressure. The total heat added and change in internal energy are

E_1

and

E_2

, respectively. If

\dfrac{E_1}{E_2}=\dfrac{x}{9}

then the value of x is _______.

Q25·PhysicsSingle correctJEE Main 2025

For a diatomic gas, if

\gamma_1=\left(\frac{C_p}{C_v}\right)

for rigid molecules and

\gamma_2=\left(\frac{C_p}{C_v}\right)

for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (

C_p

and

C_v

are specific heats of the gas at constant pressure and volume)

(A) $\gamma_2>\gamma_1$
(B) $\gamma_2=\gamma_1$
(C) $2\gamma_2=\gamma_1$
(D) $\gamma_2<\gamma_1$

Q26·PhysicsSingle correctJEE Main 2024

The temperature of a gas is

-78\,^{\circ}

C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2K is:

(A) $-39\,^{\circ}$ C
(B) $117\,^{\circ}$ C
(C) $127\,^{\circ}$ C
(D) $-78\,^{\circ}$ C

Q27·PhysicsSingle correctJEE Main 2024

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (

27^\circ C

). The ratio of specific heat of gases at constant volume respectively is:

(A) $\dfrac75$
(B) $\dfrac32$
(C) $\dfrac35$
(D) $\dfrac53$

Q28·PhysicsSingle correctJEE Main 2024

Given below are two statements: Statement (I): The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the option given below:

(A)Statement I is false but Statement II is true.
(B)Statement I is true but Statement II is false.
(C)Both Statement I and Statement II are false
(D)Both Statement I and Statement II are true.

Q29·PhysicsSingle correctJEE Main 2024

A sample contains a mixture of helium and oxygen gas. The ratio of the root mean square speed of helium to that of oxygen in the sample is:

(A) $\tfrac{1}{\sqrt{32}}$
(B) $2\sqrt{2}$
(C) $\tfrac{1}{4}$
(D) $\tfrac{1}{2\sqrt{2}}$

Q30·PhysicsSingle correctJEE Main 2024

Energy of 10 non rigid diatomic molecules at temperature T is :

(A) $\frac{7}{2}$ RT
(B) $70 K_B T$
(C)35 RT
(D) $35 K_B T$

Q31·PhysicsSingle correctJEE Main 2024

If the collision frequency of hydrogen molecules in a closed chamber at

27^{\circ}\text{C}

is

Z

, then the collision frequency of the same system at

127^{\circ}\text{C}

is:

(A) $\dfrac{\sqrt{3}}{2}Z$
(B) $\dfrac{4}{3}Z$
(C) $\dfrac{2}{\sqrt{3}}Z$
(D) $\dfrac{3}{4}Z$

Q32·PhysicsSingle correctJEE Main 2024

If

n

is the number density and

d

is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by:

(A) $\dfrac{1}{\sqrt{2n\pi d^2}}$
(B) $\sqrt{2}\,n\pi d^2$
(C) $\dfrac{1}{\sqrt{2}\,n\pi d^2}$
(D) $\dfrac{1}{\sqrt{2}\,n^2\pi^2 d^2}$

Q33·PhysicsSingle correctJEE Main 2024

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:

(A) $\rho_2<\rho_1$
(B) $\rho_1>\rho_2$
(C) $\rho_1<\rho_2$
(D) $\rho_1=\rho_2=\rho_3$

Q34·PhysicsSingle correctJEE Main 2024

The translational degrees of freedom (

f_t

) and rotational degrees of freedom (

f_r

) of

\text{CH}_4

molecule are

(A) $f_t=2$ and $f_r=2$
(B) $f_t=3$ and $f_r=3$
(C) $f_t=3$ and $f_r=2$
(D) $f_t=2$ and $f_r=3$

Q35·PhysicsSingle correctJEE Main 2024

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km/s, the root mean square velocity of oxygen at the same condition in km/s is:

(A)2.0
(B)0.5
(C)1.5
(D)1.0

Q36·PhysicsSingle correctJEE Main 2024

Two moles of a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

(A) $\dfrac94 R$
(B) $\dfrac74 R$
(C) $\dfrac32 R$
(D) $\dfrac52 R$

Q37·PhysicsSingle correctJEE Main 2024

The parameter that remains the same for molecules of all gases at a given temperature is :

(A)kinetic energy
(B)momentum
(C)mass
(D)speed

Q38·PhysicsSingle correctJEE Main 2024

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

(A)29 RT
(B)20 RT
(C)27 RT
(D)21 RT

Q39·PhysicsSingle correctJEE Main 2024

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at

47^\circ C

?

(A) $80\,K$
(B) $-73\,K$
(C) $4\,K$
(D) $20\,K$

Q40·PhysicsSingle correctJEE Main 2024

If three moles of monoatomic gas

\left(\gamma=\dfrac{5}{3}\right)

is mixed with two moles of a diatomic gas

\left(\gamma=\dfrac{7}{5}\right)

, the value of adiabatic exponent

\gamma

for the mixture is:

(A)1.75
(B)1.40
(C)1.52
(D)1.35

Q41·PhysicsSingle correctJEE Main 2024

N moles of a polyatomic gas (

f=6

) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:

(A)6
(B)3
(C)4
(D)2

Q42·PhysicsSingle correctJEE Main 2024

Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen.

P_A

and

P_B

are the pressures of the gases in A and B respectively, then

\dfrac{P_A}{P_B}

is :

(A) $16$
(B) $8$
(C) $4$
(D) $32$

Q43·PhysicsSingle correctJEE Main 2024

The temperature of a gas having

2.0\times10^{25}

molecules per cubic meter at 1.38 atm (Given,

k=1.38\times10^{-23}

JK

^{-1}

) is:

(A)500 K
(B)200 K
(C)100 K
(D)300 K

Q44·PhysicsSingle correctJEE Main 2024

The equation of state of a real gas is given by

\left(P+\dfrac{a}{V^2}\right)(V-b)=RT

, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of

\dfrac{a}{b^2}

is similar to that of :

(A)PV
(B)P
(C)RT
(D)R

Q45·PhysicsSingle correctJEE Main 2024

The total kinetic energy of 1 mole of oxygen at

27^\circ

C is : [Use universal gas constant (R) = 8.31 J/mole K]

(A)6845.5 J
(B)5942.0 J
(C)6232.5 J
(D)5670.5 J

Q46·PhysicsSingle correctJEE Main 2024

The average kinetic energy of a monatomic molecule is 0.414 eV at temperature (Use

K_B=1.38\times 10^{-23}

J/mol-K):

(A)3000 K
(B)3200 K
(C)1600 K
(D)1500 K

Q47·PhysicsSingle correctJEE Advanced 2023

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is

U_n

and the speed of sound in the gas is

v_n

. At a fixed temperature and pressure, which of the following is the correct option ?

(A) $v_3 < v_6$ and $U_3 > U_6$
(B) $v_5 > v_3$ and $U_3 > U_5$
(C) $v_5 > v_7$ and $U_5 < U_7$
(D) $v_6 < v_7$ and $U_6 < U_7$

Q48·PhysicsSingle correctJEE Main 2023

A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is 30

^{\circ}

C. The ratio of average kinetic energy per molecule of the two gases (K argon/K hydrogen) is: (Given: Atomic Weight of Ar = 39.9)

(A)1
(B)2
(C) $\frac{39.9}{2}$
(D)39.9

Q49·PhysicsSingle correctJEE Main 2023

The

rms

speed of oxygen molecules in a vessel at particular temperature is

\left(1+\dfrac{5}{x}\right)^{1/2}\,v

, where

v

is the average speed of the molecule. The value of

x

will be: (Take

\pi=\dfrac{22}{7}

)

(A) $28$
(B) $27$
(C) $8$
(D) $4$

Q50·PhysicsSingle correctJEE Main 2023

The mean free path of molecules of a certain gas at STP is 1500d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately:

(A)1098d
(B)2049d
(C)750d
(D)1500d

Q51·PhysicsSingle correctJEE Main 2023

If the r.m.s. speed of chlorine molecule is 490 m/s at 27°C, the r.m.s. speed of argon molecules at the same temperature will be (Atomic mass of argon = 39.9u, molecular mass of chlorine = 70.9u)

(A)751.7 m/s
(B)451.7 m/s
(C)651.7 m/s
(D)551.7 m/s

Q52·PhysicsSingle correctJEE Main 2023

The root mean square speed of molecules of nitrogen gas at

27^\circ

C is: (Given mass of a nitrogen molecule

=4.6\times10^{-26}

kg and take Boltzmann constant

k_B=1.4\times10^{-23}

JK

^{-1}

)

(A) $523$ m/s
(B) $1260$ m/s
(C) $91$ m/s
(D) $27.4$ m/s

Q53·PhysicsSingle correctJEE Main 2023

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed (

v_{rms}

) and choose the correct answer from the options given below:

(A) $v_{rms}(\text{mono}) = v_{rms}(\text{dia}) = v_{rms}(\text{poly})$
(B) $v_{rms}(\text{mono}) > v_{rms}(\text{dia}) > v_{rms}(\text{poly})$
(C) $v_{rms}(\text{dia}) < v_{rms}(\text{poly}) < v_{rms}(\text{mono})$
(D) $v_{rms}(\text{mono}) < v_{rms}(\text{dia}) < v_{rms}(\text{poly})$

Q54·PhysicsSingle correctJEE Main 2023

Match List I (degrees of freedom) with List II (type of gas). Choose the correct answer from the options given below:

List I	List II
A.3 Translational degrees of freedom	I.Monoatomic gases
B.3 Translational, 2 rotational degrees of freedom	II.Polyatomic gases
C.3 Translational, 2 rotational and 1 vibrational degrees of freedom	III.Rigid diatomic gases
D.3 Translational, 3 rotational and more than one vibrational degrees of freedom	IV.Nonrigid diatomic gases

(A)(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
(B)(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(C)(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
(D)(A)-(I), (B)-(IV), (C)-(III), (D)-(II)

Q55·PhysicsSingle correctJEE Main 2023

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:

(A) $8\,RT$
(B) $16\,RT$
(C) $4\,RT$
(D) $11\,RT$

Q56·PhysicsSingle correctJEE Main 2023

The temperature at which the kinetic energy of oxygen molecules becomes double of its value at

27^{\circ}

C is

(A) $1227^{\circ}$ C
(B) $927^{\circ}$ C
(C) $327^{\circ}$ C
(D) $627^{\circ}$ C

Q57·PhysicsSingle correctJEE Main 2023

The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is

v_0

, then r.m.s. speed of the gas at 800 K will be:

(A) $v_0$
(B) $4v_0$
(C) $\dfrac{v_0}{4}$
(D) $2v_0$

Q58·PhysicsSingle correctJEE Main 2023

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:

(A) $1.25$
(B) $0.25$
(C) $0.75$
(D) $0.50$

Q59·PhysicsSingle correctJEE Main 2023

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. The temperature corresponding to the point 'K' is:

(A) $-273°C$
(B) $-100°C$
(C) $-40°C$
(D) $-373°C$

Q60·PhysicsSingle correctJEE Main 2023

The average kinetic energy of a molecule of the gas is:

(A)proportional to absolute temperature
(B)proportional to pressure
(C)proportional to volume
(D)dependent on the nature of gas

Q61·PhysicsSingle correctJEE Main 2023

Heat energy of

735

J is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

(A) $525$ J
(B) $441$ J
(C) $572$ J
(D) $735$ J

Q62·PhysicsSingle correctJEE Main 2023

The correct relation between

\gamma=\frac{C_p}{C_v}

and temperature

T

is :

(A) $\gamma \alpha\, T^0$
(B) $\gamma \alpha\, T$
(C) $\gamma \alpha\, \frac{1}{\sqrt{T}}$
(D) $\gamma \alpha\, \frac{1}{T}$

Q63·PhysicsSingle correctJEE Main 2023

A flask contains hydrogen and oxygen in the ratio of 2:1 by mass at temperature

27\,^{\circ}

C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

(A) $2:1$
(B) $1:1$
(C) $1:4$
(D) $4:1$

Q64·PhysicsSingle correctJEE Main 2023

The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation

PT^2=

constant. The volume expansion coefficient of the gas will be:

(A) $\dfrac{3}{T^2}$
(B) $\dfrac{3}{T^3}$
(C) $3T^2$
(D) $\dfrac{3}{T}$

Q65·PhysicsSingle correctJEE Main 2023

A bicycle tyre is filled with air having pressure of 270 kPa at 27 °C. The approximate pressure of the air in the tyre when the temperature increases to 36 °C is:

(A)270 kPa
(B)262 kPa
(C)360 kPa
(D)278 kPa

Q66·PhysicsSingle correctJEE Main 2023

At

300\,K

the rms speed of oxygen molecules is

\sqrt{\dfrac{\alpha+5}{\alpha}}

times to that of its average speed in the gas. Then, the value of

\alpha

will be:

\left(\text{used }\pi=\dfrac{22}{7}\right)

(A) $28$
(B) $24$
(C) $32$
(D) $27$

Q67·PhysicsSingle correctJEE Main 2023

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is:

(A) $\frac{5}{2}R$
(B) $\frac{9}{2}R$
(C) $\frac{7}{2}R$
(D) $\frac{3}{2}R$

Q68·PhysicsSingle correctJEE Main 2023

The root mean square velocity of molecules of a gas is:

(A)Inversely proportional to square root of temperature $\left(\dfrac{1}{\sqrt{T}}\right)$
(B)Proportional to square of temperature $(T^2)$
(C)Proportional to temperature $(T)$
(D)Proportional to square root of temperature $(\sqrt{T})$

Q69·PhysicsSingle correctJEE Main 2023

Given below are two statements: Statement I: The temperature of a gas is

-73^{\circ}

C. When the gas is heated to

527^{\circ}

C, the root mean square speed of the molecules is doubled. Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below:

(A)Statement I is false but Statement II is true
(B)Both Statement I and Statement II are false
(C)Statement I is true but Statement II is false
(D)Both Statement I and Statement II are true

Q70·PhysicsSingle correctJEE Main 2023

Let

\gamma_1

be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and

\gamma_2

be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio

\dfrac{\gamma_1}{\gamma_2}

is:

(A) $\dfrac{25}{21}$
(B) $\dfrac{25}{27}$
(C) $\dfrac{21}{25}$
(D) $\dfrac{27}{35}$

Q71·PhysicsNumericalJEE Main 2022

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is

\frac{\alpha^2}{4}

R J/mol K; then the value of

\alpha

will be ________. (Assume that the given diatomic gas has no vibrational mode.)

Q72·PhysicsSingle correctJEE Main 2022

The root mean square speed of smoke particles of mass

5 \times 10^{-17}

kg in their Brownian motion in air at NTP is approximately. [Given k

= 1.38 \times 10^{-23}

JK

^{-1}

]

(A)60 mm s $^{-1}$
(B)12 mm s $^{-1}$
(C)15 mm s $^{-1}$
(D)36 mm s $^{-1}$

Q73·PhysicsSingle correctJEE Main 2022

A vessel contains 14 g of nitrogen gas at a temperature of 27

^\circ

C. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take R = 8.32 J

mol^{-1}k^{-1}

)

(A)2229 J
(B)5616 J
(C)9360 J
(D)13,104 J

Q74·PhysicsSingle correctJEE Main 2022

Given below are two statements : Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature. 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 will become 2v. In the light of the above statements, choose the correct answer from the options given below :

(A)Both Statement I and Statement II are true
(B)Both Statement I and Statement II are false
(C)Statement I is true but Statement II is false
(D)Statement I is false but Statement II is true

Q75·PhysicsSingle correctJEE Main 2022

Which statements are correct about degrees of freedom? A. A molecule with n degrees of freedom has n

^{2}

different ways of storing energy. B. Each degree of freedom is associated with

\frac{1}{2}RT

average energy per mole. C. A monoatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom D. CH

_4

has a total to 6 degrees of freedom Choose the correct answer from the option given below:

(A)B and C only
(B)B and D only
(C)A and B only
(D)C and D only

Q76·PhysicsSingle correctJEE Main 2022

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 A. The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will be 1 : 4 C. The ratio of pressure will be 1 : 1 D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1 : 4

(A)A and C only
(B)B and D only
(C)A and B only
(D)C and D only

Q77·PhysicsSingle correctJEE Main 2022

A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

(A) $\frac{n}{n+2}$
(B) $\frac{n+2}{n}$
(C) $\frac{n}{2n+2}$
(D) $\frac{n}{n-2}$

Q78·PhysicsSingle correctJEE Main 2022

Following statements are given : (1) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. (3) The average kinetic energy of a gas molecule decreases with increases in volume. (4) Pressure of a gas increases with increase in temperature at constant pressure. (5) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below :

(A)(1) and (4) only
(B)(1), (2) and (4) only
(C)(2) and (4) only
(D)(1), (2) and (5) only

Q79·PhysicsSingle correctJEE Main 2022

A vessel contains 16g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in

\mathrm{cm}^3

is :

(A) $72 \times 10^{5}$
(B) $32 \times 10^{5}$
(C) $27 \times 10^{4}$
(D) $54 \times 10^{4}$

Q80·PhysicsSingle correctJEE Main 2022

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be : (Given gas constant R = 8.3

JK^{-1}

-

mol^{-1}

)

(A)249 J
(B)415 J
(C)498 J
(D)830 J

Q81·PhysicsSingle correctJEE Main 2022

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?

(A)The velocity of atomic oxygen remains same
(B)The velocity of atomic oxygen doubles
(C)The velocity of atomic oxygen becomes half
(D)The velocity of atomic oxygen becomes four times

Q82·PhysicsNumericalJEE Main 2022

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be J. (Given R = 8.31 J/mol.K)

Q83·PhysicsSingle correctJEE Main 2022

For a perfect gas, two pressures

P_{1}

and

P_{2}

are shown in figure. The graph shows:

(A) $P_{1}>P_{2}$
(B) $P_{1}<P_{2}$
(C) $P_{1}=P_{2}$
(D)Insufficient data to draw any conclusion

Q84·PhysicsSingle correctJEE Main 2022

A mixture of hydrogen and oxygen has volume 2000

cm^{3}

, 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 :

(A) $\frac{1}{3}$
(B) $\frac{3}{1}$
(C) $\frac{1}{16}$
(D) $\frac{16}{1}$

Q85·PhysicsSingle correctJEE Main 2022

According to kinetic theory of gases, A. The motion of the gas molecules freezes at

0^{\circ}

C B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is

\dfrac{3}{2}k_{B}T

(for monoatomic gases) Choose the most appropriate answer from the options given below:

(A)A and C only
(B)B and C only
(C)A and B only
(D)C and D only

Q86·PhysicsSingle correctJEE Main 2022

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 : (R = universal gas constant)

(A) $\frac{Mv^{2}}{7R}$
(B) $\frac{Mv^{2}}{5R}$
(C) $2\frac{Mv^{2}}{7R}$
(D) $7\frac{Mv^{2}}{5R}$

Q87·PhysicsSingle correctJEE Main 2022

A flask contains argon and oxygen in the ratio of 3:2 in mass and the mixture is kept at 27°C. The ratio of their average kinetic energy per molecule respectively will be :

(A)3 : 2
(B)9 : 4
(C)2 : 3
(D)1 : 1

Q88·PhysicsSingle correctJEE Main 2022

The ratio of specific heats

\left(\frac{C_P}{C_V}\right)

in terms of degree of freedom (f) is given by:

(A) $\left(1 + \frac{f}{3}\right)$
(B) $\left(1 + \frac{2}{f}\right)$
(C) $\left(1 + \frac{f}{2}\right)$
(D) $\left(1 + \frac{1}{f}\right)$

Q89·PhysicsNumericalJEE Main 2022

When a gas filled in a closed vessel is heated by raising the temperature by 1°C, its pressure increase by 0.4%. The initial temperature of the gas is_______ K.

Q90·PhysicsSingle correctJEE Main 2022

The relation between root mean square speed

(v_{rms})

and most probable speed

(v_p)

for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :-

(A) $v_{rms}=\sqrt{\frac{2}{3}}v_p$
(B) $v_{rms}=\sqrt{\frac{3}{2}}v_p$
(C) $v_{rms}=v_p$
(D) $v_{rms}=\sqrt{\frac{1}{3}}v_p$

Q91·PhysicsNumericalJEE Main 2022

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of

127^{\circ}

C. The amount of heat required to double the speed of its molecules is ______ k cal. (Take R = 2 cal mole

^{-1}

K

^{-1}

)

Q92·PhysicsNumericalJEE Advanced 2021

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmospheric pressure

p_0 = 10^5

Pa so that the volume of the trapped air is

v_0

= 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure

P_0 + \Delta p

without changing its orientation. At this pressure, the volume of the trapped air is

v_0 - \Delta v

. Let

\Delta v = X

cc and

\Delta p = Y \times 10^3

Pa. The value of

Y

is ____.

Q93·PhysicsNumericalJEE Main 2021

The average translational kinetic energy of N

_{2}

gas molecules at ..........°C becomes equal to the K.E. of an electron accelerated from rest through a potential difference of 0.1 volt. (Given k

_{B}

= 1.38 × 10

^{-23}

J/K) (Fill the nearest integer).

Q94·PhysicsSingle correctJEE Main 2021

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation

\frac{dp}{dv}=-ap

. If p =

p_{0}

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)

(A) $\frac{p_{0}}{a\,e\,R}$
(B) $\frac{ap_{0}}{e\,R}$
(C)infinity
(D)0 $^\circ$ C

Q95·PhysicsSingle correctJEE Main 2021

A mixture of hydrogen and oxygen has volume 500 cm

^3

, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

(A)3 : 8
(B)3 : 16
(C)16 : 3
(D)8 : 3

Q96·PhysicsSingle correctJEE Main 2021

If the rms speed of oxygen molecules at 0°C is 160 m/s, find the rms speed of hydrogen molecules at 0°C.

(A)640 m/s
(B)40 m/s
(C)80 m/s
(D)332 m/s

Q97·PhysicsSingle correctJEE Main 2021

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 ?

(A)181.46 kg
(B)214.15 kg.
(C)219.07 kg
(D)123.54 kg

Q98·PhysicsSingle correctJEE Main 2021

The rms speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are

V_H

,

V_O

and

V_C

respectively then :

(A) $V_H > V_O > V_C$
(B) $V_C > V_O > V_H$
(C) $V_H = V_O > V_C$
(D) $V_H = V_O = V_C$

Q99·PhysicsSingle correctJEE Main 2021

A cylindrical container of volume

4.0 \times 10^{-3}

m

^{3}

contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is : [Take gas constant as 8.3 J mol

^{-1}

K

^{-1}

]

(A) $249 \times 10^{1}$ Pa
(B) $24.9 \times 10^{3}$ Pa
(C) $24.9 \times 10^{5}$ Pa
(D)24.9 Pa

Q100·PhysicsSingle correctJEE Main 2021

The number of molecules in one litre of an ideal gas at 300K and 2 atmospheric pressure with mean kinetic energy

2 \times 10^{-9}

J per molecule is :

(A) $0.75 \times 10^{11}$
(B) $3 \times 10^{11}$
(C) $6 \times 10^{11}$
(D) $1.5 \times 10^{11}$

Q101·PhysicsNumericalJEE Main 2021

A system consists of two types of gas molecules A and B having same number density

2 \times 10^{25}

/ m³. The diameter of A and B are 10 Å and 5 Å respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ________

\times 10^{-2}

.

Q102·PhysicsSingle correctJEE Main 2021

For a gas

C_P - C_V =

R in a state P and

C_P - C_V =

1.10 R in a state Q,

T_P

and

T_Q

are the temperatures in two different states P and Q respectively. Then

(A) $T_P < T_Q$
(B) $T_P = 0.9\ T_Q$
(C) $T_P > T_Q$
(D) $T_P = T_Q$

Q103·PhysicsSingle correctJEE Main 2021

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T ?

(A) $\frac{3}{2}k_B T$
(B) $\frac{1}{2}k_B T$
(C) $k_B T$
(D) $\frac{2}{3}k_B T$

Q104·PhysicsSingle correctJEE Main 2021

Consider a mixture of gas molecule of types A, B and C having masses

m_A < m_B < m_C

. The ratio of their root mean square speeds at normal temperature and pressure is :

(A) $\frac{1}{\upsilon_A} > \frac{1}{\upsilon_B} > \frac{1}{\upsilon_C}$
(B) $\upsilon_A = \upsilon_B = \upsilon_C = 0$
(C) $\frac{1}{\upsilon_A} < \frac{1}{\upsilon_B} < \frac{1}{\upsilon_C}$
(D) $\upsilon_A = \upsilon_B \neq \upsilon_C$

Q105·PhysicsSingle correctJEE Main 2021

Which of the following graphs represent the behaviour of an ideal gas? Symbols have their usual meaning.

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q106·PhysicsSingle correctJEE Main 2021

The correct relation between the degrees of freedom f and the ratio of specific heat

\gamma

is :

(A) $f = \dfrac{2}{\gamma + 1}$
(B) $f = \dfrac{2}{\gamma - 1}$
(C) $f = \dfrac{1}{\gamma + 1}$
(D) $f = \dfrac{\gamma + 1}{2}$

Q107·PhysicsSingle correctJEE Main 2021

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0°C to 50°C when no work is done is ________. (R is the universal gas constant)

(A)175 R
(B)750 R
(C)250 R
(D)500 R

Q108·PhysicsSingle correctJEE Main 2021

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T ? (k

_{B}

is Boltzmann constant)

(A) $\dfrac{1}{2}k_{B}T$
(B) $\dfrac{2}{3}k_{B}T$
(C) $\dfrac{3}{2}k_{B}T$
(D) $k_{B}T$

Q109·PhysicsSingle correctJEE Main 2021

Two ideal polyatomic gases at temperatures

T_1

and

T_2

are mixed so that there is no loss of energy. If

F_1

and

F_2

,

m_1

and

m_2

,

n_1

and

n_2

be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :

(A) $\frac{n_1 T_1 + n_2 T_2}{n_1 + n_2}$
(B) $\frac{n_1 F_1 T_1 + n_2 F_2 T_2}{n_1 F_1 + n_2 F_2}$
(C) $\frac{n_1 F_1 T_1 + n_2 F_2 T_2}{F_1 + F_2}$
(D) $\frac{n_1 F_1 T_1 + n_2 F_2 T_2}{n_1 + n_2}$

Q110·PhysicsSingle correctJEE Main 2021

If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of molar specific heats for polyatomic gas

\left(\beta = \frac{C_{P}}{C_{V}}\right)

then the value of β is :

(A)1.02
(B)1.2
(C)1.25
(D)1.35

Q111·PhysicsSingle correctJEE Main 2021

A polyatomic ideal gas has 24 vibrational modes. What is the value of

\gamma

?

(A)1.03
(B)1.30
(C)1.37
(D)10.3

Q112·PhysicsSingle correctJEE Main 2021

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 :

(A) $\frac{88RT}{V}$
(B) $\frac{3RT}{V}$
(C) $\frac{5}{2}\frac{RT}{V}$
(D) $\frac{4RT}{V}$

Q113·PhysicsSingle correctJEE Main 2021

Calculate the value of mean free path (λ) for oxygen molecules at temperature 27°C and pressure 1.01 × 10

^{5}

Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 × 10

^{-23}

JK

^{-1}

)

(A)58 nm
(B)32 nm
(C)86 nm
(D)102 nm

Q114·PhysicsNumericalJEE Main 2021

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 equilibrium, then, the common equilibrium pressure existing in the mixture is x × 10

^{-1}

atm. Value of x is _________.

Q115·PhysicsSingle correctJEE Main 2021

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4. The gas is :

(A)polyatomic only
(B)monoatomic only
(C)either monoatomic or diatomic
(D)diatomic only.

Q116·PhysicsNumericalJEE Main 2021

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R=gas constant) is

\dfrac{x}{3R}

. Value of x is ________ .

Q117·PhysicsSingle correctJEE Main 2021

Given below are two statements: Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II: in a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below:

(A)Both statement I and statement II are false.
(B)Both statement I and statement II are true.
(C)Statement I is false but statement II is true
(D)Statement I is true but statement II is false.

Q118·PhysicsNumericalJEE Main 2021

The root mean square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 ms

^{-1}

. The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is

\dfrac{x}{\sqrt{3}}

ms

^{-1}

. The value of x will be ____________.

Q119·PhysicsSingle correctJEE Main 2021

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

(A)suffer change in momentum when impinge on the walls of container.
(B)continuously stick to the walls of container.
(C)continuously lose their energy till it reaches wall.
(D)are attracted by the walls of container.

Q120·PhysicsMultiple correctJEE Advanced 2020

As shown schematically in the figure, two vessels contain water solutions (at temperature

T

) of potassium permanganate (

KMnO_4

) of different concentrations

n_1

and

n_2

(

n_1 > n_2

) molecules per unit volume with

\Delta n = (n_1 - n_2) \ll n_1

. When they are connected by a tube of small length

\ell

and cross-sectional area S,

KMnO_4

starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force

-\beta v

on each molecule, where β is a constant. Neglecting all terms of the order

(\Delta n)^2

, which of the following is/are correct? (

k_B

is the Boltzmann constant)-

(A)the force causing the molecules to move across the tube is $\Delta nk_BTS$
(B)force balance implies $n_1\beta v\ell = \Delta nk_BT$
(C)total number of molecules going across the tube per sec is $\left(\frac{\Delta n}{\ell}\right)\left(\frac{k_BT}{\beta}\right)S$
(D)rate of molecules getting transferred through the tube does not change with time

Q121·PhysicsNumericalJEE Main 2020

Initially a gas of diatomic molecules is contained in a cylinder of volume

V_1

at a pressure

P_1

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_1

is given by

P_2

. The ratio

\dfrac{P_2}{P_1}

is __________.

Q122·PhysicsSingle correctJEE Main 2020

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of

\gamma\left(=\dfrac{C_P}{C_v}\right)

are given, respectively, by:

(A) $U=\dfrac{5}{2}RT$ and $\gamma=\dfrac{6}{5}$
(B) $U=5RT$ and $\gamma=\dfrac{7}{5}$
(C) $U=\dfrac{5}{2}RT$ and $\gamma=\dfrac{7}{5}$
(D) $U=5RT$ and $\gamma=\dfrac{6}{5}$

Q123·PhysicsSingle correctJEE Main 2020

Number of molecules in a volume of 4 cm

^3

of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is

4 \times 10^{-14}

erg, g = 980 cm / s

^2

, density of mercury = 13.6 g / cm

^3

)

(A) $5.8 \times 10^{18}$
(B) $4.0 \times 10^{16}$
(C) $5.8 \times 10^{16}$
(D) $4.0 \times 10^{18}$

Q124·PhysicsSingle correctJEE Main 2020

Match the

C_{P}/C_{V}

ratio for ideal gases with different type of molecules: Match the correct option?

Molecule Type	$C_{P}/C_{V}$
A.Monatomic	I. $\frac{7}{5}$
B.Diatomic rigid molecules	II. $\frac{9}{7}$
C.Diatomic non-rigid molecules	III. $\frac{4}{3}$
D.Triatomic rigid molecules	IV. $\frac{5}{3}$

(A)A → III; B → IV; C → II; D → I
(B)A → IV; B → I; C → II; D → III
(C)A → II; B → III; C → I; D → IV
(D)A → IV; B → II; C → I; D → III

Q125·PhysicsNumericalJEE Main 2020

The change in the magnitude of the volume of an ideal gas when a small additional pressure ΔP is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity ΔT at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively. If |ΔT| = C|ΔP| then value of C in (K/atm) is ….

Q126·PhysicsSingle correctJEE Main 2020

To raise the temperature of a certain mass of gas by

50^{\circ}

C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by

100^{\circ}C

at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

(A)7
(B)5
(C)3
(D)6

Q127·PhysicsSingle correctJEE Main 2020

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:

(A) $\dfrac{5}{2}RT$
(B) $\dfrac{3}{2}RT$
(C) $3RT$
(D) $\dfrac{9}{2}RT$

Q128·PhysicsSingle correctJEE Main 2020

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 mass

\dfrac{m}{4}

. The ratio of the specific heats (

C_{V}^{A}

and

C_{V}^{B}

) of gas A and B, respectively is

(A)3 : 5
(B)5 : 7
(C)7 : 9
(D)5 : 9

Q129·PhysicsSingle correctJEE Main 2020

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)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q130·PhysicsSingle correctJEE Main 2020

Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. It C

_{P}

/C

_{V}

value will be

(A)19/13
(B)40/27
(C)67/45
(D)23/15

Q131·PhysicsSingle correctJEE Main 2020

Two moles of an ideal gas with

\dfrac{C_P}{C_V}=\dfrac{5}{3}

are mixed with 3 moles of another ideal gas with

\dfrac{C_P}{C_V}=\dfrac{4}{3}

. The value of

\dfrac{C_P}{C_V}

for the mixture is:

(A)1.42
(B)1.47
(C)1.45
(D)1.50

Q132·PhysicsMultiple correctJEE Advanced 2019

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is

L = L_0

the particle speed is

v = v_0

. The piston is moved inward at a very low speed V such that

V << \frac{dL}{L}v_0

, where dL is the infinitesimal displacement of the piston. which of the following statement(s) is/are correct ?

(A)The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from $L_0$ to $\frac{1}{2}L_0$ .
(B)After each collision with the piston, the particle speed increases by 2V.
(C)If the piston moves inward by dL, the particle speed increases by $2v\frac{dL}{L}$
(D)The rate at which the particle strikes the piston is v/L

Q133·PhysicsSingle correctJEE Main 2019

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)

(A)17.4 J/mol K
(B)15.7 J/mol K
(C)19.7 J/mol K
(D)21.6 J/mol K

Q134·PhysicsSingle correctJEE Main 2019

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 :

(A) $n_{0}\alpha^{-3/4}$
(B) $n_{0}\alpha^{-3}$
(C) $n_{0}\alpha^{1/4}$
(D) $\sqrt{n_{0}}\,\alpha^{1/2}$

Q135·PhysicsSingle correctJEE Main 2019

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is: [Given that R = 8.31 J mol

^{-1}

K

^{-1}

]

(A)350 J
(B)700 J
(C)748 J
(D)374 J

Q136·PhysicsSingle correctJEE Main 2019

When heat Q is supplied to a diatomic gas of rigid molecules at constant volume its temperature increases by ΔT. The heat required to produce the same change in temperature, at constant pressure is

(A) $\dfrac{3}{2}Q$
(B) $\dfrac{5}{3}Q$
(C) $\dfrac{7}{5}Q$
(D) $\dfrac{2}{3}Q$

Q137·PhysicsSingle correctJEE Main 2019

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be:

(A)80 m/s
(B) $80\sqrt{5}$ m / s
(C)100 m/s
(D) $100\sqrt{5}$ m / s

Q138·PhysicsSingle correctJEE Main 2019

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to: [Boltzmans 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 Gravitation acceleration on Earth = 10 ms

^{-2}

]

(A)800k
(B) $10^{4}$ K
(C) $3\times 10^{5}$
(D)650 K

Q139·PhysicsSingle correctJEE Main 2019

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 l

_1

, and that below the piston is l

_2

, such that l

_1

> l

_2

. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by: (R is universal gas constant and g is the acceleration due to gravity)

(A) $\frac{RT}{ng}\left[\frac{l_1-3l_2}{l_1l_2}\right]$
(B) $\frac{RT}{g}\left[\frac{2l_1+l_2}{l_1l_2}\right]$
(C) $\frac{nRT}{ng}\left[\frac{1}{l_2}+\frac{1}{l_1}\right]$
(D) $\frac{nRT}{g}\left[\frac{l_1-l_2}{l_1l_2}\right]$

Q140·PhysicsSingle correctJEE Main 2019

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\times10^{-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 :

(A) $2\times10^{-7}$ s
(B) $4\times10^{-8}$ s
(C) $0.5\times10^{-8}$ s
(D) $3\times10^{-6}$ s

Q141·PhysicsSingle correctJEE Main 2019

A gas mixture consists of 3 moles of oxygen and 5 moles or argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is:

(A)15 RT
(B)12 RT
(C)4 RT
(D)20 RT

Q142·PhysicsSingle correctJEE Main 2019

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°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]

(A)0.9 kJ
(B)6 kJ
(C)10 kJ
(D)14 kJ

Q143·PhysicsSingle correctJEE Main 2019

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[\dfrac{V_{rms}(helium)}{V_{rms}(argon)}\right]

, is close to:

(A)3.16
(B)0.32
(C)0.45
(D)2.24

Q144·PhysicsMultiple correctJEE Advanced 2017

A flat plate is moving normal to its plane through a gas under the action of constant force

F

. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true?

(A)The resistive force experienced by the plate is proportional to v
(B)The pressure difference between the leading and trailing faces of the plate is proportional to uv
(C)The plate will continue to move with constant non-zero acceleration, at all times
(D)At a later time the external force $F$ balances the resistive force.

Q145·PhysicsMultiple correctJEE Advanced 2015

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is(are)

(A)The average energy per mole of the gas mixture is 2RT.
(B)The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{6/5}$ .
(C)The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1/2$ .
(D)The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1/\sqrt{2}$ .

Q146·PhysicsSingle correctJEE Advanced 2013

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is

(A)1 : 4
(B)1 : 2
(C)6 : 9
(D)8 : 9

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