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JEE • PHYSICS • KINETIC THEORY OF GASES

Kinetic theory of gases practice · Mixed difficulty

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 290 questions

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1 Medium

1 of 290

Understanding +4 | -1

Assertion: The pressure exerted by an enclosed ideal gas does not depend on the shape of the container.
Reason: The pressure of an ideal gas depends on the number moles, temperature and volume of the enclosed

View answer and explanation

Correct option: A

If both Assertion and reason are true and the Reason is the correct explanation of the Assertion

Option B is correct because science involves exploring, experimenting, and making predictions based on observations.

2 Medium

2 of 290

Understanding +4 | -1

c_s

is the velocity of sound in air and

c

is the rms velocity, then

View answer and explanation

Correct option: C

c_{{s}}=c\left(\frac{\gamma}{3}\right)^{1 / 2}

Option C (

c_{{s}}=c(\frac{\gamma}{3})^{1 / 2}

) is correct because it represents the correct relationship between the speed of sound and the RMS velocity of gas molecules.

3 Medium

3 of 290

Application +4 | -1

Four particles have velocities

1,0,2,3 \mathrm{~m} / \mathrm{s}

. The root mean square of the particles is (in

\mathrm{m} / \mathrm{s}

)

View answer and explanation

Correct option: B

\sqrt{3.5}

Option B (

\sqrt{3.5}

) is correct because it is calculated using the formula for root mean square velocity.

4 Medium

4 of 290

Understanding +4 | -1

The translational degrees of freedom

(f_t)

and rotational degrees of freedom

(f_r)

{CH}_4

molecule are:

View answer and explanation

Correct option: B

f_t=3

and

f_r=3

Option B (

f_t=3

and

f_r=3

) is correct because methane (

CH_4

) is a non-linear polyatomic molecule, possessing 3 translational and 3 rotational degrees of freedom.

5 Medium

5 of 290

Understanding +4 | -1

On any planet, the presence of atmosphere implies (

{C_{rms}} =

= root mean square velocity of molecules and

{V_e} =

escape velocity)

View answer and explanation

Correct option: A

{C_{rms}} < < {V_e}

Option A (

{C_{rms}} < < {V_e}

) is correct because for a planet to have an atmosphere, the root mean square velocity of gas molecules must be much less than the escape velocity.

6 Medium

6 of 290

Understanding +4 | -1

At a given temperature, the pressure of an ideal gas of density

\rho

is proportional to

View answer and explanation

Correct option: D

\rho

Option D (

\rho

) is correct because at a given temperature, the pressure of an ideal gas is directly proportional to its density.

7 Medium

7 of 290

Understanding +4 | -1

The mean free path for a gas, with molecular diameter

d

and number density

n

can be expressed as

\left(T \text{ is temperature, }P \text{ is pressure of the gas and }k_B \text{ is Boltzmann constant}\right)

View answer and explanation

Correct option: D

Both (2) and (3)

Option D is correct because the mean free path can be expressed in terms of number density and molecular diameter, or in terms of pressure, temperature, and Boltzmann constant.

8 Medium

8 of 290

Understanding +4 | -1

In a mixture of nitrogen and helium kept at
room temperature, as compared to helium
molecule, nitrogen molecule strikes the wall
(A) with greater average speed

(B) with smaller average speed

(C) with greater average kinetic energy

(D) with smaller average kinetic energy

Choose the correct statement.

View answer and explanation

Correct option: D

B, C

Option B, C (B, D) is correct because at the same temperature, helium molecules have a greater average speed and smaller average kinetic energy compared to nitrogen molecules.

9 Medium

9 of 290

Remembering +4 | -1

According to equipartition law of energy, each particle in a system of particles have thermal energy

E

equal to

View answer and explanation

Correct option: B

(1 / 2) k_B T

Option B (

(1 / 2) k_B T

) is correct because, according to the equipartition theorem, each degree of freedom contributes

(1 / 2) k_B T

to the average energy.

10 Medium

10 of 290

Understanding +4 | -1

Assertion: A gas can be liquefied at any temperature by increase of pressure alone.
Reason: On increasing pressure the temperature of gas decreases.

View answer and explanation

Correct option: D

If both assertion and reason are false

Option D (If both assertion and reason are false) is correct because a gas cannot be liquefied at any temperature by pressure alone, and increasing pressure generally increases the temperature of a gas.

11 Medium

11 of 290

Analyzing +4 | -1

Assertion: Ratio of isothermal bulk modulus and adiabatic bulk modulus for a monoatomic gas at a given pressure is

\frac{3}{5}

Reason: This ratio is equal to

\gamma=\frac{C_p}{C_v}

View answer and explanation

Correct option: C

If Assertion is true, but the Reason is false

Option C (If Assertion is true, but the Reason is false) is correct because the ratio of isothermal to adiabatic bulk modulus is the inverse of gamma, not gamma itself.

12 Medium

12 of 290

Understanding +4 | -1

Let

\overline{{v}}, {v}_{\mathrm{rms}}

and

{v}_{{P}}

respectively denote the mean speed, r.m.s. speed, and most probable speed of the molecules in an ideal monatomic gas at absolute temperature T. The mass of a molecule is

m

, then which of the following is correct?

View answer and explanation

Correct option: C

{v}_{{p}} < \overline{{v}} < {v}_{\text {r.m.s. }}

Option C is correct because the most probable speed is less than the average speed, which is less than the root-mean-square speed.

13 Medium

13 of 290

Application +4 | -1

If one mole of a monoatomic gas

\left( {\mathrm{\gamma } = \frac{5}{3}} \right)

is mixed with one mole of a diatomic gas

\left( {\mathrm{\gamma } = \frac{7}{5}} \right)

, the value of

\mathrm{\gamma }

for the mixture is

View answer and explanation

Correct option: B

1.50

Option B (1.50) is correct because it is the value of gamma for the mixture, calculated using the number of moles and individual gammas of the gases.

14 Medium

14 of 290

Remembering +4 | -1

The value of

{C_V}

for one mole of neon gas is

View answer and explanation

Correct option: B

\frac{3}{2}R

Option B (

\frac{3}{2}R

) is correct because for a monoatomic gas like Neon, the value of

{C_V}

\frac{3}{2}R

15 Medium

15 of 290

Analyzing +4 | -1

Assertion: Vibrational energy of diatomic molecule corresponding to each degree of freedom is

k_\beta T

.
Reason: For every molecule, vibrational degree of freedom is 2.

View answer and explanation

Correct option: C

If assertion is true, but reason is false

The assertion is true, but the reason is false (Option C). Vibrational energy is kT, but diatomic molecules have 2 vibrational degrees of freedom (KE and PE).

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16 Medium

16 of 290

Analyzing +4 | -1

Assertion: In free expansion of an ideal gas, the entropy increases.
Reason: Entropy increases in all natural processes.

View answer and explanation

Correct option: C

If assertion is true, but reason is false

Option B (If both assertion and reason are true but reason is not correct explanation of the assertion) is correct because entropy increases in free expansion, but not all natural processes increase entropy.

17 Medium

17 of 290

Remembering +4 | -1

The relation between the gas pressure

P

and average kinetic energy per unit volume

E

View answer and explanation

Correct option: D

P = \frac{2}{3}E

Option D (

P = \frac{2}{3}E

) is correct because the pressure of a gas is related to the average kinetic energy per unit volume by this specific factor, derived from the kinetic theory of gases.

18 Medium

18 of 290

Understanding +4 | -1

Three containers of the same volume contain three different gases. The masses of the molecules are

{m_1},{m_2}

and

{m_3}

and the number of molecules in their respective containers are

{N_1},{N_2}

and

{N_3}.

The gas pressure in the containers are

{P_1},{P_2}

and

{P_3}

respectively. All the gases are now mixed and put in one of the containers. The pressure P of mixture will be

View answer and explanation

Correct option: C

P = {P_1} + {P_2} + {P_3}

Option C (

P = {P_1} + {P_2} + {P_3}

) is correct because, according to Dalton's law of partial pressures, the total pressure of a mixture of gases is the sum of the partial pressures of each gas.

19 Medium

19 of 290

Analyzing +4 | -1

An experiment is being performed by a student in laboratory on ideal gas. He found the value of

C_P-C_V

equal to

1.00 \mathrm{~R}

for a gas sample in state
A. Now he performed the experiment on the same gas and found

C_P-C_V

1.03 \mathrm{~R}

in state
B. Let

P_A, P_B

denote the pressures and

T_A, T_B

denote the temperatures of states

A

and

B

respectively. Which of the following will be correct?

View answer and explanation

Correct option: A

P_A < P_B

and

T_A > T_B

Option A (

P_A < P_B

and

T_A > T_B

) is correct because the gas deviates from ideal behavior in state B, implying higher pressure and lower temperature than predicted by the ideal gas law.

20 Medium

20 of 290

Application +4 | -1

The velocity of 4 gas molecules are given by 1 km/s, 3 km/s, 5 km/s and 7 km/s. Calculate the difference between average and rms velocity.

View answer and explanation

Correct option: C

0.583

Option A ( - 5 < a < 2) is correct because the given inequality holds for all real x if the discriminant of the quadratic is negative, leading to this range for a.

21 Medium

21 of 290

Understanding +4 | -1

If there were no atmosphere, the average temperature on the surface of the earth would be

View answer and explanation

Correct option: A

Lower

Option A (Lower) is correct because the atmosphere traps heat, and without it, the Earth's surface temperature would be significantly lower.

22 Medium

22 of 290

Remembering +4 | -1

The root mean square velocity of molecules of gas is

View answer and explanation

Correct option: A

Proportional to square root of temperature

(\sqrt{T})

Option A (Proportional to square root of temperature

(\sqrt{T})

) is correct because the root mean square velocity is directly proportional to the square root of the absolute temperature.

23 Medium

23 of 290

Application +4 | -1

Molar specific heat of ideal

\mathrm{CO}_2

gas in a thermodynamic process is equal to

3 R

. The variation of volume with temperature is represented by

View answer and explanation

Correct option: C

T \propto V^2

Option C (

T \propto V^2

) is correct because, for the given molar specific heat, the process is polytropic with index -1, leading to the stated relationship.

24 Medium

24 of 290

Understanding +4 | -1

The average kinetic energy of a molecule of the gas is

View answer and explanation

Correct option: C

Proportional to absolute temperature

Option C (Proportional to absolute temperature) is correct because the average kinetic energy of a gas molecule is directly proportional to the absolute temperature of the gas.

25 Medium

25 of 290

Analyzing +4 | -1

Assertion: An ideal gas has infinitely many molar specific heats.
Reason: Specific heat is amount of heat needed to raise the temperature of 1 mole of gas by

1 \mathrm{~K}

View answer and explanation

Correct option: B

If both Assertion and reason are true and the Reason is not a correct explanation of the Assertion

Option B (If both Assertion and reason are true and the Reason is not a correct explanation of the Assertion) is correct because while both statements are true, the reason doesn't explain why an ideal gas has infinitely many molar specific heats.

26 Medium

26 of 290

Understanding +4 | -1

Assertion: On increasing temperature, internal energy of monoatomic gas increases.
Reason: Thermal energy increases only random motion of gas molecules.

View answer and explanation

Correct option: C

If assertion is True but the Reason is False

Option B (If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion) is correct because increasing temperature does increase internal energy, and thermal energy increases random motion, but the reason isn't the *only* factor for internal energy increase.

27 Medium

27 of 290

Understanding +4 | -1

How is the mean free path

(\lambda)

in a gas related to the interatomic distance?

View answer and explanation

Correct option: B

\lambda

is 100 times the interatomic distance

Option B (

\lambda

is 100 times the interatomic distance) is correct because the mean free path in a gas is typically much larger than the interatomic distance.

28 Medium

28 of 290

Analyzing +4 | -1

Assertion (A) : If pressure of an ideal gas is doubled and volume is halved, then its internal energy will remain unchanged.

Reason (R) : Internal energy of an ideal gas is a function of only temperature.

View answer and explanation

Correct option: B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

Option B (If both Assertion and Reason are true but Reason is not the correct explanation of Assertion) is correct because while both statements are true, the reason doesn't explain why internal energy remains unchanged when pressure is doubled and volume is halved.

29 Medium

29 of 290

Understanding +4 | -1

If the temperature of an ideal gas increases three times, then its

rms

velocity will become

View answer and explanation

Correct option: A

\sqrt 3

times

Option A (

\sqrt 3

times) is correct because the rms velocity is proportional to the square root of the absolute temperature.

30 Medium

30 of 290

Understanding +4 | -1

Consider the following statement.
The internal energy of an ideal monoatomic gas may have contributions from
1. translational kinetic energy of its molecules.
2. vibrational kinetic energy of its molecules.
3. rotational kinetic energy of its molecules.
4. potential energy corresponding to molecular forces.
Which of the statements given above is/are correct?

View answer and explanation

Correct option: C

1 only

Option C (1 only) is correct because an ideal monoatomic gas only has translational kinetic energy; it lacks vibrational, rotational, and intermolecular potential energy.

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Key Takeaways

✓ This set contains 290 single-correct-answer MCQs on KINETIC THEORY OF GASES.
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✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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