Assertion A: Oxygen and nitrogen molecules in a gas mixture at one temperature have equal rms speeds. Reason R: The average translational kinetic energy per molecule of an ideal gas depends only on its temperature. Choose the correct answer.

A is not correct but R is correct

Both A and R are correct but R is not the correct explanation of A

A is correct but R is not correct

Both A and R are correct and R is the correct explanation of A

Kinetic Theory

24 NEET-UG practice questions on Kinetic Theory, part of Physics. The first 24 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
Examine these statements about an ideal gas. A. The mean free path increases when the number density of the molecules falls. B. At a given temperature, the average kinetic energy per molecule is greater for a heavier gas. C. At a given temperature, the rms speed varies inversely as the square root of the molar mass. D. The mean free path is directly proportional to the molecular diameter. Which statements are correct?
1. AB and D only
2. BA, B and C only
3. CC and D only
4. DA and C only
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Answer: D · A and C only
The mean free path is 1/(√2 π n d²), so it rises as n falls (A) but falls as d rises (D is false). Average kinetic energy depends only on temperature (B is false). v(rms) = √(3RT/M) supports C.
- A: Both B and D are false.
- B: B is false: the energy does not depend on the mass.
- C: D is false: the path falls as the diameter rises.
Remember this
Mean free path varies as 1/(n d²), so doubling the diameter cuts it to one quarter.
Question 2 · Medium
Assertion A: Oxygen and nitrogen molecules in a gas mixture at one temperature have equal rms speeds. Reason R: The average translational kinetic energy per molecule of an ideal gas depends only on its temperature. Choose the correct answer.
1. AA is not correct but R is correct
2. BBoth A and R are correct but R is not the correct explanation of A
3. CA is correct but R is not correct
4. DBoth A and R are correct and R is the correct explanation of A
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Answer: A · A is not correct but R is correct
R is true: the average translational kinetic energy is (3/2)kT. Equal kinetic energy with different molecular masses means different speeds, and v(rms) varies as 1/√M, so oxygen is slower and A is false.
- B: A is false, since the heavier molecule moves more slowly.
- C: This reverses the truth values of A and R.
- D: A is false, so R cannot explain it.
Remember this
At equal temperature, molecules share average kinetic energy, not speed.
Question 3 · Easy
The rms speed of oxygen molecules in a flask at 27 °C is v. What is it at 927 °C?
1. A2v
2. B5.9v
3. C34.3v
4. D4v
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Answer: A · 2v
The rms speed varies as the square root of the absolute temperature. The temperatures are 300 K and 1200 K, a ratio of 4, so the speed doubles to 2v.
- B: This takes the square root of the Celsius ratio.
- C: This takes the ratio of the Celsius temperatures.
- D: This forgets the square root.
Remember this
Always use kelvin for v(rms) = √(3RT/M), which varies as √T.
Question 4 · Medium
One mole of a monatomic ideal gas is mixed with one mole of a rigid diatomic ideal gas. What is the ratio of specific heats, γ, of the mixture?
1. A1.53
2. B1.50
3. C1.67
4. D1.40
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Answer: B · 1.50
Cv of the mixture = (3R/2 + 5R/2)/2 = 2R, and Cp = Cv + R = 3R, so γ = 1.5. Check: the mean number of degrees of freedom is (3 + 5)/2 = 4, and γ = 1 + 2/f = 1.5.
- A: This averages the two γ values directly.
- C: This is the γ of the monatomic gas alone.
- D: This is the γ of the diatomic gas alone.
Remember this
For mixtures, average Cv by moles; never average the γ values.
Question 5 · Hard
A heat Q raises the temperature of 2 mol of a rigid diatomic ideal gas by 30 K at constant pressure. If the same heat Q is given to 4 mol of a monatomic ideal gas at constant volume, what is its rise in temperature?
1. A21 K
2. B35 K
3. C30 K
4. D25 K
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Answer: B · 35 K
Q = nCpΔT = 2(7R/2)(30) = 210R. For the monatomic gas, Cv = 3R/2, so ΔT = 210R/(4 × 3R/2) = 210/6 = 35 K.
- A: This uses Cp instead of Cv for the monatomic gas.
- C: This assumes equal heat means an equal temperature rise.
- D: This uses Cv instead of Cp for the diatomic gas.
Remember this
Choose Cp or Cv by the process and f by the molecule: Cv = fR/2, Cp = Cv + R.
Question 6 · Easy
A rigid diatomic molecule is drawn with three mutually perpendicular axes through its centre of mass. Rotation about which axis does NOT count as a degree of freedom?
Figure: MedExams
1. AAxis Q
2. BAxis R
3. CAxis P
4. DNo axis; all three count
Answer and explanation in LearnFree account
Question 7 · Hard
The partition between the two gases drawn is removed and they mix without reaction. Treating O₂ as a rigid diatomic gas, what is the ratio γ = Cp/Cv of the mixture?
Figure: MedExams
1. A22/15
2. B23/15
3. C7/5
4. D13/9
Answer and explanation in LearnFree account
Question 8 · Medium
Speeds of four gas molecules are shown in the bar chart. Determine their root mean square speed.
Figure: MedExams
1. A100 m/s
2. B300 m/s
3. C500 m/s
4. D250 m/s
Answer and explanation in LearnFree account
Question 9 · Hard
A sealed vessel holds 2 mol of oxygen and 4 mol of argon at absolute temperature T. Treating oxygen as a rigid diatomic gas and both as ideal, what is the total internal energy of the mixture? (R is the gas constant.)
1. A11RT
2. B15RT
3. C9RT
4. D13RT
Answer and explanation in LearnFree account
Question 10 · Medium
Under certain conditions a gas has a pressure of 1.0 × 10⁵ Pa and a density of 1.2 kg/m³. Treating it as ideal, what is the root mean square speed of its molecules?
1. A500 m/s
2. B289 m/s
3. C408 m/s
4. D250 m/s
Answer and explanation in LearnFree account
Question 11 · Easy
According to the kinetic theory of gases, the average kinetic energy of translation of a molecule of an ideal gas depends only on
1. AThe absolute temperature of the gas
2. BThe volume of the gas
3. CThe pressure of the gas
4. DThe mass of the molecule
Answer and explanation in LearnFree account
Question 12 · Medium
Given below are two statements: Statement I: At constant temperature, doubling the pressure of a gas halves the mean free path of its molecules. Statement II: At constant pressure, the mean free path of the molecules of a gas does not depend on its temperature. Choose the correct answer.
1. AStatement I is incorrect but Statement II is correct
2. BStatement I is correct but Statement II is incorrect
3. CBoth Statement I and Statement II are correct
4. DBoth Statement I and Statement II are incorrect
Answer and explanation in LearnFree account
Question 13 · Hard
At what temperature will hydrogen molecules have the same root mean square speed as oxygen molecules at 527 °C? (Molar masses: H₂ = 2 g/mol, O₂ = 32 g/mol)
1. A50 K
2. B200 K
3. C33 K
4. D12 800 K
Answer and explanation in LearnFree account
Question 14 · Medium
Assertion A: The molar specific heat of an ideal gas at constant pressure is greater than that at constant volume. Reason R: At constant pressure, part of the heat supplied is used by the gas to do work as it expands. Choose the correct answer.
1. AA is correct but R is not correct
2. BBoth A and R are correct and R is the correct explanation of A
3. CBoth A and R are correct but R is not the correct explanation of A
4. DA is not correct but R is correct
Answer and explanation in LearnFree account
Question 15 · Easy
The mean free path of molecules of diameter d in a gas of number density n is l = 1/(√2 nπd²). If the gas is compressed at constant temperature to half its volume, its mean free path
1. Adoubles
2. Bstays the same
3. Cbecomes one-fourth
4. Dbecomes half
Answer and explanation in LearnFree account
Question 16 · Medium
Consider ideal gases in equilibrium at absolute temperature T. A. The average translational kinetic energy of a molecule is (3/2)kT, where k is Boltzmann's constant, whatever the gas. B. At the same temperature, molecules of every gas have the same root mean square speed. C. The internal energy of n moles of a monatomic ideal gas is (3/2)nRT. D. For a diatomic gas with rigid molecules, the molar specific heat at constant volume is (5/2)R. Which of the statements given above are correct?
1. AA and C only
2. BB and D only
3. CA, C and D only
4. DA, B and C only
Answer and explanation in LearnFree account
Question 17 · Medium
The root mean square speed of the molecules of an ideal gas in a closed rigid vessel is doubled by heating. How do its absolute temperature and its pressure change?
1. ATemperature becomes four times; pressure doubles
2. BTemperature doubles; pressure becomes four times
3. CBoth double
4. DBoth become four times
Answer and explanation in LearnFree account
Question 18 · Easy
At a fixed temperature, the number of molecules per unit volume of a gas is doubled. Treating the molecules as hard spheres of fixed diameter, what happens to the mean free path?
1. AIt doubles
2. BIt becomes half
3. CIt stays the same
4. DIt becomes one-fourth
Answer and explanation in LearnFree account
Question 19 · Easy
According to the law of equipartition of energy, what is the average energy associated with each translational degree of freedom of a molecule in thermal equilibrium at absolute temperature T?
1. A(1/2)k_BT
2. B(3/2)k_BT
3. C(1/2)RT
4. Dk_BT
Answer and explanation in LearnFree account
Question 20 · Medium
For an ideal gas, the absolute temperature is doubled while the pressure is halved. By what factor does the mean free path of its molecules change?
1. AIt becomes 4 times
2. BIt becomes one-fourth
3. CIt stays the same
4. DIt doubles
Answer and explanation in LearnFree account
Question 21 · Medium
Molecules of a gas in a container have a root mean square speed of 1000 m/s, and the density of the gas is 0.3 kg/m³. What pressure does the gas exert on the walls?
1. A1.5 × 10⁵ Pa
2. B3.0 × 10⁵ Pa
3. C1.0 × 10² Pa
4. D1.0 × 10⁵ Pa
Answer and explanation in LearnFree account
Question 22 · Medium
Heat Q is supplied to a rigid diatomic ideal gas at constant pressure. What fraction of Q goes into increasing the internal energy of the gas?
1. A5/7
2. B7/5
3. C2/7
4. D3/5
Answer and explanation in LearnFree account
Question 23 · Medium
In a rigid vessel, the number of molecules of an ideal gas is doubled by pumping in more of the same gas, while its absolute temperature is halved. How does the pressure change?
1. AIt stays the same
2. BIt becomes four times
3. CIt becomes half
4. DIt doubles
Answer and explanation in LearnFree account
Question 24 · Hard
When heat is supplied to an ideal gas at constant pressure, one-fourth of it is used in doing work. The molecules are rigid, with only translational and rotational degrees of freedom. How many degrees of freedom does each molecule have?
1. A8
2. B4
3. C3
4. D6
Answer and explanation in LearnFree account

Kinetic Theory

Assertion A: Oxygen and nitrogen molecules in a gas mixture at one temperature have equal rms speeds. Reason R: The average translational kinetic energy per molecule of an ideal gas depends only on its temperature. Choose the correct answer.

The rms speed of oxygen molecules in a flask at 27 °C is v. What is it at 927 °C?

One mole of a monatomic ideal gas is mixed with one mole of a rigid diatomic ideal gas. What is the ratio of specific heats, γ, of the mixture?

A heat Q raises the temperature of 2 mol of a rigid diatomic ideal gas by 30 K at constant pressure. If the same heat Q is given to 4 mol of a monatomic ideal gas at constant volume, what is its rise in temperature?

A rigid diatomic molecule is drawn with three mutually perpendicular axes through its centre of mass. Rotation about which axis does NOT count as a degree of freedom?

The partition between the two gases drawn is removed and they mix without reaction. Treating O₂ as a rigid diatomic gas, what is the ratio γ = Cp/Cv of the mixture?

Speeds of four gas molecules are shown in the bar chart. Determine their root mean square speed.

A sealed vessel holds 2 mol of oxygen and 4 mol of argon at absolute temperature T. Treating oxygen as a rigid diatomic gas and both as ideal, what is the total internal energy of the mixture? (R is the gas constant.)

Under certain conditions a gas has a pressure of 1.0 × 10⁵ Pa and a density of 1.2 kg/m³. Treating it as ideal, what is the root mean square speed of its molecules?

According to the kinetic theory of gases, the average kinetic energy of translation of a molecule of an ideal gas depends only on

Given below are two statements: Statement I: At constant temperature, doubling the pressure of a gas halves the mean free path of its molecules. Statement II: At constant pressure, the mean free path of the molecules of a gas does not depend on its temperature. Choose the correct answer.

At what temperature will hydrogen molecules have the same root mean square speed as oxygen molecules at 527 °C? (Molar masses: H₂ = 2 g/mol, O₂ = 32 g/mol)

Assertion A: The molar specific heat of an ideal gas at constant pressure is greater than that at constant volume. Reason R: At constant pressure, part of the heat supplied is used by the gas to do work as it expands. Choose the correct answer.

The mean free path of molecules of diameter d in a gas of number density n is l = 1/(√2 nπd²). If the gas is compressed at constant temperature to half its volume, its mean free path

The root mean square speed of the molecules of an ideal gas in a closed rigid vessel is doubled by heating. How do its absolute temperature and its pressure change?

At a fixed temperature, the number of molecules per unit volume of a gas is doubled. Treating the molecules as hard spheres of fixed diameter, what happens to the mean free path?

According to the law of equipartition of energy, what is the average energy associated with each translational degree of freedom of a molecule in thermal equilibrium at absolute temperature T?

For an ideal gas, the absolute temperature is doubled while the pressure is halved. By what factor does the mean free path of its molecules change?

Molecules of a gas in a container have a root mean square speed of 1000 m/s, and the density of the gas is 0.3 kg/m³. What pressure does the gas exert on the walls?

Heat Q is supplied to a rigid diatomic ideal gas at constant pressure. What fraction of Q goes into increasing the internal energy of the gas?

In a rigid vessel, the number of molecules of an ideal gas is doubled by pumping in more of the same gas, while its absolute temperature is halved. How does the pressure change?

When heat is supplied to an ideal gas at constant pressure, one-fourth of it is used in doing work. The molecules are rigid, with only translational and rotational degrees of freedom. How many degrees of freedom does each molecule have?