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

8 NEET-UG practice questions on Kinetic Theory, part of Physics. The first 8 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

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.