Select the correct statement. (a) The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. (b) The temperature of gas is -73. When the gas is heated to 527, the r.m.s. speed of the molecules is doubled. (c) The temperature of gas is -100. When the gas is heated to +627, the r.m.s. speed of the molecules is four times. (d) The product of pressure and volume of an ideal gas will be equal to half the translational kinetic energy.

Answer: (b). PV = 2/3Etrans, so (a) and (d) are wrong. (b): T₁ = 200 K, T₂ = 800 K; vrms ∝ √ T gives √(4) = 2 times. Correct. (c): T₁ = 173 K, T₂ = 900 K; ratio √(900/173) ≈ 2.3, not 4. Wrong. So the answer is (b).

Select the correct statement. | MHT CET 2025 (23 Apr, Shift 2)

Q19MHT CET 2025 · 23 APR · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

Select the correct statement.

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Answer: (b)

$PV = \frac{2}{3}E_{trans}$ , so (a) and (d) are wrong.
(b): $T_1 = 200\text{ K}$ , $T_2 = 800\text{ K}$ ; $v_{rms} \propto \sqrt T$ gives $\sqrt{4} = 2$ times. Correct.
(c): $T_1 = 173\text{ K}$ , $T_2 = 900\text{ K}$ ; ratio $\sqrt{900/173} \approx 2.3$ , not 4. Wrong.
So the answer is (b).

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Molecular Speeds & Maxwell Distribution question from MHT CET 2025 (23 Apr, Shift 2)

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