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MHT CET 2023 (13 May, Shift 2) · Pressure & Kinetic Energy of a Gas

Pressure & Kinetic Energy of a Gas question from MHT CET 2023 (13 May, Shift 2)

Q24MHT CET 2023 · 13 MAY · SHIFT 2Medium

Pressure & Kinetic Energy of a Gas

A gas at pressure $p_0$ is contained in a vessel. If the masses of all the molecules are halved and their velocities are doubled, then the resulting pressure would be equal to

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Answer: (b)

$P = \frac{1}{3}\frac{N m v_{rms}^2}{V}$ , so $P \propto m v^2$ .
$m \to \frac{m}{2}$ , $v \to 2v$ : $mv^2 \to \frac{m}{2} \times 4v^2 = 2mv^2$
$P = 2p_0$
So the answer is (b) $2p_0$ .

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