A perfect gas of volume 5 litre is compressed isothermally to volume of 1 litre. The r.m.s. speed of the molecules will (a) increase by 10 times (b) decrease by 10 times (c) increase by 5 times (d) remain unchanged

Answer: (d). vrms = √(3RT/M) depends only on T, not on volume. Isothermal: T is unchanged, so vrms is unchanged. So the answer is (d) remain unchanged.

A perfect gas of volume 5 litre is compressed isothermally to volume… | MHT CET 2024 (4 May, Shift 2)

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Thermodynamic Processes

A perfect gas of volume 5 litre is compressed isothermally to volume of 1 litre. The r.m.s. speed of the molecules will

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Answer: (d)

$v_{rms} = \sqrt{\frac{3RT}{M}}$ depends only on $T$ , not on volume.
Isothermal: $T$ is unchanged, so $v_{rms}$ is unchanged.
So the answer is (d) remain unchanged.

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