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MHT CET 2023 (14 May, Shift 1) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from MHT CET 2023 (14 May, Shift 1)

Q41MHT CET 2023 · 14 MAY · SHIFT 1Medium

Molecular Speeds & Maxwell Distribution

The temperature of a gas is $-68^\circ\text{C}$ . To what temperature should it be heated, so that the r.m.s. velocity of the molecules be doubled?

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Answer: (c)

$v_{rms} \propto \sqrt T$ ; doubling $v_{rms}$ needs $T_2 = 4T_1$ .
$T_1 = -68 + 273 = 205\text{ K}$ , $T_2 = 820\text{ K}$
$820 - 273 = 547^\circ\text{C}$
So the answer is (c) $547^\circ\text{C}$ .

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