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MHT CET 2024 (9 May, Shift 1) · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from MHT CET 2024 (9 May, Shift 1)

Q30MHT CET 2024 · 9 MAY · SHIFT 1Medium

Molecular Speeds & Maxwell Distribution

The temperature of a gas is $-80^\circ\text{C}$ . To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?

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Answer: (a)

$v_{rms} \propto \sqrt T$ ; to make $v_{rms}$ twice, $T$ must become 4 times.
$T_1 = -80 + 273 = 193\text{ K}$ , $T_2 = 4 \times 193 = 772\text{ K}$
$772 - 273 = 499^\circ\text{C}$
So the answer is (a) $499^\circ\text{C}$ .

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