Question:medium

If the heat required to increase the rms speed of 4 moles of a diatomic gas from $v$ to $\sqrt{3}v$ is $83.1\,\mathrm{kJ}$, then the initial temperature of the gas is (Universal gas constant $= 8.31\,\mathrm{J\,mol^{-1}\,K^{-1}}$)

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RMS speed depends only on temperature ($v_{rms} = \sqrt{3RT/M}$). Increasing speed by factor $k$ requires temperature to increase by factor $k^2$.

Updated On: Mar 26, 2026

$377\,^\circ\mathrm{C}$
$327\,^\circ\mathrm{C}$
$227\,^\circ\mathrm{C}$
$277\,^\circ\mathrm{C}$

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The Correct Option is C

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