A vessel contains 14 g of nitrogen gas at a temperature of 27. The… | JEE Main 2022 (28 Jul, Shift 2)

Q58JEE Main 2022 · 28 JUL · SHIFT 2Difficult

Molecular Speeds & Maxwell Distribution

A vessel contains $14\text{ g}$ of nitrogen gas at a temperature of $27^\circ\text{C}$ . The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be:

Take $R = 8.32\text{ J mol}^{-1}\text{ K}^{-1}$ .

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Answer: (c)

$n = \dfrac{14}{28} = 0.5$ mol, $T_1 = 300$ K.
$v_{rms} \propto \sqrt{T}$ : doubling $v_{rms}$ needs $T_2 = 1200$ K, $\Delta T = 900$ K.
Heated in a closed vessel: $Q = nC_V\Delta T$ with $C_V = \dfrac{5}{2}R = 20.8$ J mol $^{-1}$ K $^{-1}$ .
$Q = 0.5 \times 20.8 \times 900 = 9360$ J
So the answer is (c) 9360 J.

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