First slide

Rms speed

Question

The temperature of an ideal gas increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is y, at 480 K it becomes

Moderate

A

4 v
B

2 v
C

v/2
D

v/4

Solution

$C_{rms} = \sqrt{(\frac{3 RT}{M})} or C_{rms} \propto \sqrt{T} \begin{array}{l} ∴ (C_{rms}) T_{1} = {(C_{rms})}_{T_{1}} \times \sqrt{(T_{2} / T_{1})} \\ = V \times \sqrt{(480 / 120)} = 2 v \end{array}$

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