Heat and Thermodynamics 4 Question 27
29. The temperature of an ideal gas is increased from $120 K$ to $480 K$. If at $120 K$ the root mean square velocity of the gas molecules is $v$, at $480 K$ it becomes
(1996, 2M)
(a) $4 v$
(b) $2 v$
(c) $v / 2$
(d) $v / 4$
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Solution:
$$ \begin{aligned} & v _{rms}=\sqrt{\frac{3 R T}{M}} \\ & v _{rms} \propto \sqrt{T} \end{aligned} $$
When temperature is increased from $120 K$ to $480 K$ (i.e. four times), the root mean square speed will become $\sqrt{4}$ or 2 times i.e. $2 v$.
