Question

An ideal diatomic gas $(\gamma =\frac{7}{5})$ undergoes a process in which its internal energy relates to the volume as $U=\alpha \sqrt{V}$, where $\alpha$ is a constant. Find the molar specific heat of the gas.

Answer 1

Given : For diatomic gas $\gamma =\frac{7}{5}=1.4$

The process is $U=\alpha \sqrt{V}$

$\therefore$ $\frac{f}{2}RT=\alpha \sqrt{V}$

$⟹$ $T^2{V}^{-1}=K=constant$

OR $T{V}^{-1/2}=K^{\prime }=constant$

Comparing with $T{V}^{m-1}=constant$ we get $m-1=-\frac{1}{2}$

$⟹m=\frac{1}{2}$

$\therefore$ Molar heat capacity of the gas $C=\frac{R}{\gamma -1}+\frac{R}{1-m}$

$C=\frac{R}{1.4-1}+\frac{R}{1-0.5}=\frac{9}{2}R$