Question

If P-V diagram of a diatomic gas is plotted, it is a straight line passing through origin. The molar heat capacityof the gas in the process is $nR$, where $n$ is an integer, then the value of $n$ is

Answer 1

The molar heat capacity is given by,
$C=nR$
In general $C$ is given by
$C=\frac{R}{\gamma -1}+\frac{R}{1-x}$______(1)

Equating them we get,
$n=\frac{1}{\gamma -1}+\frac{1}{1-x}$

From graph we conclude,
$P\propto V$
$P=CV$
$P{V}^{-1}=C$
In general, $P{V}^x=C$
$\therefore x=-1$
For a diatomic gas $\gamma =1.4$

Substituting in (1) we get, $n=3$