Question

$P-V$ diagram of an ideal diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process is $x R$. Find $x$. (Here $R=$ Universal gas constant)

Answer 1

$P-V$ graph is a straight line passing through origin.
$\therefore P \propto V $
$P V^{-1}=$ Constant
Polytropic index, $m=-1$
$C=\frac{R}{\gamma-1}+\frac{R}{-m+1}$
$C=\frac{R}{1.4-1}+\frac{R}{1-(-1)}=x R$
$\therefore x=3$