d
$\rightarrow$ Given, $C=$ Molar Heat Capacity $=R$ $C_v$ for diatomic gas $=\frac{5}{2} R$
$P V^m=\text { constant }$
Molar Heat capacity is given by,
$C =C_V+\frac{R}{1-x} \quad\left(P V^x=\text { Const }\right)$
$R =\frac{S}{2} R+\frac{R}{1-m}$
$\frac{R}{1-m} =R-\frac{S}{2} R$
$\therefore \quad \frac{R}{m-1} =\frac{3}{2} R$
$2 =3(m-1) \quad \Rightarrow \quad \frac{2}{3}+1=m$
$\therefore m =\frac{5}{3}$
$\therefore$ The value of $m$ is $\frac{5}{3}$