One mole of an ideal monoatomic gas undergoes a process described by the equation $\rho$V³ = constant.
The heat capacity of the gas during this process is  

For polytropic process of index n,

specific heat capacity $=C_V+\frac{R}{1-n}$

$\because \text{ Process, }p{V}^3=\text{ constant }\Rightarrow n=3$

$\therefore C=C_V+\frac{R}{1-n}=\frac{fR}{2}+\frac{R}{1-3}$

For monoatomic gas, f = 3

So,      $C_V=\frac{fR}{2}=\frac{3R}{2}$

$\Rightarrow$$C=\frac{3R}{2}-\frac{R}{2}=R$