One mole of an ideal monoatomic gas undergoes a process described by the equation $P{V}^3=\mathrm{constant}$ constant. The heat capacity of the gas during this process is

Process described by PV^x = constant is a polytropic process.
Here, x = 3.
The heat capacity in a polytropic process is given by

$\mathrm{C}={\mathrm{C}}_{\mathrm{v}}+\frac{\mathrm{R}}{1-\mathrm{x}}$

$(\because \text{The gas is monoatomic,}{C}_v=\frac{3}{2}R)$

$\Rightarrow C=\frac{3}{2}R+\frac{R}{(1-3)}$

$=\frac{3\mathrm{R}}{2}-\frac{\mathrm{R}}{2}=\mathrm{R}$