When a quantity of heat ‘Q’ is supplied to a monoatomic gas work done by the gas is $\frac{\mathrm{Q}}{4}$ . Molar heat capacity of the gas in that process is

if $\frac{\mathrm{Q}}{4}$  heat is the  work done then
$\frac{3\mathrm{Q}}{4}$  is the heat for internal energy
$\frac{3\mathrm{Q}}{4}={\mathrm{nC}}_{\mathrm{v}}\mathrm{dT}$
$\frac{3\mathrm{Q}}{4}=\mathrm{n}\frac{3\mathrm{R}}{2}\mathrm{dT}$  (monoatomic gas)
$\left(\frac{\mathrm{Q}}{\mathrm{ndT}}\right)\to$   molar specific heat - $\frac{\mathrm{Q}}{\mathrm{ndT}}=2\mathrm{R}$