Physics - Heat & Thermo Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{dQ}=\mathrm{du}+\mathrm{dW}\\ & \mathrm{CdT}={\mathrm{C}}_{\mathrm{V}}\mathrm{dT}+\mathrm{PdV}\\ & \therefore {\mathrm{PV}}^2=\mathrm{RT}\\ & \mathrm{P}=\text{ constant }\\ & \mathrm{P}(2\mathrm{VdV})=\mathrm{RdT}\\ & \mathrm{PdV}=\frac{\mathrm{RdT}}{2\mathrm{V}}\\ & \end{array}$
Put in equation (1) $\mathrm{C}={\mathrm{C}}_{\mathrm{V}}+\frac{\mathrm{R}}{2\mathrm{V}}$