An ideal gas with  $\gamma$=4/3 undergoes a process in which internal energy is related to volume as $U=V^2$, then $P{V}^x then x is equal to$

$\begin{array}{l}\mathrm{given} \mathrm{U}={\mathrm{V}}^2; \\ \mathrm{we} \mathrm{know} \mathrm{U}=\frac{\mathrm{nRT}}{\mathrm{\gamma }-1} \mathrm{substitute} \mathrm{in} \mathrm{given} \mathrm{relation}\\ \frac{nRT}{\gamma -1}=V^2\\ \Rightarrow \frac{PV}{\frac{4}{3}-1}=V^2\end{array}$

$\begin{array}{l}\Rightarrow P \alpha V\\ \Rightarrow {\mathrm{PV}}^{-1}=\text{ constant }\\ compare with P{V}^x=cons\tan t\Rightarrow \mathrm{x}=-1;given \gamma =\frac{4}{3}\end{array}$

$\begin{array}{r}substitute in C=\frac{R}{\gamma -1}+\frac{R}{1-x}\\ C=\frac{R}{\frac{4}{3}-1}+\frac{R}{1-(-1)}=3R+0.5R\\ \end{array}$

$C=3.5R$