In a thermodynamic process helium gas obeys the law $T{P}^{-2/5}=$constant. If temperature of $2$ moles of the gas is raised from $T$ to $3T$, then

The given process can be written as $\left(PV\right)P^{-\frac{2}{5}}=cons\tan t \Rightarrow P{V}^{\frac{5}{3}}=cons\tan t .For helium \gamma =\frac{5}{3 }. So the given process is adiabatic .$

In adiabatic process $∆Q=0$

$$\begin{gathered} ∆U=n{c}_v∆T=2\left(\frac{3}{2}R\right)\left(3T-T\right)=6RT \\ ∆W=-∆U=-6RT \end{gathered}$$