A gas is expanded from an initial state to a final state along a path on a $P-V$ diagram. The path consists of (i) an isothermal expansion of work $50 \mathrm{J}$, (ii) an adiabatic expansion and (iii) an isothermal expansion of work $20 \mathrm{J}$. If the internal energy of gas is changed by $-30 \mathrm{J}$, then the work done by gas during adiabatic expansion is

Internal energy is a state function and the change in the internal energy is zero for isothermal process.

In the given information, two processes are isothermal and one process is adiabatic. Therefore, the net change in the internal energy is equal to the change in the internal energy during the adiabatic process. Therefore,

$∆U_{\mathrm{adiabatic}}=-30 \mathrm{J}$

For adiabatic process $∆Q=0$. Therefore,

$$\begin{gathered} ∆U_{\mathrm{adiabatic}}=-W_{\mathrm{adiabatic}} \\ \Rightarrow W_{\mathrm{adiabatic}}=30 \mathrm{J} \end{gathered}$$