We consider a thermodynamic system. If Δ U represents the increase...

An isothermal process is a constant temperature process. In this process, $$\begin{aligned} & T=\text{ constant or } \Delta T=0 . \\ \therefore & \Delta U=n C_V \Delta T=0\end{aligned}$$ An adiabatic process is defined as one with no heat transfer into or out of a system. Therefore, $Q=0$ From first law of thermodynamics $W=-\Delta U or \quad \Delta U=-W$