During thermodynamic process, the increase in internal energy of a system is equal to the work done on the system. Which process does the system undergo?

The First Law of Thermodynamics states that the change in internal energy ΔU equals the heat added to the system Q plus the work done on the system W: $\Delta U = Q + W$.

Given that ΔU = W, substitution yields $W = Q + W$, which simplifies to $Q = 0$. A process with no heat exchange (Q = 0) is adiabatic.

Other processes are incompatible: isothermal implies $\Delta U = 0$ but not necessarily W = 0; isochoric gives W = 0 but not necessarily $\Delta U = 0$; isobaric has no inherent constraint linking ΔU and W.

The process is adiabatic, corresponding to option B.