For a quasi-static adiabatic process, δ δ Q = 0 so that Q = ∫ ∫ δ δ Q = 0. Also δ δ W = P d V so that W = ∫ ∫ δ δ W = ∫ ∫ P d V . It follows that d U = − − δ δ W so that Δ Δ U = − − ∫ ∫ P d V . Internal energy is a state function so its change depends only on the initial and final states of a process. For a quasi-static adiabatic process, the change in internal energy is equal to minus the integral amount of work done by the system, so the work also depends only on the initial and final states of the process and is one and the same for every intermediate path. As a result, the work done by the system also depends on the initial and final states.