Work done in an adiabatic process between two states depends on the

End states can be determined from the internal energy levels at those states. If we are considering a system S, the heat energy (dQ) can be used to do work (dW) or to store energy as potential energy (dU).
$${\text{dQ}} = {\text{dW}} + {\text{dU}}$$
The interesting thing is that, for an adiabatic process dQ will be zero. So, the work done in an adiabatic process depends only on the internal energy. i.e. end states.