enthalpy per unit mass)), and dV_k/dt are the rates of change of the volume of the system due to a moving boundary at position k while p_k is the pressure behind that boundary; P represents all other forms of power application (such as electrical).

The first and second law have been formulated in terms of time derivatives of U and S rather than in terms of total differentials dU and dS where it is tacitly assumed that dt > 0. So, the formulation in terms of time derivatives