Question
Derive a relationship between ∆H and ∆U.
Solution
Let H1 be the enthalpy of a system in the initial state and H2 be the enthalpy of a system in the final state. Let U1 and V1 be the internal energy and volume in the initial state and let U2 and V2 be the corresponding values in the final state.

Subtracting (1) from (2), we have,

In the above expression ∆U represents a change in internal energy and P∆V represents a change in work energy.
Thus, the change in enthalpy at constant pressure is equal to the increase in internal energy plus pressure-volume work done (work energy).

Subtracting (1) from (2), we have,

In the above expression ∆U represents a change in internal energy and P∆V represents a change in work energy.
Thus, the change in enthalpy at constant pressure is equal to the increase in internal energy plus pressure-volume work done (work energy).