Let Hi be the enthalpy of a system in the initial state and Hf be the enthalpy of a system in the final state.
Let Ui and Vi be the internal energy and volume in the initial state and Uf and Vf be the internal energy and volume in the final state.
Now, as we know that, H=U+PV
Therefore, Hi=Ui+PVi …..(1)
Hf = Uf + PVf …..(2)
Subtracting equation (1) from (2),
we have Hf − Hi= (Uf + PVf) − (Ui+PVf)
⇒ Hf − Hi = (Uf−Ui) + P(Vf−Vi)
⇒ ΔH = ΔU + PΔV …..(3)
Here, ΔU and PΔV are the change in internal energy and work-energy, respectively.
Hence, equation (3) is the relationship between H and U.