U=q+w U is the total kinetic and potential energy of the system. H=U+PV Enthalpy is the internal energy of the system, plus how much energy it takes to set up the system. I don't understand how the PV term from enthalpy is not included in the internal energy. It seems like it would be a part of the potential energy. For example, at constant pressure I heat a gas and it expands. q=H in this case. To calculate U, you have to add the work that it took to change the volume to q. Why? Why is the work used for the w in U=q+w but not in the PV from H=U+PV? It looks like w is used in the U calculation because it would be part of the new potential energy of the gas. But that work was done to set up the system, so why isn't it used in calculating enthalpy? Do you see what my confusion is arising from here?