Show that the enthalpy, 𝐻 ≡ 𝐸 + 𝑃 𝑉, is the appropriate free energy for the case where the entropy and number of particl

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Show that the enthalpy, 𝐻 ≡ 𝐸 + 𝑃 𝑉, is the appropriate freeenergy for the case where the entropy and number of particles isfixed, but the volume can change. In this case we consider a systemconnected to a larger body such that the pressure of the systemequals that of the large body with the constraint that the largerbody and the system do not exchange energy. use cp = dp/dt,p is const. and cv = dE/DT, v is const.