In Sec. 5.4.1, we explained the experimental meaning of the free energy F for a system in contact with a heat bath so its temperature is held constant, and in Ex. 5.5h we did the same for contact with a pressure bath. By combining these, give an experimental interpretation of the Gibbs potential Gas the free energy for a system in contact with a heat and pressure bath—the “chemical free energy.”

Data from Exercises  5.5h.

(h) As another interpretation of the enthalpy, think of the system as enclosed in an impermeable box of volume V . Inject into the box a “sample” of additional material of the same sort as is already there. (It may be helpful to think of the material as a gas.) The sample is to be put into the same thermodynamic state (i.e.,macrostate) as that of the box’s material (i.e., it is to be given the same values of temperature T , pressure P, and chemical potential μ̃). Thus, the sample’s material is indistinguishable in its thermodynamic properties from the material already in the box, except that its extensive variables (denoted by △) are far smaller:

Perform the injection by opening up a hole in one of the box’s walls, pushing aside the box’s material to make a little cavity of volume △V equal to that of the sample, inserting the sample into the cavity, and then closing the hole in the wall. The box now has the same volume V as before, but its energy has changed. Show that the energy change (i.e., the energy required to create the sample and perform the injection) is equal to the enthalpy △H of the sample. Thus, enthalpy has the physical interpretation of energy of injection at fixed volume V . Equivalently, if a sample of material is ejected from the system, the total energy that will come out (including the work done on the sample by the system during the ejection) is the sample’s enthalpy △H. From this viewpoint, enthalpy is the system’s free energy.

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ΔV/V = Δε/ε = ΔS/S « 1.