“–∆G is the maximum useful work, such as electrical work, available from the net process carried out along the reversible path under special constraints. These constraints consist of the same temperature and the same pressure at the beginning and the end of the process, often misleadingly called constant temperature and pressure.”

The assertion should give a jolt of surprise to the watchful chemist, because most of the chemical thermodynamics textbooks say that the useful work of a reversible process is numerically equal to ∆G if the process is carried out at constant temperature and constant pressure, the same as a heat reservoir R and maintained by a manostat MS, respectively, present in the environment interacting with the system. That is under considerably more restrictive conditions than mentioned in the above sentence. Further, it appears difficult to understand how a process can be reversible if heat exchanges take place between a system of variable temperature and a thermal reservoir of fixed temperature.

For the cited sentence to be correct, two hypotheses are necessary (2):

1. Any heat exchange should take place only with a single heat reservoir that has the fixed temperature T_R equal to that of the system at the beginning (T_I) and the end (T_F) of the process;
2. Any heat exchange should be carried out reversibly, that is, using a reversible thermal (for instance Carnot) engine performing a whole number of cycles.

The second condition is surely not the common way of heat exchange, normally carried out just through a diatermic wall, without the intervention of one or more reversible thermal engines. The fixed temperature of the heat reservoir and the fixed pressure imposed by the manostat mimic the “room” temperature and pressure, where any system begins and at last ends its processes. If we are interested in this more realistic process, where T_I = T_F = T_R and P_I = P_F = P_MS, we are sent back to the “misleading” constant temperature and pressure, equal, respectively, to the fixed temperature T_R of the single heat reservoir and the fixed pressure P_MS of the manostat.

Thus, I think that the words “often misleadingly called” should more appropriately read “or, if heat exchanges are carried out only through diatermic walls (rather than by means of reversible thermal engines),”.

Literature Cited

1. Craig, N. C. J. Chem. Educ. 2005, 82, 827–828.
2. For instance, see: Beattie, J. A.; Oppenheim, I. Principles of Thermodynamics; Elsevier: Amsterdam, 1979; p 200.

See the author's reply.