Physical Chemistry Third Edition

154 4 The Thermodynamics of Real Systems

IfTandPare constant, this equation becomes

dGdU+PdV−TdS (TandPconstant) (4.1-16)

The relation in Eq. (4.1-12) is the same as

dG≤0 (simple system,TandPconstant) (4.1-17)

The criteria for finite processes are completely analogous to those for infinitesimal

processes. For example, for a simple system at constant pressure and temperature,

a finite spontaneous process must obey

∆G≤0 (simple system,TandPconstant) (4.1-18)

Constant temperature and pressure are the most common circumstances in the lab-

oratory, so Eq. (4.1-18) is the most useful criterion for the spontaneity of chemical

reactions. Thermodynamics does not distinguish between chemical and physical pro-

cesses, and Eq. (4.1-17) is valid for physical processes such as phase transitions as well

as for chemical reactions.

In the 19th century, Berthelot incorrectly maintained that all spontaneous chemical

reactions must beexothermic(∆H<0). The incorrectness of Berthelot’s conjecture

was shown by Duhem, who established Eq. (4.1-18), which can be written in the form

∆H−T∆S≤ 0

(simple system,

TandPconstant)

(4.1-19)

The∆Hterm dominates at sufficiently low temperature, but theT∆Sterm becomes

important and can dominate at sufficiently high temperature. In many chemical reac-

tions near room temperature theT∆Sterm is numerically less important than the∆H

term, and most spontaneous chemical reactions are exothermic, a fact that presumably

led Bertholet to his thermodynamically incorrect assertion.

Pierre Eugene Marcelin Berthelot,
1827–1907, was a French chemist who
synthesized many useful compounds,
but who argued against Dalton’s atomic
theory of matter.

Pierre-Maurice-Marie Duhem,
1861–1916, was a French physicist
whose doctoral dissertation showing
Berthelot’s conjecture to be false was
initially rejected because of Berthelot’s
objection.

We can illustrate the interplay of∆Hand∆Swith the vaporization of a liquid, for

which∆Hand∆Sare both positive. At a given pressure there is some temperature at

which the vaporization is a reversible process so that∆G0 and∆HT∆S. When

Tis smaller than this equilibrium temperature, the∆Hterm dominates and∆G> 0

for the vaporization process. That is, condensation is spontaneous and the equilibrium

phase is the liquid phase. At a higher temperature theT∆Sterm dominates and∆G< 0

for the vaporization process, which is spontaneous. The gas phase is the equilibrium

phase.

Some people say that there are two tendencies: (1) that of the enthalpy or energy

of a system tends to decrease, and (2) that the entropy of the system tends to increase.

In fact, there is only one fundamental tendency, that of the entropy of the universe to

increase. We can separately focus on the two terms in Eq. (4.1-19), but you should

remember that the lowering of the enthalpy corresponds to an increase in the entropy

of the surroundings.

We summarize our results for the cases considered:

1. If a system is isolated, its entropy cannot decrease.


2. IfSof a closed system is fixed and no work is done,Ucannot increase.


3. If a simple closed system is at constantTandV, Acannot increase.


4. If a simple closed system is at constantTandP, Gcannot increase.