154
4 The Thermodynamics of Real Systems
If T and P are constant, this equation becomes
dG dU + PdV − TdS (T and P constant)
(4.1-16)
The relation in Eq. (4.1-12) is the same as
dG ≤ 0 (simple system, T and P constant)
(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, T and P constant)
(4.1-18)
Constant temperature and pressure are the most common circumstances in the laboratory, so Eq. (4.1-18) is the most useful criterion for the spontaneity of chemical
reactions. Thermodynamics does not distinguish between chemical and physical processes, 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 be exothermic (∆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,
T and P constant)
(4.1-19)
The ∆H term dominates at sufficiently low temperature, but the T ∆S term becomes
important and can dominate at sufficiently high temperature. In many chemical reactions near room temperature the T ∆S term 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 ∆H and ∆S with the vaporization of a liquid, for
which ∆H and ∆S are both positive. At a given pressure there is some temperature at
which the vaporization is a reversible process so that ∆G 0 and ∆H T ∆S. When
T is smaller than this equilibrium temperature, the ∆H term 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 the T ∆S term 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. If S of a closed system is fixed and no work is done, U cannot increase.
3. If a simple closed system is at constant T and V, A cannot increase.
4. If a simple closed system is at constant T and P, G cannot increase.
4 The Thermodynamics of Real Systems
If T and P are constant, this equation becomes
dG dU + PdV − TdS (T and P constant)
(4.1-16)
The relation in Eq. (4.1-12) is the same as
dG ≤ 0 (simple system, T and P constant)
(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, T and P constant)
(4.1-18)
Constant temperature and pressure are the most common circumstances in the laboratory, so Eq. (4.1-18) is the most useful criterion for the spontaneity of chemical
reactions. Thermodynamics does not distinguish between chemical and physical processes, 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 be exothermic (∆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,
T and P constant)
(4.1-19)
The ∆H term dominates at sufficiently low temperature, but the T ∆S term becomes
important and can dominate at sufficiently high temperature. In many chemical reactions near room temperature the T ∆S term 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 ∆H and ∆S with the vaporization of a liquid, for
which ∆H and ∆S are both positive. At a given pressure there is some temperature at
which the vaporization is a reversible process so that ∆G 0 and ∆H T ∆S. When
T is smaller than this equilibrium temperature, the ∆H term 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 the T ∆S term 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. If S of a closed system is fixed and no work is done, U cannot increase.
3. If a simple closed system is at constant T and V, A cannot increase.
4. If a simple closed system is at constant T and P, G cannot increase.