Page 106 - Modern physical chemistry

96 Entropy and the Second Law

Function G is called the Gibbs free energy. Any increase in it during a process at con-
stant T and P may reappear as net work when the process is reversed.
During an irreversible process, dissipation of work into heat occurs. At constant tem-
perature and pressure, we have
dWnet > dWnet,rev, [5.68]
Combining inequality (5.68) with equality (5.65) yields

[5.69]
A spontaneous process does not require any net work to be done on the system. Then
(5.69) reduces to
dGT,p ~O. [5.70]
At constant temperature and pressure, the Gibbs free energy of a system decreases
spontaneously until it can decrease no more and equilibrium is reached. The condition
for equilibrium is that
dGT,p =0 [5.71 ]

for possible small changes.

Example 5.5

Calculate M and AG for the vaporization of 1 mole water at 372.778 K and 1 bar pres-
sure, where the heat of vaporization is 40,893 J mo!"l.
The increments of
A=E-TS and G=H-TS
at constant temperature are

M=AE-TAS and !).G = m - TAS.
But with equation (5.23),

with equation (4.13),
AE=qp +Wp,

and with formula (4.27),
m=qp,
we find that
M=qp +Wp -qp =Wp
and
AG=qp-qp=OJ.
The work done was estimated in example 4.3 as

Wp =-3099J.
So
M=-3099J.

5.11 Key Thermodynamic Relations
Let us now summarize the main conditions relating the thermodynamic properties of
a system when no material moves in or out and when no reaction occurs.