Page 134 - Physical Chemistry

lev38627_ch04.qxd 2/29/08 3:13 PM Page 115

115
manner, then dw PdV dw ; Eq. (4.23) becomes dG dw or G Section 4.4
non-P-V non-P-V
w w . Therefore Thermodynamic Relations for a
non-P-V by,non-P-V System in Equilibrium
¢G w non-P-V and w by,non-P-V ¢G const. T and P, closed syst. (4.24)
For a reversible change, the equality sign holds and w G. In many cases
by,non-P-V
(for example, a battery, a living organism), the P-V expansion work is not useful work,
but w is the useful work output. The quantity G equals the maximum possi-
by,non-P-V
ble nonexpansion work output w done by a system in a constant-T-and-P
by,non-P-V
process. Hence the term “free energy.” (Of course, for a system with P-V work only,
dw 0 and dG 0 for a reversible, isothermal, isobaric process.) Examples of
by,non-P-V
nonexpansion work in biological systems are the work of contracting muscles and of
transmitting nerve impulses (Sec. 13.15).

Summary
The maximization of S leads to the following equilibrium conditions. When a
univ
closed system capable of only P-V work is held at constant T and V, the condition for
material equilibrium (meaning phase equilibrium and reaction equilibrium) is that the
Helmholtz function A (defined by A U TS) is minimized. When such a system is
held at constant T and P, the material-equilibrium condition is the minimization of the
Gibbs function G H TS.

4.4 THERMODYNAMIC RELATIONS FOR A SYSTEM
IN EQUILIBRIUM
The last section introduced two new thermodynamic state functions, A and G. We shall
apply the conditions (4.18) and (4.19) for material equilibrium in Sec. 4.6. Before doing
so, we investigate the properties of A and G. In fact, in this section we shall consider the
broader question of the thermodynamic relations between all state functions in systems
in equilibrium. Since a system undergoing a reversible process is passing through only
equilibrium states, we shall be considering reversible processes in this section.
Basic Equations
All thermodynamic state-function relations can be derived from six basic equations.
The first law for a closed system is dU dq dw. If only P-V work is possible, and if
the work is done reversibly, then dw dw PdV. For a reversible process, the re-
rev
lation dS dq /T [Eq. (3.20)] gives dq dq T dS. Hence, under these conditions,
rev rev
dU TdS PdV. This is the first basic equation; it combines the first and second laws.
The next three basic equations are the definitions of H, A, and G [Eqs. (2.45), (4.14), and
(4.17)]. Finally, we have the C and C equations C dq /dT (
U/
T) and C
P V V V V P
dq /dT (
H/
T ) [Eqs. (2.51) to (2.53)]. The six basic equations are
P P
dU T dS P dV closed syst., rev. proc., P-V work only (4.25)*
H U PV (4.26)*
A U TS (4.27)*

G H TS (4.28)*
0U
C a b closed syst. in equilib., P-V work only (4.29)*
V
0T V
0H
C a b closed syst. in equilib., P-V work only (4.30)*
P
0T P