4.1 Criteria for Spontaneous Processes and for Equilibrium: The Gibbs and Helmholtz Energies
157
In the case of constant temperature and constant pressure with P equal to P(transmitted), Eq. (4.1-24) is
dU − TdS + PdV − dw net dG − dw net ≤ 0 (T and P constant)
dG ≤ dw net (T and P constant)
(4.1-31)
For a finite process
∆G ≤ w net (T and P constant)
(4.1-32)
It is possible to increase the Gibbs energy of a nonsimple system at constant T and P
by doing net work on the system, but the increase in the Gibbs energy cannot be greater
than the net work done on the system. In electrolysis or charging a battery, a chemical
reaction is caused to proceed in the nonspontaneous direction (the direction of increase
of the Gibbs energy) by passing an electric current through an electrochemical cell,
performing net work.
A nonsimple system can do work on the surroundings by lowering its Gibbs energy,
but Eq. (4.1-31) provides a limit to the net work that can be done on the surroundings:
dw net,surr ≤ −dG (T and P constant)
(4.1-33)
For a finite process,
w net,surr ≤ −∆G (T and P constant)
(4.1-34)
To do net work on the surroundings at constant T and P, a process with a negative
value of ∆G must be found.
Equilibrium Criteria for Nonsimple Systems
If a system at equilibrium undergoes an infinitesimal change at constant T and V ,
dA − dw net 0
(equilibrium,
constant T and V )
(4.1-35)
In the case of constant T and P,
dG − dw net 0
(equilibrium,
constant T and P)
(4.1-36)
The equilibrium state of a nonsimple system is affected by the agent that can do net
work on it. For example, a galvanic cell such as a lead storage battery has an equilibrium
state that depends on the external voltage applied to it. With an external voltage you
can charge a lead storage battery to an equilibrium state with large amounts of reactants
(Pb, PbO 2 , and H 2 SO 4 ). If you remove the external voltage and attach a short circuit,
the battery will tend toward an equilibrium state in which the battery is fully discharged
and the reactants are depleted, leaving a large amount of products (PbSO 4 ).
157
In the case of constant temperature and constant pressure with P equal to P(transmitted), Eq. (4.1-24) is
dU − TdS + PdV − dw net dG − dw net ≤ 0 (T and P constant)
dG ≤ dw net (T and P constant)
(4.1-31)
For a finite process
∆G ≤ w net (T and P constant)
(4.1-32)
It is possible to increase the Gibbs energy of a nonsimple system at constant T and P
by doing net work on the system, but the increase in the Gibbs energy cannot be greater
than the net work done on the system. In electrolysis or charging a battery, a chemical
reaction is caused to proceed in the nonspontaneous direction (the direction of increase
of the Gibbs energy) by passing an electric current through an electrochemical cell,
performing net work.
A nonsimple system can do work on the surroundings by lowering its Gibbs energy,
but Eq. (4.1-31) provides a limit to the net work that can be done on the surroundings:
dw net,surr ≤ −dG (T and P constant)
(4.1-33)
For a finite process,
w net,surr ≤ −∆G (T and P constant)
(4.1-34)
To do net work on the surroundings at constant T and P, a process with a negative
value of ∆G must be found.
Equilibrium Criteria for Nonsimple Systems
If a system at equilibrium undergoes an infinitesimal change at constant T and V ,
dA − dw net 0
(equilibrium,
constant T and V )
(4.1-35)
In the case of constant T and P,
dG − dw net 0
(equilibrium,
constant T and P)
(4.1-36)
The equilibrium state of a nonsimple system is affected by the agent that can do net
work on it. For example, a galvanic cell such as a lead storage battery has an equilibrium
state that depends on the external voltage applied to it. With an external voltage you
can charge a lead storage battery to an equilibrium state with large amounts of reactants
(Pb, PbO 2 , and H 2 SO 4 ). If you remove the external voltage and attach a short circuit,
the battery will tend toward an equilibrium state in which the battery is fully discharged
and the reactants are depleted, leaving a large amount of products (PbSO 4 ).