32
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
the probability of a given state. Boltzmann's fundamental equation expresses this relation:
S = RlnP
(38)
A state in which the molecules are assigned to definite locations is
highly improbable and would be characterized by low entropy. We
may, therefore, regard entropy as a direct measure of the randomness
of a system.
We are now prepared to make a precise statement of the Second
Law in the most general terms: "Every system, left to itself, will, on
the average, change toward a condition of maximum probability" (2).
All real processes are accompanied by an increase in entropy. The
extent of increase depends upon the energy and volume of the system.
This can be seen most simply from the following argument: the change
in entropy for a process is defined as
dS Ϊ dQ/T
(39)
where the inequality sign refers to a real process. From the First law,
e.g.,
dE = dQ + dW
one sees that
dQ
, σ ^dE + dW
-ψ = ab £
ψ
or
TdS^
dE + dW
(40)
If for a given process E is constant, then dE = 0. If no work is done
against an external pressure, then dW = 0. A sufficient condition for
dW to equal zero is for V to be constant. Writing these conditions as
subscripts, we have
(dS) E ,v Ϊ 0
(41)
Thus it is that the entropy of a system increases spontaneously until it
is a maximum consistent with the energy and volume of the system.
Stated in other words, the entropy of a system at equilibrium is a
maximum at constant energy and volume. This obviously provides a
criterion for equilibrium.
2. Statistical Nature of the Second Law
The Second Law considered from a molecular-kinetic point of view
is a statistical law. It expresses the tendency toward randomness or disorder in a system which consists of a large number of particles. As an
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
the probability of a given state. Boltzmann's fundamental equation expresses this relation:
S = RlnP
(38)
A state in which the molecules are assigned to definite locations is
highly improbable and would be characterized by low entropy. We
may, therefore, regard entropy as a direct measure of the randomness
of a system.
We are now prepared to make a precise statement of the Second
Law in the most general terms: "Every system, left to itself, will, on
the average, change toward a condition of maximum probability" (2).
All real processes are accompanied by an increase in entropy. The
extent of increase depends upon the energy and volume of the system.
This can be seen most simply from the following argument: the change
in entropy for a process is defined as
dS Ϊ dQ/T
(39)
where the inequality sign refers to a real process. From the First law,
e.g.,
dE = dQ + dW
one sees that
dQ
, σ ^dE + dW
-ψ = ab £
ψ
or
TdS^
dE + dW
(40)
If for a given process E is constant, then dE = 0. If no work is done
against an external pressure, then dW = 0. A sufficient condition for
dW to equal zero is for V to be constant. Writing these conditions as
subscripts, we have
(dS) E ,v Ϊ 0
(41)
Thus it is that the entropy of a system increases spontaneously until it
is a maximum consistent with the energy and volume of the system.
Stated in other words, the entropy of a system at equilibrium is a
maximum at constant energy and volume. This obviously provides a
criterion for equilibrium.
2. Statistical Nature of the Second Law
The Second Law considered from a molecular-kinetic point of view
is a statistical law. It expresses the tendency toward randomness or disorder in a system which consists of a large number of particles. As an