Page 112 - Physical Chemistry

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3.5 ENTROPY, REVERSIBILITY, AND IRREVERSIBILITY Section 3.5
Entropy, Reversibility, and
Irreversibility
In Sec. 3.4, we calculated S for the system in various processes. In this section we
shall consider the total entropy change that occurs in a process; that is, we shall exam-
ine the sum of the entropy changes in the system and the surroundings: S syst S surr .
We call this sum the entropy change of the universe:

¢S univ ¢S syst ¢S surr (3.34)*
where the subscript univ stands for universe. Here, “universe” refers to the system plus
those parts of the world that can interact with the system. Whether the conclusions of
this section about S univ apply to the entire universe in a cosmic sense will be consid-
ered in Sec. 3.8. We shall examine separately S univ for reversible processes and irre-
versible processes.

Reversible Processes
In a reversible process, any heat flow between system and surroundings must occur
with no finite temperature difference; otherwise the heat flow would be irreversible.
Let dq rev be the heat flow into the system from the surroundings during an infinitesi-
mal part of the reversible process. The corresponding heat flow into the surroundings
is dq . We have
rev
dq rev dq rev dq rev dq rev
dS univ dS syst dS surr 0
T syst T surr T syst T syst

Integration gives
¢S univ 0 rev. proc. (3.35)
Although S syst and S surr may both change in a reversible process, S syst S surr S univ is
unchanged in a reversible process.

Irreversible Processes
We first consider the special case of an adiabatic irreversible process in a closed sys-
tem. This special case will lead to the desired general result. Let the system go from
state 1 to state 2 in an irreversible adiabatic process. The disconnected arrowheads
from 1 to 2 in Fig. 3.10 indicate the irreversibility and the fact that an irreversible
process cannot in general be plotted on a P-V diagram since it usually involves non-
equilibrium states.
To evaluate S S S syst , we connect states 1 and 2 by the following reversible
1
2
path. From state 2, we do work adiabatically and reversibly on the system to increase
its temperature to T , the temperature of a certain heat reservoir. This brings the system
hr

Figure 3.10

Irreversible and reversible paths
between states 1 and 2.