Page 114 - Physical Chemistry

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We have proved that the entropy of a closed system must increase in an irre- Section 3.5
versible adiabatic process: Entropy, Reversibility, and
Irreversibility
¢S syst 7 0 irrev. ad. proc., closed syst. (3.37)
A special case of this result is important. An isolated system is necessarily closed,
and any process in an isolated system must be adiabatic (since no heat can flow be-
tween the isolated system and its surroundings). Therefore (3.37) applies, and the
entropy of an isolated system must increase in any irreversible process:
¢S syst 7 0 irrev. proc., isolated syst. (3.38)
Now consider S univ S syst S surr for an irreversible process. Since we want to
examine the effect on S univ of only the interaction between the system and its surround-
ings, we must consider that during the irreversible process the surroundings interact only
with the system and not with any other part of the world. Hence, for the duration of the
irreversible process, we can regard the system plus its surroundings (syst surr) as
forming an isolated system. Equation (3.38) then gives S syst surr S univ 0 for an
irreversible process. We have shown that S univ increases in an irreversible process:
¢S univ 7 0 irrev. proc. (3.39)

where S univ is the sum of the entropy changes for the system and surroundings.
We previously showed S univ 0 for a reversible process. Therefore
¢S univ 0 (3.40)*
depending on whether the process is reversible or irreversible. Energy cannot be cre-
ated or destroyed. Entropy can be created but not destroyed.
The statement that
dq /T is the differential of a state function S that has the property S univ 0 for
rev
every process
can be taken as a third formulation of the second law of thermodynamics, equivalent
to the Kelvin–Planck and the Clausius statements. (See Prob. 3.23.)
We have shown (as a deduction from the Kelvin–Planck statement of the second
law) that S univ increases for an irreversible process and remains the same for a re-
versible process. A reversible process is an idealization that generally cannot be pre-
cisely attained in real processes. Virtually all real processes are irreversible because of
phenomena such as friction, lack of precise thermal equilibrium, small amounts of tur-
bulence, and irreversible mixing; see Zemansky and Dittman, chap. 7, for a full dis-
cussion. Since virtually all real processes are irreversible, we can say as a deduction
from the second law that S univ is continually increasing with time. See Sec. 3.8 for
comment on this statement.

Entropy and Equilibrium
Equation (3.38) shows that, for any irreversible process that occurs in an isolated sys-
tem, S is positive. Since all real processes are irreversible, when processes are oc-
curring in an isolated system, its entropy is increasing. Irreversible processes (mixing,
chemical reaction, flow of heat from hot to cold bodies, etc.) accompanied by an in-
crease in S will continue to occur in the isolated system until S has reached its maxi-
mum possible value subject to the constraints imposed on the system. For example,
Prob. 3.19 shows that heat flow from a hot body to a cold body is accompanied by an
increase in entropy. Hence, if two parts of an isolated system are at different temper-
atures, heat will flow from the hot part to the cold part until the temperatures of the
parts are equalized, and this equalization of temperatures maximizes the system’s