CHAPTER 4 THE SECOND LAW
4.7 SUMMARY 129
limit. Consider an irreversible adiabatic process with workwirr. The same change of state
can be accomplished reversibly by the following two steps: (1) a reversible adiabatic change
of the work coordinate with workwrev, followed by (2) reversible transfer of heatqrevwith
no further change of the work coordinate. Sincewrevis algebraically less thanwirr,qrev
must be positive in order to makeÅU the same in the irreversible and reversible paths.
The positive heat increases the entropy along the reversible path, and consequently the
irreversible adiabatic process has a positive entropy change. This conclusion agrees with
the second-law inequality of Eq.4.6.1.
4.7 Summary
Some of the important terms and definitions discussed in this chapter are as follows.
Any conceivable process is either spontaneous, reversible, or impossible.
Areversibleprocess proceeds by a continuous sequence of equilibrium states.
Aspontaneousprocess is one that proceeds naturally at a finite rate.
Anirreversibleprocess is a spontaneous process whose reverse is impossible.
Apurely mechanical processis an idealized process without temperature gradients,
and without friction or other dissipative effects, that is spontaneous in either direction.
This kind of process will be ignored in the remaining chapters of this book.
Except for a purely mechanical process, the termsspontaneousandirreversibleare
equivalent.
The derivation of the mathematical statement of the second law shows that during a
reversible process of a closed system, the infinitesimal quantity∂q=Tbequals the infinites-
imal change of a state function called the entropy,S. Here∂qis heat transferred at the
boundary where the temperature isTb.
In each infinitesimal path element of a process of a closed system, dSis equal to∂q=Tb
if the process is reversible, and is greater than∂q=Tbif the process is irreversible, as sum-
marized by the relation dS∂q=Tb.
Consider two particular equilibrium states 1 and 2 of a closed system. The system can
change from stateR 1 to state 2 by either a reversible process, withÅSequal to the integral
.∂q=Tb/, or an irreversible process, withÅSgreater than
R
.∂q=Tb/. It is important to
keep in mind the point made by Fig.4.12on the next page: becauseSis a state function, it
is the value of the integral that is different in the two cases, and not the value ofÅS.
The second law establishes no general relation between entropy changes and heat in an
open system, or for an impossible process. The entropy of an open system may increase or
decrease depending on whether matter enters or leaves. It is possible to imagine different
impossible processes in which dSis less than, equal to, and greater than∂q=Tb.
4.8 The Statistical Interpretation of Entropy
Because entropy is such an important state function, it is natural to seek a description of its
meaning on the microscopic level.
Entropy is sometimes said to be a measure of “disorder.” According to this idea, the
entropy increases whenever a closed system becomes more disordered on a microscopic