Lecture-Notes (Thermodynamics) - niser

4.5. ENTROPY 33
The entropy is defined up to an additive constant. The difference between entropies of
any two states A and B is
B
δQ
S(B) − S(A) ≡
T ,
where the integral extends along any reversible path connecting A and B, and the result
of the integration is independent of the path.
What happens when the integration is along an irreversible
path? Since I − R is a cycle (see Fig. 4.8), it
follows from Clausius’ theorem that
⇒
I
δQ
T ≤
Therefore, in general
B
A
I−R
δQ
T
R
δQ
T
δQ
T
≤ 0 ⇒
= S(B) − S(A) .
≤ S(B) − S(A) ,
and the equality holds for a reversible process.
A
Figure 4.8: I − R (irreversiblereversible)
cycle.
In particular, for an isolated system, which does not exchange heat with a reservoir,
δQ = 0 and therefore
∆S ≥ 0 .
This means that the entropy of an isolated system never decreases and remains constant
during a reversible transformation.
Note:
i) The joint system of a system and its environment is called ”universe”. Defined in this
way, the ”universe” is an isolated system and, therefore, its entropy never decreases.
However, the entropy of a non-isolated system may decrease at the expense of the
system’s environment.
ii) Since the entropy is a state function, S(B) − S(A) is independent of the path, regardless
whether it is reversible or irreversible. For an irreversible path, the entropy
of the environment changes, whereas for a reversible one it does not.
iii) Remember that the entropy difference
B
S(B) − S(A) =
only when the path is reversible; otherwise the difference is larger that the integral.
A
δQ
T