Page 17 - Entrophy Analysis in Thermal Engineering Systems

Fundamental concepts 7

receives heat, and the system entropy will decrease if it loses heat [6]. In the
latter case, the change in the system entropy will be negative contrary to the
former where the entropy change is positive, as demonstrated in the above
examples.

1.6 Third law of thermodynamics
Eq. (1.10) enables one to calculate the difference in the entropy of a
substance at two different states. To determine the entropy at any state,
Eq. (1.10) needs to be integrated from a reference state, which is defined
using the third law. Known also as the Nernst theorem [7], the third law
says that the entropy of a system at absolute zero temperature is zero [8].
Unlike the first and the second laws, the nature of the third law is not based
on experimental observations; it is rather a postulation.

The entropy of a system at any given state, S, where the temperature is T
is thus obtained by substituting S 1 ¼0at T¼0 as the lower limit of the inte-
gral in Eq. (1.10).
Z
T
δQ
S ¼ (1.11)
0 T
rev
Notice that the integral in both Eqs. (1.10) and (1.11) is taken along a revers-
ible path from any state at zero Kelvin to a state at which the temperature is T.

1.7 Entropy generation

The concept of reversibility introduced by Carnot refers to a process
that spontaneously takes place from state A to state B, and from B to A (i.e.,
in reverse direction) without an external effect. For example, if a quantity of
heat is transferred along a reversible path from a warmer body to a cooler
body, the same quantity of heat could be transferred from the cooler to
the warmer body without a need to an external effect (i.e., power).
Natural processes, as we know, occur in certain directions. To reverse
the direction of a process requires an external force that would not be needed
in the spontaneous direction. In other words, natural processes are irrevers-
ible. The concept of entropy generation is a consequence of the irreversibil-
ity in thermodynamic processes. It was first introduced by Clausius as the
uncompensated transformation who viewed the second law as the principle
of the equivalence of transformations.