Modern Engineering Thermodynamics

7.3 The Second Law of Thermodynamics 207
FOR WHAT IS THE THIRD LAW USED?
This law is used to define an absolute measurement scale for entropy, but it does not otherwise contribute to a thermodynamic
analysis of an engineering system. Numerical values for specific entropy are listed in thermodynamic tables along
with values for specific volume, specific internal energy, and specific enthalpy. For convenience, most thermodynamic
tables are developed around a “relative” measurement scale, where the values of entropy and internal energy are arbitrarily
set equal to zero at a point other than at absolute zero temperature. For example, in the steam tables, the specific internal
energy and specific entropy of saturated liquid water are arbitrarily set equal to zero at the triple point of water (0.01°C,
0.6113 kPa or 32.018°F, 0.0887 psia). Thus, the specific internal energies and specific entropies of the less-disordered molecular
states of water (like ice) have negative values on this relative scale.
THE TRUTH ABOUT ENTROPY
1. Entropy is a measure of the amount of molecular disorder within a system.
2. Entropy can only be produced (but not destroyed) within a system.
3. The entropy of a system can be increased or decreased by entropy transport across the system boundary.
Since it always takes an input of energy to create order within a system, it seems reasonable to postulate that a
relation exists between the energy transports of a system and its order, or entropy value. Thus, we arrive at the
three basic elements of the second law of thermodynamics:
We begin this chapter by assuming the existence of a disorder-measuring thermodynamic property that we call
entropy. WeusethesymbolS to represent the total entropy (an extensive property), and use s = S/m for the
specific entropy (an intensive property).
7.3 THE SECOND LAW OF THERMODYNAMICS
We can use the general balance equation of Chapter 2 to analyze any concept whatsoever. Introducing the total
entropy S into balance Eq. (2.11) provides the following total entropy balance (SB):
S G = S T + S P (7.2)
where S G is the gain or loss of total entropy of the system due to the transport of total entropy S T into or out of
the system and the production or destruction of total entropy S P by the system. A total entropy rate balance (SRB)
is easily obtained from Eq. 7.2 by differentiating it with respect to time to give
where the overdot indicates material time differentiation (i.e., _S = dS/dt).
_S G = _S T + _S P (7.3)
Unlike energy, mass, and momentum, entropy is not conserved in any real process. Processes that have zero
entropy production are called reversible and are characterized by the fact that they can occur equally well in
either the forward or backward direction of time. The thing that makes entropy a unique concept worthy of a
thermodynamic law of its own is that entropy is never destroyed in any real process. Now, it happens that
some processes have very small amounts of entropy production, and it is a useful approximation for these
processes to set their entropy production equal to zero. This can be stated in a very succinct mathematical
form as
The second law of thermodynamics
and
The entropy production, S P ≥ 0
The entropy production rate, _S P ≥ 0
(7.4a)
(7.4b)
where the equality sign applies only to a reversible process. Equations (7.2) and (7.3), as modified by Eqs. (7.4a)
and (7.4b), form the mathematical basis for a working form of the entropy balance and the entropy rate balance.