Modern Engineering Thermodynamics

Summary 241
■
Indirect method involves calculating the amount of entropy production for a process from an entropy
balance on the system. For example, for closed systems with isothermal boundaries, the indirect method of
calculating the entropy production rate is
_S P =
dS
−
_
Q
dt system
T b
act
Both the direct method and indirect methods give accurate answers for entropy production if applied correctly.
Which method you choose to solve a particular problem depends entirely on the type of information given to
you in the problem statement (usually only one of the two methods works for a given problem scenario). The
examples presented in the next two chapters illustrate the use of both of these methods.
SUMMARY
In this chapter, we study the classical and the modern development of the second law of thermodynamics and
the resulting entropy and entropy rate balances for closed systems. We find that entropy, unlike energy, is not
conserved in any process and the second law of thermodynamics requires that entropy always be produced in a
process. Kelvin used the classical results of Carnot to develop an absolute temperature scale and produced a
definition of thermal efficiency based only on temperature. Numerical values for entropy can be computed from
simple entropy equations of state for incompressible materials and ideal gases, but the tables in Thermodynamic
Tables to accompany Modern Engineering Thermodynamics must be used for more complex materials, such as
mixtures of liquid and vapor. Two important new process terms introduced in this chapter are reversible process,
a process in which the entropy production inside the system is always zero (S P = _S P = 0), and isentropic process, a
process in which the system’s entropy is maintained constant (s 2 − !s 1 = 0).
Then we develop entropy balance (SB) and entropy rate balance (SRB) equations by using the same three transport
modes (heat, work, and mass flow) as to develop the energy and energy rate balance equations in Chapter 4.
However, since entropy is such an ambiguous concept, we have to be very careful how we define entropy transport
and production modes. The resulting closed system constant boundary temperature entropy and entropy rate
balance equations and other important equations introduced in this chapter follow.
1. The general closed system entropy balance equation for a system that has a constant temperature T b on the
boundaries where the heat transfer occurs is
1Q 2
T b
+ 1 ðS P Þ 2 = mðs 2 − s 1 Þ (7.76)
act
2. The general closed system entropy rate balance equation for a system that has a constant temperature T b on
the boundaries where the heat transfer occurs is
_Q
+ _S P = dS
(7.78)
dt system
3. The second law of thermodynamics is simply
or
T b
act
S P ≥ 0
_S P ≥ 0
(7.4a)
(7.4b)
4. The third law of thermodynamics is this: The entropy of a pure substance at absolute zero temperature is
zero, or
lim ðEntropy of a pure substanceÞ= 0 (7.1)
T¼0
5. The definition of the absolute temperature scale based on the heat transports of a (reversible) Carnot engine is
jQ out j
= jQ
Lj
= T L
(7.15)
Q in Q H T H
rev
6. The thermal efficiency of a Carnot reversible heat engine and the maximum thermal efficiency of any other
heat engine operating between the temperature limits of T H and T L is
ðη T
Þ max
= ðη T
rev
Þ rev
= ðη T Þ Carnot
= 1 − T L
(7.16)
T H