Modern Engineering Thermodynamics

212 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
the inherent irreversibilities. We then correct for using the reversibility assumption in the design through an
appropriate efficiency calculation.
Though reversible processes do not actually exist in nature, they are conceptually necessary for creating performance
limits for heat engine technology. William Thomson used Carnot’s second conclusion regarding maximum
(i.e., reversible) engine energy conversion efficiency to develop the concept of an absolute temperature scale.
7.5 THE ABSOLUTE TEMPERATURE SCALE
After studying the operation of steam engines for several years, Sadi Carnot concluded in 1824 that the efficiency
of a heat engine depended only on the temperatures of the engine’s hot and cold thermal reservoirs and not on the
fluid used inside the engine. In 1848, Thomson used Carnot’s conclusion to develop the concept of an absolute
temperature scale. Soon afterward, an absolute temperature scale based on the size of the celsius degree (°C)
became popular and was given his titled name kelvin (K) by his admirers.
By using Eq. (4.70), we can define the thermal energy conversion efficiency (also called the thermal efficiency) η T
of a continuously operating closed system heat engine with a net output work or power as
η T = ðW outÞ net
Q in
= ð _W out Þ net
_Q in
(7.5)
A closed system heat engine can operate continuously only if it operates in a thermodynamic cycle. A system
that undergoes a thermodynamic cycle must end up at the same thermodynamic state at the end of the cycle as
it started from at the beginning of the cycle. Because the total system energy E is a point function, the closed
system first law of thermodynamics energy balance (EB) applied to a cyclic process yields
Now, from Figure 7.5, we see that the heat input to a cyclic heat engine is
ðQ − WÞ cycle = ðE 2 − E 1 Þ cycle = 0 (7.6)
ðQÞ cycle
= Q in − jQ out j (7.7)
High-temperature
thermal source
at temperature T H
Cyclic
heat
engine
Q in = Q H
Q out = Q L
Low-temperature
thermal sink
at temperature T L
W out
and
where jQ out j is the absolute value of this energy flow.
ðWÞ cycle
= W out (7.8)
Note that we introduce the correct sign with the absolute value of the symbol in Eqs.
(7.7) and (7.8) to indicate the proper flow direction (+ for heat in and work out, and −
for heat out and work in). Normally we do not introduce the sign convention
directly into the equations themselves. The usual custom is to attach the correct flow
direction sign to the number and not the symbol. However, we change this notational
scheme here to help you understand the operation of closed system heat engines.
Later in this chapter, we revert to the conventional notation scheme for algebraic signs.
Combining Eqs. (7.5) through (7.8) and using the simplified notation shown in
Figure 7.5 yields
FIGURE 7.5
Schematic of a cyclic heat engine.
η T = ðW outÞ net ð
= Q in − jQ out jÞ
Q in
Q in
= 1 − jQ outj
Q in
= 1 − jQ Lj
Q H
(7.9)
IS IT K OR ºK?
In 1967, the International Bureau of Weights and Measures dropped the prefix degree from the SI absolute temperature
scale. So we say “100 degrees celsius is equal to 373.15 kelvin” (or 100.00°C = 373.15 K). Notice that we do not capitalize
the terms Celsius and Kelvin, even though they are proper names. Remember that, in Chapter 1, we discussed why (a) we
do not capitalize the first letter of a unit whose name is derived from that of a person when the unit’s name is written out
and (b) the first letter is capitalized when the unit’s name is abbreviated.
Also, in this book, we follow the same scheme of omitting the degree symbol on the Rankine absolute temperature scale,
so 100.00°F = 559.67 R (and “559.67 R” is written out in lower case as “559.67 rankine”).