Modern Engineering Thermodynamics

456 CHAPTER 13: Vapor and Gas Power Cycles
WHAT IS A STEAM ENGINE INDICATOR? Continued
FIGURE 13.6
Steam engine indicator.
13.3 CARNOT POWER CYCLE
In Chapter 7, we discuss how the young French military engineer Sadi Carnot (1796–1832) came to understand
the rudiments of heat engine theory in the 1820s using a water wheel analogy. His theory was based on the
caloric (or fluid) theory of heat, and he believed that heat passed through a heat engine undiminished (like
water passes through a water wheel undiminished), and in so doing, the heat engine could perform work.
Today, we know that this is incorrect. The heat flow through an engine is diminished (i.e., reduced) by its conversion
into work. Carnot’s ideas were so revolutionary that they were largely ignored. Soon after Carnot’s death
from scarlet fever, Emile Clapeyron (1799–1864), in 1834, strengthened Carnot’s ideas by using more precise
mathematical derivations. From Carnot’s description of a reversible heat engine, Clapeyron constructed its
thermodynamic cycle. He deduced that it must be composed of two isothermal processes and two reversible
adiabatic processes. Using the pressure-volume steam engine indicator diagram format common at that time, he
deduced the cycle shape shown in Figure 13.7a. This cycle is still known as Carnot’s cycle, but because it is
defined to be a reversible cycle, no heat engine can ever be made to operate using it.
The Carnot cycle is important because it was the first heat engine cycle ever to be properly conceptualized and
because no other heat engine, reversible or irreversible, can ever be more efficient than a Carnot cycle heat
engine (though even a reversible heat engine may be less efficient), thus it can be used as a benchmark or standard
for comparison, for gauging both real and reversible (ideal) heat engine performance.
When Rudolph Clausius (1822–1888) formalized the second law of thermodynamics and defined entropy
in 1860, Carnot’s reversible adiabatic processes became an isentropic process, and the Carnot cycle was defined
by two T = constant processes and two s = constant processes. The Carnot cycle then took on its characteristic
rectangular shape on a T–s diagram, as shown in Figure 13.7b.
In Chapter 7, we also discuss how Carnot’s ideas led to the development of the Kelvin absolute temperature
scale and, finally, to an expression for the thermal efficiency of a reversible heat engine (see Eq. (7.16)), which
we call in this chapter the Carnot thermal efficiency:
ðη T Þ Carnot
= 1 − T L /T H (13.2)