Modern Engineering Thermodynamics

13.4 Rankine Cycle 457
A
B
Reversible
adiabatics
T H
A
Reversible
adiabatics
B
p
T
Isotherms
D
C
Isotherms
T L
D
C
V
(a) Carnot’s power cycle as
described by Clapeyron in 1834
s
(b) Carnot’s power cycle using
Clausius’ entropy concept of 1860
FIGURE 13.7
(a) Carnot’s power cycle as described by Clapeyron in 1834. (b) Carnot’s power cycle using Clausius’ entropy concept of 1860.
The reversible Carnot p V cycle diagram was chosen as the logo for the Mechanical Engineering Honor Society, ΠΤΣ
(Pi Tau Sigma).
where T H and T L are the absolute isothermal temperatures of the high-temperature heat addition and
low-temperature heat rejection reservoirs, respectively.
13.4 RANKINE CYCLE
Intheperiodfrom1850to1880,thesubjectofthermodynamics was formally developed. One of its early
practical goals was to provide a scientific foundation for the empirical steam technology that had by then grown
to dominate the economy of the Western World. By 1850, it had been determined that heat was a form of
energy, and by 1860, the first and second laws of thermodynamics had been accurately formulated by Clausius,
Kelvin, Joule, and others. But, it was the Scottish engineer William John Macquorn Rankine (1820–1872) who
first worked out the thermodynamic cycle for a steam engine with an external condenser. 6 Because Rankine was
the first person to understand how this type of steam engine worked thermodynamically, the thermodynamic
cycle for adiabatic cylinder engines is called the Rankine cycle today.
Though the Newcomen cycle is obsolete, the Rankine cycle is still in common use. Therefore, we carry out an
analysis of the thermal efficiency of the Rankine cycle and focus on its further development throughout the
remainder of this chapter. The difference between the Newcomen and Rankine cycles can be seen by comparing
parts a and b of Figure 13.8.
The Rankine cycle is a thermodynamic representation of a high-pressure or expansion type of steam engine cycle,
and because of the shape of the T-s saturation curve for water, the ideal or reversible Rankine cycle without
superheat is very close to the (reversible) Carnot cycle. The difference between the Rankine and Carnot cycles is
shown in Figure 13.8c. Because it is very difficult to efficiently pump wet vapor back into the boiler in the
Rankine cycle, the vapor is completely condensed into a liquid in the condenser and, using a common liquid
pump, pumped into the boiler as a compressed liquid. The Rankine cycle boiler feed pump raises the pressure
of the liquid condensate to only that of the boiler (state 4), leaving its temperature nearly equal to that of the
condenser (state 3).
The thermal efficiency η T of a heat engine is defined in Eq. (7.5) as
η T =
=
Net work output
Total heat input
Engine work output − Pump work input
Boiler heat input
(7.5)
6 An adiabatic cylinder steam engine is any expansion engine or any atmospheric engine with an external condenser. Rankine’s work
on this subject was published in his classic Manual of the Steam Engine and Other Prime Movers, first published in 1859. This text went
through 17 editions and was in print for over 50 years. It is considered to be the first comprehensive engineering thermodynamics
textbook.