Modern Engineering Thermodynamics

7.4 Carnot’s Heat Engine and the Second Law of Thermodynamics 209
By the 1820s, a great deal of work had already been done on the efficiency of water wheels, and the water
wheel–steam engine analogy must have seemed to Carnot like a good way to approach the problem of improving
steam engine efficiency. Two important conclusions came from his work with this analogy.
First, he knew that no one could build a water wheel that would produce a continuous work output unless
water actually entered and exited the wheel. And, if water with a certain kinetic and potential energy entered the
wheel, then the same amount of water with a lower energy level must also exit the wheel. In other words, it is
impossible to make a water wheel that converts all the energyoftheinletwaterintooutputshaftwork.There
must also be an outflow of water from the wheel, and this outflow must have some energy. These rather
obvious statements are illustrated in Figure 7.1.
Now, if you extend this idea to a steam engine (or any type of heat engine) by replacing the word water by the
hypothetical heat fluid caloric, then it is easy to conclude that when caloric at a certain energy level (temperature)
enters a work-producing heat engine, it must also exit the engine at a lower energy level (temperature).
This concept was later refined into the following form, known today as the Kelvin-Planck statement of the second
law of thermodynamics: You cannot make a continuously operating heat engine that converts all of its heat input
directly into work output (see Figure 7.2).
Second, Carnot observed that the maximum efficiency of a water wheel was independent of the type of liquid
used and depended only on the inlet and outlet flow energies. This led him to the conclusion that
The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by
the temperatures of the bodies between which is effected, finally, the transfer of caloric.
Or, the maximum efficiency of a steam engine (or any type of heat engine) is dependent only on the temperatures
of the high- and low-temperature thermal reservoirs of the engine (the boiler and condenser temperatures
inthecaseofasteamengine)andisindependentoftheworkingfluidoftheengine(waterinthecaseofa
steam engine). Of course, to achieve the maximum possible efficiency, the water wheel and the heat engine
must be completely reversible; that is, they cannot possess any mechanical friction or other losses of any kind.
Water flow
in
Water flow
in
Shaft
work out
Water
flow out
Shaft
work out
No
water
leaving
the wheel
Common overshot
water wheel
A clearly impossible
type of water wheel
FIGURE 7.1
Water wheel operation.
High-temperature
thermal source
High-temperature
thermal source
Heat in
Heat in
Cyclic
heat
engine
Work
out
Cyclic
heat
engine
Work
out
Heat out
No heat leaving
the engine
Low-temperature
thermal sink
An impossible type of
continuously operating
heat engine
A common continuously
operating heat engine
FIGURE 7.2
Heat engine operation.