In 1824 Sadi Carnot, a young French engineer, conceived of an idealized
heat engine. This ideal engine had an efficiency given by
e = 1 - T_c/T_h = (T_h - T_c)/T_h
where
e = the so-called Carnot efficiency (no units)
T_c = the temperature of the waste heat reservoir (in degrees
Kelvin, °K[4])
T_h = the temperature of the heat source (in °K)
Unhappily, T_c cannot be made zero (and e therefore made equal to 1,
which is 100% efficiency). Physicists have shown absolute zero to be
unattainable, although they have approached to within a hundredth of a
degree in the laboratory.
Waste heat, since it must be rejected to the surrounding atmosphere,
outer space, or water (rivers, the ocean, etc.), must be rejected at T_c
greater than 300°K. The reason for this is that these physical
reservoirs have average temperatures around 300°K (about 80°F)
themselves. The fact that T_c must be 300°K or more is a basic
limitation on the Carnot efficiency. The loss in efficiency with
increased T_c explains why a jet plane has a harder job taking off on a
hot day.
One way to improve the Carnot efficiency, which is the maximum
efficiency for any heat engine, is to raise T_h as high as possible
without melting the engine. For a coal-fired electrical power plant, T_h
= 600°K and T_c = 300°K, so that
e = 1 - 300/600 = 0.5 = 50%
The actual efficiency is somewhat less than this ideal value because
some power is diverted to pumps and other equipment and to unavoidable
heat losses. Later on, we shall see that magnetohydrodynamic (MHD)
generators hold prospects for increasing T_h by hundreds of degrees.
Everything that has been said about the Second Law of Thermodynamics
(You can’t even break even) applies to heat engines, where we begin with
thermal energy. Suppose instead that we start with kinetic or chemical
energy and convert it into electricity without turning it into heat
first. We can then escape the Carnot efficiency strait jacket. Chemical
batteries perform this trick. So do fuel cells, solar cells, and many
other direct conversion devices we shall discuss. Thus, we circumvent
the Carnot efficiency limitation by using processes to which it does not
apply.