Waste heat, since it must be rejected to the surrounding atmosphere, outer space, or water (rivers, the ocean, etc.), must be rejected at Tc 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 Tc must be 300°K or more is a basic limitation on the Carnot efficiency. The loss in efficiency with increased Tc 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 Th as high as possible without melting the engine. For a coal-fired electrical power plant, Th = 600°K and Tc = 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 Th 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.
Problem 3
Some space power plants contemplate using the space cabin heat (Th = 300°K) to drive a heat engine which rejects its waste heat to the liquid-hydrogen rocket fuel stored at Tc = 20°K. What would be the Carnot efficiency of this engine?
THERMOELECTRICITY
After 140 Years: Seebeck Makes Good
The oldest direct conversion heat engine is the thermocouple. Take two different materials (typically, two dissimilar metal wires), join them, and heat the junction. A voltage, or electromotive force, can be measured across the unheated terminals. T. J. Seebeck first noticed this effect in 1821 in his laboratory in Berlin, but, because of a mistaken interpretation of what was involved, he did not seek any practical application for it. Only recently has any real progress been made in using his discovery for power production. To use the analogy of A. F. Joffe, the Russian pioneer in this field, thermoelectricity lay undisturbed for over a hundred years like Sleeping Beauty. The Prince that awoke her was the semiconductor.