Direct Energy, 2018a

190 8.7 Thermoelectric Eciency
Eq. 8.42 is known as the Carnot eciency. It provides a serious limitation
on the eciency of energy conversion devices which involve converting
energy of a temperature dierence to another form. The Carnot eciency
applies to thermoelectric devices, steam turbines, coal power plants, pyroelectric
devices, and any other energy conversion device that convert a
temperature dierence into another form of energy. It does not, however,
apply to photovoltaic or piezoelectric devices. If the hot side of a device is
at the same temperature as the cold side, we cannot extract any energy. If
the cold side of a device is at room temperature, then the eciency cannot
be 100%. The Carnot eciency represents the best possible eciency, not
the actual eciency of a particular device because it is likely that other
energy conversion processes occur too. We can extract more energy from a
steam turbine with T h = 495 K than T h = 295 K. However, in both cases,
the amount of energy we can extract is limited by the Carnot eciency.
Note that when using Eq. 8.42, T c and T h must be specied on an absolute
temperature scale, where T =0is absolute zero. In SI units, we use
temperature in kelvins.
As an example, consider a device that converts a temperature dierence
into kinetic energy. The cold side of the device is at room temperature,
T c = 300 K. How hot must the hot side of the device be heated to so that
the device achieves 40% eciency?
η eff =1− T c
T h
(8.43)
0.4 =1− 300
(8.44)
T h
According to Eq. 8.42, we nd that T h = 500 K.
As another example, suppose we want to convert a temperature differential
to electrical energy using a thermoelectric device. Assume that
the cold side of the device is at room temperature of T c =72 ◦ F and the
hot side is at human body temperature of T h =96 ◦ F . What is the best
possible eciency? First the temperatures must be converted from degrees
Fahrenheit to kelvins. The resulting temperatures are T c = 295 K and
T h = 309 K. Next, using Eq. 8.42, we nd the best possible eciency is
only 4.5%.
η eff =1− 295 =0.045 (8.45)
309
As another example, assume that the temperature outside on a December
day is T c =20 ◦ F and inside room temperature is T h =72 ◦ C.
What is the Carnot eciency of a thermoelectric device operating at these