Direct Energy, 2018a

8 THERMOELECTRICS 189
or mass involved starts and ends in the same state, so the processes can
continue indenitelyas long as the input is continuallysupplied.
How much energyis supplied in to the system from the heater? The
amount of energyrequired to maintain the hot side at temperature T h is
given by
E in = k B T h . (8.37)
The device is composed of atoms. Each of these atoms has some internal
energy. A device at temperature T contains k B T joules of energywhere
k B is the Boltzmann constant. Energyows from the hot side to the cold
side of the device. Above, we assumed that the device was in a room that
was so large that the heat from the heater did not raise the temperature of
the room. Thus, we must continuallysupplythis energyat a constant rate
to keep the hot side of the device at temperature T h . While the cold side
of the device is at a lower temperature T c , it maintains that temperature
regardless of the fact that there is a heater in the room.
How much energy is extracted out of the system as electrical energy?
In the Seebeck device, the hot side is held xed at temperature T h , and
because of the environment it is in, the cold side remains at temperature T c .
Energyis conserved in this system. Thus, the electrical energyextracted
from the device is given by
E out = k B T h − k B T c . (8.38)
What is the eciencyof this system? Above we assumed that no other
energyconversion processes occur, so this is an idealized case. The resulting
eciencythat we calculate represents the best possible eciencyof
a thermoelectric device operating with sides at temperatures T h and T c .
Eciencyis dened as
η eff = E out
. (8.39)
E in
Using Eqs. 8.37 and 8.38 and some algebra, we can simplifythe eciency
expression.
η eff = E out
E in
= k BT h − k B T c
k B T h
(8.40)
η eff = T h − T c
T h
(8.41)
η eff =1− T c
T h
(8.42)