Direct Energy, 2018a

8 THERMOELECTRICS 183
gradient across a piece of metal or semiconductor and also apply a current
through the length of the material.Heating or cooling can be measured,
and this eect is described by another coecient.The Thomson coecient
τ also has units
K V .It is dened as the rate of heat generated over the
product of the current and temperature dierence.
τ =
dQ
dt
I (T h − T c )
(8.27)
The Thomson and Seebeck coecients for a single material are related by
ˆ T
0
τ
T ′ dT ′ =$ (8.28)
where the integral is over temperature [110, p.24].
These eects work both ways.We can use the Peltier eect, for example,
to make either a heating or a cooling device.We can supply a current
across a junction to produce a temperature dierential, or we can supply
a temperature dierence to generate a current.All three eects relate to
the fact that when the electrical conductivity is larger than the thermal
conductivity, energy can be converted between a temperature dierential
and electricity.As an aside, materials with low electrical conductivity and
high thermal conductivity are also used to make energy conversion devices.
Components of motors and generators are often made from layers of metal
and dielectrics with these properties [111, ch.8].
8.6.2 Electrical Conductivity
1
Electrical conductivity σ, in units
Ω·m
, is a measure of the ability of charges
to ow through a material.Resistivity is the inverse of electrical conductivity,
ρ = 1 .Example electrical conductivity values are listed in Table 8.4,
σ
found in Section 8.3. Few tools are needed to measure these quantities.
An ohmmeter can be used to nd the resistance R, in ohms, of a sample
with known length l and cross sectional area A.The conductivity can be
calculated directly,
σ =
l
AR . (8.29)
Electrical conductivity is the product of the number of charges owing
and their mobility.For conductors, valence electrons are charge carriers
that ow, so conductivity can be expressed as [9, p.84]
σ = nqμ n . (8.30)