ABSTRACT
Ohm’s law is given by J ¼ sE ¼ 2s7V for an isothermal sample ð7T ¼ 0Þ with electrical conductivity s
and the heat flux is q ¼ 2k7T for a sample with no electric fields present. For inhomogeneous samples
or when temperature gradients are present, then variations in the chemical potential m; as well as the
electrostatic potential V ; must be included in the potential gradient. The forces and flows given in
Equation 12.3 can be rewritten in terms of particle current density J
and entropy current density J
; as
J
¼ 2L
m2 L
7T J
¼ 2L
m2 L
7T ð12:4Þ
where
m ¼ mþ eV is the electrochemical potential. The heat current density (or heat flux) and energy
current density (or energy flux) are given by
q ¼ TJ
W ¼ qþ
mJ
ð12:5Þ
For charge carriers being electrons, e ¼ 21:602 £ 10
Coulombs, and
L
¼
s
e
¼
e
r
T
L
L
2 L
L
{ !
