Direct Energy, 2018a

352 Appendices
for voltage. (As an aside, reference [6] carefully distinguishes between these
three terms.)In this context, potential, like voltage, has the units volts.
The term chemical potential μ chem has units of joules per atom, and it
represents energy where the probability of nding an electron is one half.
For a pure semiconductor, the chemical potential is in the middle of the
energy gap. Semiconductor scientists typically use the term Fermi energy
level E f instead. These terms are discussed in Sec. 6.3.3 and 9.2.3. Voltage
times charge is energy, so chemical potential can be thought of as a
voltage times the charge of an electron. The term redox potential V rp is
equivalent to the term voltage used by electrical engineers, and it has the
units volts. It was introduced in Sec. 9.2.5. It is used, typically by experimentalists,
in discussing the voltage that develops across electrodes due
to oxidation reduction chemical reactions. In the discussion of calculus of
variations in Chapter 11, the idea of generalized potential was introduced.
It is a parameter used to describe the evolution of an energy conversion
process. Voltage and chemical potential can both be examples of generalized
potentials. Generalized potential has units of joules over the units
of the generalized path. The choice of the word generalized potential in
calculus of variations follows reference [194, p.II-19]. Another related term
is potential energy. Potential energy is a form of energy, and it is measured
in joules. If we raise an object against gravity, we say that the object gains
potential energy, and if we compress a spring, we say the spring gains spring
potential energy.
The related words capacitor, capacitance, theoretical capacity, and generalized
capacity are used in this text. A capacitor is one of the most
common circuit components, and capacitors are discussed in Sec. 1.6.3. A
capacitor is a device constructed from conductors separated by a dielectric
layer. It is specied by a capacitance C, in farads, which is a measure of
the ability of the device to store a built up charge, hence store energy. The
permittivity ɛ describes the distributed capacitance, in m F , of an insulating
material. As discussed in Sec. 9.4.1, chemists use the related term theoretical
capacity in a dierent way, as a measure of the charge stored in
an battery or fuel cell. It is measured in coulombs or ampere hours. The
adjective theoretical refers to the total amount of charge stored, not the
charge that can be practically extracted. The idea of generalized capacity
was introduced in Sec. 12.2 as the general ability to store energy. As with
other concepts of calculus of variations, the units of generalized capacity
depend on the choice of generalized path and generalized potential.
Conductivity describes ability of some particles to ow. Electrical conductivity
σ describes the ability of charges to ow. It was introduced in Sec.
1.6.3 and discussed further in Sec. 8.6.2 and 9.2.1. Thermal conductivity