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CHAPTER
20
IRREVERSIBLE

THERMODYNAMICS

Classical thermodynamics deals with transitions from one equilibrium state to another and since it
does not analyse the changes between state points it could be called thermostatics (see Tribus (1961)).
The term thermodynamics will be reserved, in this chapter, for dynamic nonequilibrium processes.
Phenomenological laws should have been met previously which describe irreversible processes in
the form of proportionalities, e.g. Fourier’s law of heat conduction, Ohm’s law relating electrical
current and potential gradient, Fick’s law relating ﬂow of matter (Fick, 1856) and concentration
gradient etc. When two of these phenomena occur simultaneously they interfere, or couple, and give
rise to new effects. One such cross-coupling is the reciprocal effect of thermoelectricity and electrical
conduction: the Peltier effect (evolution or absorption of heat at a junction due to the ﬂow of electrical
current) and thermoelectric force (due to maintenance of the junctions at different temperatures). It is
necessary to formulate coupled equations to deal with these phenomena, which are ‘phenomenolog-
ical’ inasmuch as they are experimentally veriﬁed laws but are not a part of the comprehensive theory
of irreversible processes.
It is possible to examine irreversible phenomena by statistical mechanics and the kinetic theory but
these methods are on a molecular scale and do not give a good macroscopic theory of the processes.
Another method of considering nonequilibrium processes is based on ‘pseudo-thermostatic theories’.
Here the laws of thermostatics are applied to a part of the irreversible process which is considered to be
reversible and the rest of the process is considered as irreversible and not taken into account. Thomson
applied the Second Law of thermostatics to thermoelectricity by considering the Thomson and Peltier
effects to be reversible and the conduction effects to be irreversible. The method was successful as the
predictions were conﬁrmed by experiment but it has not been possible to justify Thomson’s hypothesis
from general considerations.
A systematic macroscopic and general thermodynamics of irreversible processes can be obtained
from a theorem published by Onsager (1931a, b). This was developed from statistical mechanics and
the derivation will not be shown but the results will be used. The theory, based on Onsager’s theorem,
also shows why the incorrect thermostatic methods give correct results in a number of cases.

20.1 DEFINITION OF IRREVERSIBLE OR STEADY-STATE
THERMODYNAMICS
All previous work on macroscopic ‘thermodynamics’ has been related to equilibrium. A system was
said to be in equilibrium when no spontaneous process took place and all the thermodynamic prop-
erties remained unchanged. The macroscopic properties of the system were spatially and temporally
invariant.

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