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16.1 Introduction
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.
The term
thermodynamics
will be reserved, in this chapter, for dynamic nonequilibrium
processes.
In previous work,
phenomenological
laws have been given 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 and
concentration gradient etc. When two of these phenomena occur simultaneously they
interfere, or couple, and give rise to new effects. One such crosscoupling 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 ‘phenomenological’
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 ‘pseudothermostatic theories’. Here, the laws of thermostatics
are applied to a part of the irreversible process that 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.
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.
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View Full DocumentEntropy
flow
and entropy production
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17
16.2 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 properties remained unchanged. The macroscopic properties of the system
were spatially and temporally invariant.
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 Spring '10
 Prof.William
 Statics, Thermodynamics, Eqn, irreversible thermodynamics

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