16 - 16 Ir reversi ble The rmodyna mics 16.1 Introduction...

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16 I r reve rsi bl e The rmod yna m ics 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 non-equilibrium 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 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 ‘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 non-equilibrium processes is based on ‘pseudo-thermostatic 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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Entropy flow and entropy production 3 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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16 - 16 Ir reversi ble The rmodyna mics 16.1 Introduction...

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