Acta Physica Academiae Scientiarum Hungaricae 13. (1961)
1960 / 3. szám - G. Pataki: On the time Dependence of Irreversible Processes
ON THE TIME DEPENDENCE OF IRREVERSIBLE PROCESSES By G. Pataki RESEARCH INSTITUTE FOR TECHNICAL PHYSICS OF THE HUNGARIAN ACADEMY OF SCIENCES, BUDAPEST (Presented by G. Szigeti. — Received 29. III. 1961) In this paper the time dependence of the so-calied thermodynamic “forced” (non-spontaneous) processes is examined in homogeneous systems, when in case of t —► °o not a static equilibrium results, but a stationary process determined by external forces. The “equations of motion” are given for an arbitrary number of variables and an arbitrary generation G(l) of the extensive quantities. In case of two variables we write down the differential equations holding for the components and for a constant G0 we give also the solutions. As an application we examine in Kundsen gas the time dependence of the quotient AP AT of the thermonuclear pressure and the temperature difference. Finally, the analogy between mechanics and thermodynamics is studied taking the generation into consideration. Introduction The description of the approach to equilibrium in time in homogeneous systems near the equilibrium, has been given by I. Fényes [1]. By integrating the equations of motion a more exact picture of the process of the approach to equilibrium could be obtained. So, e. g. it could be established that because of the matrix gL = A being off-diagonal the forces X,- can change their signs during the decay. The relation between the reversal of signs and the initial conditions in case of two variables has in general been examined by G. FÁY and G. Tábori [2], while in [3] we have studied the approach to the equilibrium in Knudsen gas by means of two parameters of the conduction matrix. As a further application, we gave the thermodynamic formulation of the recombination in semi-conductors [4], on the basis of the theory of Shockley— Read. The equations of motion given in [1] describe such processes in which, supposing an arbitrary initial state, the final state will be the static equilibrium. But, from both the theoretical and the practical point of view, the case seems to be interesting, when for { —> oo not necessarily the static equilibrium sets in, but a stationary process ensues determined by the external forced conditions. In this paper the thermodynamic equations of motion describing the forced processes near the equilibrium in case of an arbitrary number of variables and an arbitrary generation G(t) of the extensive quantities are given by Acta Phys. Hung. Тот. XIII. Fasc. 3.