| [ sciEncE ] in KIDS 글 쓴 이(By): Tao (懶不自惜) 날 짜 (Date): 2001년 8월 8일 수요일 오후 03시 28분 17초 제 목(Title): 열역학 4 법칙. 에공, 그때 몰라서 뉴스그룹에 올렸었는데, 온 답 중에서, 제일 근사해 보이는 걸 올릴께요. From michaelb@deq.state.la.us The so-called "Fourth Law" of thermodynamics refers to the work of Lars Onsager and his proof that the cross coefficients for coupled effects form a symmetrical matrix. These coefficients are called the "phenomenological coefficients", however, in general, they are not easily measurable. It had been noted for many years that the cross coefficients, in such phenomena as the coupling of heat flow and electrical flow in bimetallic systems (the Peltier effect) or the coupling of heat flow and mass flow through an orifice (the Knudsen effect), give rise to symmetrical coefficient matrices. Onsager's proof demonstrated that these symmetries were not accidental but could be proved to be the consequence of the dynamics of systems near equilibrium. He defined "fluxes" to be the rate of material transported across boundaries, either physical boundaries or from one compound identity to another. He defined "forces" to be the difference from one side of the boundary to the other of the entropy per unit of material. The vector dot product of the forces and the fluxes give rise to the rate of entropy production in the system. I.e., dS/dt = Transpose(J) * X where S is the entropy, J is a vector of the fluxes and X is a vector of the forces. For instance the J-component for electrical currents would be the current in Amps, and the corresponding X-component for electricity would be the voltage divided by the temperature. The entropy production due to simply electrical discharge would be the power loss divided by the temperature, or dS/dt = current*voltage/temperature The so-called "phenomenological" coefficients are found in the dependence of J upon X. For small deviations we can usually assume the dependence is linear such as, J = L X where L is the phenomenological matrix. So we can express the entropy production as dS/dt = Transpose(X)*Transpose(L)*X which is a set of differential equations in quadratic form. Onsager's genius was in his statistical mechanical proof that L is symmetric. This proof is based on the so-called "principle of microscopic reversibility". This principle is nothing more than the fact that at true equilibrium there are no net fluxes. At the time Onsager published his theory, microscopic reversibility had recently been put on a sound theoretical footing by Richard Tolman in his classic treatise on statistical thermodynamics. A related concept used in chemistry is the principle of "detailed balance". "Detailed balance" simply says that at equilibrium each reaction in a pot must be at equilibrium separate from any other reaction in the pot. This denies the possibility of one-way cyclic fluxes that may, nonetheless, sustain an equilibrium concentration of the components of the cycle. Hence A a B a C a back to A, is not a possible scenario in an equilibrium system. Detailed balance demands that the processes A a B and BaA occur at the same rate at equilibrium and the same can be said for the pair Ba C and C a B and for the pair A a C and C a A. The fact that L is symmetric is of limited utility to the average scientist because most identifiable forces and fluxes when multiplied yield energy dissipation, not entropy dissipation. Entropy is a more theoretical concept and not a directly measurable quantity. Also, most complex systems of interest are driven far from equilibrium where the linear relation between the forces and the fluxes no longer applies. Brian Swift, Ph.D. |