The misunderstanding of Clausius statement of the second law of thermodynamics and its aftermath

Abstract

As with the first law of thermodynamics, the second law of thermodynamics has been proven by countless examples. The Clausius statement of the second law of thermodynamics given in most of the literatures is “heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time”. After carefully studying Clausius’ mechanical theory of heat published from 1850 to 1865, we found that this is not true. Actually, Clausius already clearly stated that the second law of thermodynamics is “Theorem of the equivalence of the transformation of work to heat and the transformation of heat at a higher to a lower temperature”. The former statement is only a basic principle that can lead to the theorem of the equivalence of transformations. In addition, all processes in derivation of the theorem of the equivalence of transformations and proof of the equivalence between Clausius statement and Kelvin statement are reversible processes. The statement “Heat can never pass from a colder to a warmer body without some other change” only illuminates the spontaneous natural phenomenon in opposite direction that heat flows from high temperature to low temperature, which tells that heat at different temperatures are nonequivalent. Admittedly, Clausius discussed the process irreversibility and thereby obtained Clausius Inequality. But he only used the state change to measure the process irreversibility, which did not involve the concept of space, time and speed. Clausius just expressed that the process irreversibility will reduce heat efficiency and did not focus exclusively on the laws of process irreversibility. The misunderstanding of viewing Clausius statement as “Heat can never pass from a colder to a warmer body without some other change”, easily produces such a viewpoint that the second law of thermodynamics is the rule about process direction and irreversibility, consequently leading to the faulty assumption that the minimum entropy generation principle can be used to derive the transport law of heat conduction and optimize the heat transfer process. However, theory and practice analyses have proven that it is problematic. The action of heat conduction process is just half of entransy dissipation, whose variation points to the linear Fourier’s heat conduction law, which thereby has a better application for the optimization of heat transfer process. Transfer process has different laws from conversion process, so they should be treated distinguishingly and analyzed with different methods and indexes. It is not advisable to simply put heat transfer issues into category of non-equilibrium thermodynamics.