关于“关于克劳修斯等式证明的再讨论”的讨论

REVIEW “ON THE PROOF OF CLAUSIUS EQUALITY(CONTINUED)”

指出"关于克劳修斯等式证明的再讨论"一文论证过程中存在的问题,提出了一种在相邻卡诺循环之间过渡的循环路径,并证明了用若干个卡诺循环逼近任意可逆循环的可行性及其等价性。本文的研究支持主流热学教材中"用若干个完整的卡诺循环去分解任意循环,相邻的两个卡诺循环之间的重叠部分在两次循环中相互抵消"的论证方法。但现行教材的论述过程确实存在过于简略、不够严谨的问题,本文在阐明用卡诺循环分解任意循环的"等效性"内涵的基础上,采用泰勒级数展开及极限理论等高等数学方法,完善了克劳修斯等式的证明过程.

Several problems occurred in the argumentation process of the paper ＂On the Proof of Clausius Equality （Continued）＂ have been pointed out. One kind of cycling path serving as a transition among neighboring Carnot cycles has been proposed. The feasibility and equiva- lence of approaching arbitrary cycle by several Carnot cycles has been proven. This article stands with the argumentation method for dividing arbitrary cycle by several complete Carnot cycles, where the overlapping part between neighboring Carnot cycles are neutralized due to the opposite loop directions, in main stream thermal physics textbooks. But it is a real fact that the proof procedure in textbooks is too sketchy and rather loosely in mathematics. Using Taylor＇s series and limit theorem, a complete proof of Clausius equality with the necessary process have been presented in this paper.