A Graphical Proof of the Positive Entropy Change in Heat Transfer Between Two Objects

Abstract

It is well known that heat transfer between two objects results in a positive change in the total entropy of the two-object system. The second law of thermodynamics states that the entropy change of a naturally irreversible process is positive. In other words, if the entropy change of any process is positive, it can be inferred that such a process is irreversible. Analytic examples such as ice melting,1 free expansion of gas,2 and thermal conduction between two fixed-temperature reservoirs3 are often demonstrated in the introductory classroom, providing convincing evidence of this law. Specific numeric examples can be helpful, but they may not convince talented students wholeheartedly. In this paper, we show graphically via a ln T‒T curve that the total entropy change due to heat transfer within a two-object system is positive even in the case of unequal masses.