When two blocks with distinct initial temperatures are placed in thermal contact, heat flows from the hotter block to the cooler until thermal equilibrium is reached. Given the initial temperatures, it is easy to predict the final temperature and, for identical blocks, to find a closed-form expression for the overall change of entropy, showing that it is a positive quantity. The change of entropy in the more general case of distinct blocks, however, is not mentioned in the introductory physics textbooks, which sounds as an indication of very complex mathematics underlying the problem. In this shortnote, I show that this is not the case by deriving a simple expression for the change of entropy and developing an elementary proof, at one-variable calculus level, that this change is a positive quantity.
heat transfer; thermal equilibrium; entropy change
