A simple but rigorous proof that heat flow is reversible if temperature difference is infiniteimal
At the beginning of thermodynamics studies, it is commonly stated
that a reversible process is one in which the system can be returned to
its initial state without any change in the universe. Subsequently, it is
claimed that an example of a reversible process is the heat exchanged
between two bodies with a very small temperature dierence. However,
clear links between these two statements are lacking. This article aims
to bridge the gap between these two assertions by providing a clear and
coherent link. The demonstration of the link is based on a simple yet
powerful hypothesis: two identical bodies brought into contact will reach
an equilibrium temperature that is the average of the initial temperatures
(we will assume work is always negligible). A signicant thermodynamic
result will be achieved with a straightforward (though somewhat labori-
ous) mathematical approach. The article presents all the necessary cal-
culations, allowing the reader to focus on understanding the underlying
reasoning.
