Reversible limit of processes of heat transfer

TL;DR

This paper analyzes the entropy change during a heat transfer process involving a body and multiple reservoirs, revealing a reversible limit as the number of reservoirs increases and non-monotonic behavior at small N.

Contribution

It provides a detailed analysis of the entropy change in a multi-reservoir heat transfer process and identifies the conditions for reversibility and non-monotonic entropy behavior.

Findings

Entropy change scales with (T_N - T_0)/N for large N

Non-monotonic entropy behavior occurs at small N

Reversible limit approached as N increases

Abstract

We study a process of heat transfer between a body of heat capacity C(T) and a sequence of N heat reservoirs, with temperatures equally spaced between an initial temperature T_0 and a final temperature T_N. The body and the heat reservoirs are isolated from the rest of the universe, and the body is brought in thermal contact successively with reservoirs of increasing temperature. We determine the change of entropy of the composite thermodynamic system in the total process in which the temperature of the body changes from T_0 to T_N. We find that for large values of N the total change of entropy of the composite process is proportional to (T_N-T_0)/N, but eventually a non-monotonic behavior is found at small values of N.