A note on heat reservoirs and the like

Abstract

From Clausius's principle, the entropy change in a closed system satisfies ΔS ⩾ ∑kQk/Tk, where the equality holds for reversible processes and the inequality holds for irreversible processes. However, the entropy changes of infinite heat reservoirs are routinely calculated as ΔS = Q/T, independently of the nature of the heat exchange, whether reversible or irreversible. We show how this result comes about by considering the direct thermal contact between two systems, and then by allowing one of them to be much larger than the other. We then re-examine the usual definition of reversibility to reconcile it with the expression found for the entropy change.

Reply to Comment on ‘A note on heat reservoirs and the like’

“…Note that a heat source is regarded as reversible even though the total process it might be involved in is irreversible. This is totally consistent with example we provided in [1] of temporal heat transfer between two infinite heat reservoirs, A and B, in which 'the process of the system can be irreversible, although all the processes of its subsystems, A and B are reversible'.…”

“…oil , as proved mathematically in [1]. As for the ants, the only thing that can be said about them is that…”

Comment on ‘A note on heat reservoirs and the like’

“…That thermodynamics is a subtle subject is manifest in de los Santos and López-Lacomba's paper [1], where the main topics addressed are the Clausius relation, reversibility and reservoirs (of heat or work). Despite the merit of the authors in addressing these topics, we believe their treatment is based on incorrect premises.…”

“…< The temperature in the Clausius relation (3) is always that of the surroundings, which is different in the two situations described T T T . e e ¢ =  ( ) However, in (3), the authors of [1] wrongly considered the temperature always to be the system's (i.e. the oil vat temperature), leading to incorrect conclusions, which in turn prompted a new definition of reversible process that undermines the role of the surroundings and, therefore, makes no sense.…”

“…In [1] the authors often refer to the system (or surroundings) undergoing per se reversible or irreversible processes, thus ignoring completely that it is the process that is reversible or irreversible (not the system or surroundings alone). To emphasize this, note that for a process the total entropy variation satisfies…”