In a recent Note,1 the entropy production in a process of thermalization between a system and a heat reservoir was depicted graphically for given initial temperatures T1<T2. The process may occur via heating the system or by cooling it, depending on how the temperatures are assigned to the system and the reservoir. A simple extension of this Note considers a cyclic process involving two heat reservoirs, where the system, initially in equilibrium with the reservoir at temperature T1, undergoes heating followed by cooling (121). In each iteration of the cycle, an amount of heat Q=C(T2T1)>0 is transferred from the reservoir 2 to reservoir 1. Then, the total entropy production is the sum of contributions from each process and is depicted by the area of the rectangle (Fig. 1, Ref. 1) with sides [C/T2,C/T1] and [T1,T2], given by
(1)
(2)
which, as expected, yields the entropy produced if Q amount of heat flows from reservoir 2 to reservoir 1.

Diagrammatic representations of irreversible processes depicting entropy production have been studied earlier via the so-called Bucher diagram,2,3 in which the heat exchanged with the reservoir Q and its temperature T are displayed by mutually orthogonal lines, so that the entropy production in the above-mentioned cyclic process is represented by the difference in the slopes Q/T1 and Q/T2. This Note joins those works in providing useful ways for students to visualize entropy changes.

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Andrés
Vallejo
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A diagrammatic representation of entropy production
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Inefficiency and irreversibility in the Bucher diagram
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Manfred
Bucher
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Diagram of the second law of thermodynamics
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