Imagine one such infinitesimal step taken by the system, during which the Carnot
engine goes through one complete microcycle and receives heat dQ R from the
reservoir and supplies heat dQ system to the system. The system is at an instantaneous
uniform temperature of T(t) at that point in time t. Let the work produced by the
Carnot engine be dW Carnot and the work performed by the system be dW System . Now
denote the combined system (the system–with–reversible-Carnot-machine) as C,
which is identified by the dotted-line box in Fig. 5.1. The combined work output of
the Carnot engine and the system will be expressed as dW C
dW Carnot þ dW System ¼ dW C
Applying the energy balance to the combined system C yields
dW C ¼ dQ R À dU C
Since the Carnot machine undergoes a cyclic process, there is no change in the
internal energy of its working fluid; the internal energy change of the system
dU System in the above equation represents a change in the internal energy of the
combined system C.
dW C ¼ dQ R ÀdU System
Applying either Eq. (46) or Eq. (55) to the Carnot machine
δW C = δW Carnot + δW system
The combined system
undergoes a CYCLIC
PROCESS, in which,
∫
= 0
system
dU
Combined System C
TR – surrounding reservoir
T
dU system
Carnot
δQ R
δQ sys
Fig. 5.1 Thought experiment to demonstrate the first Clausius theorem
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5 Entropy and the Entropy Principle