Theoretical Limits on Perpetual Motion Kelvins and Clausius Principles

4 THEORETICAL LIMITS ON PERPETUAL MOTION KELVIN S AND CLAUSIUS PRINCIPLES 

Carnot s principle (4.10) may not seem particularly compelling from experience. However, we can easily derive some consequences from (4.10) that are indeed more obvious statements about the irreversibility of natural events, and hence provide compelling inductive proof of the truth of Carnot s principle. These derivative principles were first obtained by Thomson (Kelvin) and Clausius. 

The derivations presented below illustrate the logical technique of proof by contradiction. In this method of proof, we begin by assuming that Carnot s principle is untrue, then demonstrate that we could easily produce crazy consequences that contradict experience if this assumption were valid. That is, we conclude that Carnot s principle must be true, because the contrary assumption leads to inconsistencies with inductive experience. 

Let us therefore begin by assuming that Carnot s principle is false, i.e., that there exists some new and improved model C whose efficiency exceeds that of the reversible Carnot cycle. The hypothetical C engine can be represented as 

With the improved C in hand, we can now envision operating the old Carnot cycle as a heat pump C, then coupling this to C as shown in (4.15), using the heat output qh from heat pump C, to drive the improved heat engine C (i.e., with qh = gj )  

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