Heat and Thermodynamics

9.5 Carnot's Theorem

All reversible engines working between the same limits of temperature must have the same efficiency.

Proof (A): If not, let an engine S be more efficient than an engine R (Fig. 9.3). This means that by drawing the same quantity of heat from the source, the work W_S produced by S is greater than the work W_R produced by R. Accordingly, S can be made to drive R backwards.

 

 

Fig. 9.3 Scheme representing Carnot's theorem

 

Let the quantity of heat drawn by S from the source be Q. Then, the quantity of heat given by S to the refrigerator is (Q − W_s). Let the quantity of working substance in R be so adjusted that in each reverse ...