Physic Labs

Problem 2

A reversible Carnot engine operates between reservoirs at absolute temperatures Th>TcT_h>T_c. In each cycle it absorbs heat QhQ_h from the hot reservoir. Find its efficiency η\eta, rejected heat QcQ_c, and work output WW. (a) Apply the Clausius equality for a reversible cycle to relate Qh,Qc,Th,TcQ_h,Q_c,T_h,T_c. (b) Use the first law to find work WW and efficiency η\eta. (c) Examine Tc→ThT_c\to T_h and Tc→0T_c\to0, explain their physical meaning, and state why absolute temperatures are required.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
Tc→Th:η→0;Tc→0:η→1T_c\to T_h:\eta\to0;\quad T_c\to0:\eta\to1
problems.proof.analysis

As reservoir temperatures approach equality, the available temperature difference vanishes and both work and efficiency tend to zero. The ideal efficiency approaches one only as TcT_c tends to zero.