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.
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QhTh−QcTc=0\frac{Q_h}{T_h}-\frac{Q_c}{T_c}=0
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The working substance returns to its initial state after a cycle, so its entropy change is zero. Clausius equality for a reversible cycle gives Qh/Th=Qc/TcQ_h/T_h=Q_c/T_c.