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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W=Qh−QcW=Q_h-Q_c
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Over a full cycle the internal-energy change is zero. The first law therefore splits absorbed heat into rejected heat and work: W=Qh−QcW=Q_h-Q_c.