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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Qc=QhTc/Th, W=Qh(1−Tc/Th), η=1−Tc/Th; lim⁡Tc→Thη=0, lim⁡Tc→0η=1\boxed{Q_c=Q_hT_c/T_h,\ W=Q_h(1-T_c/T_h),\ \eta=1-T_c/T_h;\ \lim_{T_c\to T_h}\eta=0,\ \lim_{T_c\to0}\eta=1}
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This is the collected answer to all parts. It obeys the stated assumptions and conventions.