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
η=1−TcTh\eta=1-\frac{T_c}{T_h}
problems.proof.analysis

Insert the reversible heat ratio to obtain Carnot’s limit η=1−Tc/Th\eta=1-T_c/T_h. Temperatures must be absolute, and efficiency remains below one.

problems.proof.pitfall. Pitfall: adding absorbed and rejected heat to find work. For a cycle, the first law gives W=Qh−QcW=Q_h-Q_c when Qh,QcQ_h,Q_c are magnitudes.