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
Qc=QhTcThQ_c=Q_h\frac{T_c}{T_h}
problems.proof.analysis

Solving the reversible relation gives rejected heat Qc=QhTc/ThQ_c=Q_hT_c/T_h. Since Tc<ThT_c<T_h, this satisfies 0<Qc<Qh0<Q_c<Q_h.

problems.proof.pitfall. Pitfall: inserting Celsius temperatures into the Carnot expression. The ratio Tc/ThT_c/T_h is valid only for absolute temperatures in kelvin.