Problem 2

A reversible Carnot engine operates between reservoirs at absolute temperatures

T_h>T_c

. In each cycle it absorbs heat

Q_h

from the hot reservoir. Find its efficiency

\eta

, rejected heat

Q_c

, and work output

W

. (a) Apply the Clausius equality for a reversible cycle to relate

Q_h,Q_c,T_h,T_c

. (b) Use the first law to find work

W

and efficiency

\eta

. (c) Examine

T_c\to T_h

and

T_c\to0

, explain their physical meaning, and state why absolute temperatures are required.

problems.proof.stepOf

\eta=W/Q_h=1-Q_c/Q_h

problems.proof.analysis

Efficiency is output work divided by input heat $Q_h$ . Substituting the energy balance gives $\eta=1-Q_c/Q_h$ .