A Carnot engine operates between two finite heat reservoirs of total heat capacity C ^t_H and C^t_C
(a) Develop an expression relating T_C to T_H at any time.
(b) Determine an expression for the work obtained as a function of C ^t_H, C^t_C , T_H , and the initial temperatures T_H0 and T_C0 .
(c) What is the maximum work obtainable? This corresponds to infinite time, when the reservoirs attain the same temperature.

In approaching this problem, use the differential form of Carnot’s equation,
and a differential energy balance for the engine,
                             dW − dQ_C − dQ_H = 0
Here, Q_C and Q_H refer to the reservoirs.

Transcribed Image Text:

TH dQH dQc Tc