A Carnot engine operates between an infinite hot reservoir and a finite cold reservoir of total heat capacity C^t_C.
(a) Determine an expression for the work obtained as a function of C^t_C, T_H (= constant), T_C, and the initial cold-reservoir temperature T_C0.
(b) What is the maximum work obtainable? This corresponds to infinite time, when T_C becomes equal to T_H.
The approach to this problem is the same as for Prob. 5.13.

Problem 5.13

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