$5\mathrm{.}14.$ A Carnot engine operates between an infinite hot reservoir and a finite cold reservoir of total heat capacity $C_C^t.$

$($a$)$ Determine an expression for the work obtained as a function of $C_C^t,T_H(=$ constant$),T_C,$ and the initial cold$-$reservoir temperature $T_{C_0}.$

$($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. $5\mathrm{.}13.$