Question

A real heat engine operates between temperatures tc and th. during a certain time, an amount qc of heat is released to the cold reservoir. during that time, what is the maximum amount of work wmax that the engine might have performed?

Answer 1

$q_{c}$ = Heat released to cold reservoir

$q_{h}$ = Heat released to hot reservoir

$W_{max}$ = maximum amount of work

$t_{c}$ = temperature of cold reservoir

$t_{h}$ = temperature of hot reservoir

we know that

$\frac{q_{c}}{q_{h}}=\frac{t_{c}}{t_{h}}$

$q_{h} = (\frac{t_{h}}{t_{c}})q_{c}$                                eq-1

maximum work is given as

$W_{max}$ = $q_{h}$ - $q_{c}$

using eq-1

$W_{max}$ =  $(\frac{t_{h}}{t_{c}})q_{c}$ - $q_{c}$