Question

A carnot engine absorbs $1000J$ of heat from a reservoir at ${127}^{\circ }C$ and reject $600J$ of heat during each cycle.
Calculate (a) The efficiency of engine
(b) The temperature of the sink
(c) The amount of the useful work done during each cycle.

Answer 1

Given : $Q_H=1000J$ $Q_L=600J$
Also, $T_H={127}^{o}C=127+273=400K$
(a) : Efficiency of engine $\eta =1-\frac{Q_L}{Q_H}$
$⟹\eta =1-\frac{600}{1000}=0.4$
Thus efficiency of engine is $40$%.
(b) : Using $\frac{T_L}{T_H}=\frac{Q_L}{Q_H}$
$\therefore$ $\frac{T_L}{400}=\frac{600}{1000}$
$⟹T_L=240K$
(c) : Amount of useful work done during each cycle $W=Q_H-Q_L$
$⟹W=1000-600=400J$