Question

A reversible heat engine receives $2kJ$ of heat from a reservoir at $1000K$ and a certain amount of heat to a reservoir at $400K$. The net work ouput (in$kJ$) of the cycle is

• A. $1.0$
• B. $0.8$
• C. $1.4$
• D. $2.0$

Answer 1

The correct option is C $1.4$


For reversible heat engine,
$\oint \frac{\delta Q}{T}=0$
$ie.,(\Delta S{)}_{Reservsiblecycle}=0$
or $\frac{Q_1}{T_1}+\frac{Q_2}{T_2}-\frac{Q_3}{T_3}=0$
or $\frac{Q_1}{1000}+\frac{Q_2}{800}-\frac{1}{400}=0$
or $Q_2=0.4kJ$
From energy balance,
$Q_1+Q_2=W+Q_3$
or $2+0.4=W+1$
or $W=1.4kJ$