Question

A Carnot engine $(CE-1)$ works between two temperature reservoirs $A$ and $B$, where $T_A=900K$ and $T_B=500K.$ A second Carnot engine $(CE-2)$ words between temperature reservoirs $B$ and $C$, where $T_C=300K$. In each cycle of $CE-1$ and $CE-2$, all the heat rejected by $(CE-1)$ to reservoir $B$ is used by $CE-2$. For one cycle of operation, if the net $Q$ absorbed by $CE-1$ from reservoir $A$ is $150MJ$, the net heat rejected to reservoir $C$ by $CE-2$ (in $MJ$) is

• A. 50

Answer 1

The correct option is A 50

Carnot engiens $(CE-1,CE-2)$ are in series,
For Carnot engine $(CE-1)$
${\eta }_1=1-\frac{T_B}{T_A}$
also ${\eta }_1=1-\frac{Q_B}{Q_A}$
$\therefore 1-\frac{T_B}{T_A}=1-\frac{Q_B}{Q_A}$
or $\frac{T_B}{T_A}=\frac{Q_B}{Q_A}$
$\frac{500}{900}=\frac{Q_B}{150}$
or $Q_B=\frac{5\times 150}{9}MJ$
For Carnot engine $(CE-2)$
${\eta }_2=1-\frac{T_C}{T_B}$
also ${\eta }_2=1-\frac{Q_C}{Q_B}$
$\therefore 1-\frac{T_C}{T_B}=1-\frac{Q_C}{Q_B}$
or $\frac{T_C}{T_B}=\frac{Q_C}{Q_B}$
$\frac{300}{500}=\frac{Q_C}{\frac{5\times 150}{9}}$
or $Q_c=50MJ$