Question

A Carnot's engine is made to work between $227{}^{\circ }C$ and $27{}^{\circ }C$ first and then between $27{}^{\circ }C$ and $-173{}^{\circ }C$. The ratio of efficiency of second process to first process $\left(\frac{{\eta }_2}{{\eta }_1}\right)$ of the engine in the two cases is

• A. $1:1.5$
• B. $1:1$
• C. $1:2$
• D. $1.66:1$

Answer 1

The correct option is D $1.66:1$

Given,
$T_1=227{}^{0}C=500K$
$T_2=27{}^{0}C=300K$
$T_3=-173{}^{0}C=100K$

Carnot's engine will take heat from source of higher temperature and rejects heat to sink of lower temperature.

For case 1;
${\eta }_1=1-\frac{T_2}{T_1}$
${\eta }_1=1-\frac{300}{500}=\frac{200}{500}$

For case 2;
${\eta }_2=1-\frac{T_3}{T_2}$
$n_2=1-\frac{100}{300}=\frac{200}{300}$
$\frac{n_2}{n_1}=\frac{500}{300}=1.66$