Question

A Carnot engine works first between ${200}^{o}C$ and $0^{o}C$ and then between $0^{o}C$ and $-{200}^{o}C$. The ratio of its efficiency in two cases is

• A. $1.0$
• B. $0.577$
• C. $0.34$
• D. $0.68$

Answer 1

The correct option is B $0.577$

$\eta =1-\frac{T_2}{T_1}$
= $1-\frac{273+0}{273+200}$
= $\frac{200}{473}$

${\eta }^{{}^{\prime }}=1-\frac{T_2}{T_1}$
= $1-\frac{(273-200)}{273+0}$
= $\frac{200}{473}$

$\frac{\eta }{{\eta }^{{}^{\prime }}}=\frac{200}{473}\times \frac{273}{200}=0.577$