Question

A carnot's engine is made to work between ${200}^{o}C$ and $0^{o}C$ first and then between $0^{o}C$ and ${-200}^{o}C$. The ratio of efficiencies of the engine in the two cases is:

• A. $1.73:1$
• B. $1:1.73$
• C. $1:1$
• D. $1:2$

Answer 1

The correct option is B $1:1.73$

Case 1:

$T_1=0°C=(0+273)K=273K$

$T_2=200°=(200+273)K=473K$

${\eta }_1=1-\frac{T_1}{T_2}=1-\frac{273}{473}=0.422$

Case 2:

$T_1=-200°C=(-200+273)K=73K$

$T_2=0°=(0+273)K=273K$

${\eta }_2=1-\frac{T_1}{T_2}=1-\frac{73}{273}=0.73$

Ratio of efficiencies, ${\eta }_1:{\eta }_2=0.42:0.73=1:1.73$