Question

A Carnot’s engine is made to work between 200°C and 0°C first and then between 0°C and –200°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

Answer: (B)

1 : 1.73

Answer 2

In first case

$\eta_{1} = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{(273 + 0)}{(273 + 200)} = \frac{200}{473}$

In second case $\eta_{2} = 1 - \frac{(273 - 200)}{(273 + 0)} = \frac{200}{273}$

⇒ $\frac{\eta_{1}}{\eta_{2}} = \frac{1}{\left( \frac{473}{273} \right)} = 1:1.73$