First slide

Heat engine

Question

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

Moderate

A

1 : 73 . 1
B

1 : 1.73
C

1 : 1
D

1 : 2

Solution

In first case $η_{1} = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{(273 + 0)}{(273 + 200)} = \frac{200}{473}$
In second case $η_{2} = 1 - \frac{(273 - 200)}{(273 + 0)} = \frac{200}{273}$
$\Rightarrow \frac{η_{1}}{η_{2}} = \frac{1}{(\frac{473}{273})} = 1 : 1 . 73$

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