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Let $η_{1}$ is the efficiency of an engine at $T_{1} = 447^{0} C$ and $T_{2} = 147^{0} C$ while $η_{2}$ is the efficiency at $T_{1} = 947^{0} C$ and $T_{2} = 47^{0} C$ . Then the ratio of $\frac{η_{1}}{η_{2}}$ will be

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0.70

0.41

0.73

0.56

answer is D.

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Detailed Solution

case (i)

$η_{1} = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{420}{720} = \frac{300}{720}$

Case(ii)

$η_{2} = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{320}{1220} = \frac{900}{1220}$

$\frac{η_{1}}{η_{2}} = \frac{300}{720} \times \frac{1220}{900} = \frac{122}{216} = 0.56$

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