In a Carnot engine, when ${T_2} = {0^o}C$ and ${T_1} = {200^o}C,$ its efficiency is ${\eta _1}$ and when ${T_1} = 0{\,^o}C$ and ${T_2} = - 200{\,^o}C$, Its efficiency is ${\eta _2}$, then what is ${\eta _1}/{\eta _2}$
A$0.577$
B$0.733$
C$0.638$
D
Can not be calculated
Medium
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A$0.577$
a (a) $\eta = 1 - \frac{{{T_2}}}{{{T_1}}} = \frac{{{T_1} - {T_2}}}{{{T_1}}}$ $ \Rightarrow \,{\eta _1} = \frac{{(473 - 273)}}{{473}} = \frac{{200}}{{473}}$
and ${\eta _2} = \frac{{273 - 73}}{{273}} = \frac{{200}}{{273}}$
So required ratio $\frac{{{\eta _1}}}{{{\eta _2}}} = \frac{{273}}{{473}} = 0.577$
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