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
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(b) In first case ${\eta _1} = 1 - \frac{{{T_2}}}{{{T_1}}} = 1 - \frac{{(273 + 0)}}{{(273 + 200)}} = \frac{{200}}{{473}}$
In second case ${\eta _2} = 1 - \frac{{(273 - 200)}}{{(273 + 0)}} = \frac{{200}}{{273}}$
==> $\frac{{{\eta _1}}}{{{\eta _2}}} = \frac{1}{{\left( {\frac{{473}}{{273}}} \right)}} = 1:1.73$
In second case ${\eta _2} = 1 - \frac{{(273 - 200)}}{{(273 + 0)}} = \frac{{200}}{{273}}$
==> $\frac{{{\eta _1}}}{{{\eta _2}}} = \frac{1}{{\left( {\frac{{473}}{{273}}} \right)}} = 1:1.73$
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