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  4. A Cannot engine whose efficiency is 40%, receives heat at 500 K. If the efficiency is to be 50%, the source temperature for the same exhaust temperature is

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Q. A Cannot engine whose efficiency is 40%, receives heat at 500 K. If the efficiency is to be 50%, the source temperature for the same exhaust temperature is

KEAMKEAM 2011

Solution:

Cannot efficiency relation $ \eta =\frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}} $
Case I $ \frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}}=0.4 $
$ {{T}_{1}}-{{T}_{2}}=0.4{{T}_{1}} $
$ {{T}_{2}}=0.6{{T}_{1}} $
Case II $ \frac{T_{1}^{}-{{T}_{2}}}{T_{1}^{}}=0.5 $
$ T_{1}^{}=\frac{0.6}{0.5}{{T}_{1}}=600\,K $