A Carnot engine whose heat $\operatorname{sinks}$ at $27\,^{\circ} C$, has an efficiency of $25 \%$. By how many degrees should the temperature of the source be changed to increase the efficiency by $100 \%$ of the original efficiency $?$
JEE MAIN 2022, Diffcult
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$1-\frac{300}{ T }=0$
$\frac{300}{ T }=0.75$
$1-\frac{300}{ T }=0$
$\frac{300}{ T }=0.75$
$T =400 K$
If efficiency increased by $\,100 \%$ then new efficiency $\Rightarrow n ^{\prime}=50 \%$
$1-\frac{300}{T^{\prime}}=0.5$
$T^{\prime}=600 \,K$
Increase in temp $=600-400$
$=200\, K \text { or } 200^{\circ} C$
$T =400\, K$
If efficiency increased by $100 \%\,$ then new efficiency $\Rightarrow n ^{\prime}=50 \%$
$1-\frac{300}{T^{\prime}}=0.5$
$T^{\prime}=600\,K$
Increase in temp $=600-400$
$=200 K \text { or } 200\,^{\circ} C$
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