An ideal Carnot engine, whose efficiency is $40 \%$ receives heat at $500\; K$. If its efficiency is $50 \%$ then the intake temperature for the same exhaust temperature is ......... $K$
AIPMT 1995, Medium
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Efficiency of Carnot engine $\left(\eta_{1}\right)=40 \%=0.4 ;$ Heat intake $=500 K$ and New efficiency $\left(\eta_{2}\right)=50 \%=0.5$
The efficiency $(\eta)=1-\frac{T_{2}}{T_{1}}$ or $\frac{T_{2}}{T_{1}}=1-\eta$
For first case, $\frac{T_{2}}{500}=1-0.4$
$T_{2}=300 K$.
For sewnd case, $\frac{300}{T_{1}}=1-0.5$
$T_{1}=6 00 K .$
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