A Carnot engine whose efficiency is $50 \%$ has an exhaust temperature of $500 \mathrm{~K}$. If the…

A Carnot engine whose efficiency is $50 \%$ has an exhaust temperature of $500 \mathrm{~K}$. If the efficiency is to be $60 \%$ with the same intake temperature, the exhaust temperature must be (in $\mathrm{K}$ )
  1. 800
  2. 200
  3. 400
  4. 600

Solution

$\eta=1-\frac{T_{2}}{T_{1}}$ or $\frac{50}{100}=1-\frac{500}{T_{1}} \Rightarrow T_{1}=1000 \mathrm{~K}$
Also, $\quad \frac{60}{100}=1-\frac{T_{2}}{1000} \Rightarrow T_{2}=400 \mathrm{~K}$ *

Asked in: JEE-TOPICTESTS-CHEMISTRY

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