A Carnot engine operating between temperatures $T_{1}$ and $T_{2}$ has efficiency $\frac{1}{6} .$ When…

A Carnot engine operating between temperatures $T_{1}$ and $T_{2}$ has efficiency $\frac{1}{6} .$ When $T_{2}$ is lowered by $62 \mathrm{~K}$ its efficiency increases to $\frac{1}{3} .$ Then $T_{1}$ and $T_{2}$ are, respectively
  1. $372 \mathrm{~K}$ and $330 \mathrm{~K}$
  2. $330 \mathrm{~K}$ and $268 \mathrm{~K}$
  3. $310 \mathrm{~K}$ and $248 \mathrm{~K}$
  4. $372 \mathrm{~K}$ and $310 \mathrm{~K}$

Solution

$\eta_{1}=1-\frac{T_{2}}{T_{1}} \Rightarrow \frac{1}{6}=1-\frac{T_{2}}{T_{1}} \Rightarrow \frac{T_{2}}{T_{1}}=\frac{5}{6} \ldots$
$\eta_{2}=1-\frac{T_{2}-62}{T_{1}} \Rightarrow \frac{1}{3}=1-\frac{T_{2}-62}{T_{1}} \ldots$
On solving Eqs. (i) and (ii) $T_{1}=372 \mathrm{~K}$ and $T_{2}=310 \mathrm{~K}$ ,

Asked in: JEE-TOPICTESTS-CHEMISTRY

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