1. Tardigrade
  2. Question
  3. Physics
  4. A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62°C, the efficiency of the engine is doubled. The temperatures of the source and sink are

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Q. A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62$^{\circ}$C, the efficiency of the engine is doubled. The temperatures of the source and sink are

AIIMSAIIMS 2010

Solution:

$\eta_{1}=1-\frac{T_{L}}{T_{H}}=\frac{W}{Q_{1}}=\frac{1}{6}$
or $5T_{H}-6T_{L}=0 ...\left(i\right)$
$\eta_{2}=1-\frac{T_{L}-62}{T_{H}}=2\eta_{1}=\frac{1}{3} \left(Given\right)$
$\Rightarrow 1-\frac{1}{3}=\frac{T_{L}-62}{T_{H}}$
or $2T_{H}-3T_{L}=-186 ...\left(ii\right)$
Solving $\left(i\right)$ and $\left(ii\right)$, we get
$\therefore T_{H} = 372 \,K = 99^{\circ}C$
$T_{L}=\frac{5}{6}T_{H}=\frac{5}{6}\times 372\, K=310\, K =37^{\circ}C$