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  4. The efficiency of a Carnot engine is 60 %. If the temperature of source is 127°C, the sink must be maintained at

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Q. The efficiency of a Carnot engine is $60\%$. If the temperature of source is $127^{\circ}C$, the sink must be maintained at

UP CPMTUP CPMT 2012Thermodynamics

Solution:

Efficiency of a Carnot engine, $\eta=1-\frac{T_{2}}{T_{1}}$
where $T_{1}$ and $T_{2}$ are the temperature of the source and sink respectively.
Here, $\eta=60\%=\frac{60}{100}=0.6$
$T_{1}=127^{\circ}C=\left(127+273\right)\,K=400\,K, T_{2}=?$
$\therefore 0.6=1-\frac{T_{2}}{400}$
$\frac{T_{2}}{400}=1-0.6=0.4$
$T_{2}=160\,K=\left(160-273\right)^{\circ}C$
$=-113^{\circ}C$