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  4. A Carnot heat engine has an efficiency of 10 %. If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

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Q. A Carnot heat engine has an efficiency of $10 \%$. If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

Thermodynamics

Solution:

$\eta=1-\frac{T_{2}}{T_{1}}, \frac{T_{1}}{T_{2}}=\frac{1}{1-\eta}$
$\omega =\frac{T_{2}}{T_{1}-T_{2}}=\frac{1}{\left(T_{1} / T_{2}\right)-1}$
$=\frac{1}{[1 /(1-\eta)]-1}=\frac{1-\eta}{\eta}$
As $\eta =10 \%=0.1,$
$\omega=\frac{1-0.1}{0.1}=9$