Question

The efficiency of a Carnot heat engine is $\frac{1}{3}.$ Find the coefficient of performance of Carnot refrigerator when both heat engine and refrigerator are working between similar source and sink.

• A. $2$
• B. $3.25$
• C. $4$
• D. $7.1$

Answer 1

The correct option is A $2$

Here same source and sink have been used for the heat engine and refrigerator both, hence the same Carnot engine is involved for both cases.
Efficiency of heat engine is,
$\eta =\frac{1}{3}$
The relation between $\beta \&\eta$ when same Carnot engine is used,
$\Rightarrow \beta =\frac{1-\eta }{\eta }$
$\therefore \beta =\frac{1-\frac{1}{3}}{\frac{1}{3}}=2$