Question

The relation between efficiency $\eta$ of a heat engine and the co-efficient of performance $\alpha$ of a refrigerator is:

• A. $\eta =\frac{1}{1-\alpha }$
• B. $\eta =\frac{1}{1+\alpha }$
• C. $\eta =1+\alpha$
• D. $\eta =1-\alpha$

Answer 1

The correct option is B $\eta =\frac{1}{1+\alpha }$

Efficeiency if a heat engine is given by:

$\Rightarrow \eta =1-\frac{T_2}{T_1}$

$=\frac{T_1-T_2}{T_1}$

$=\frac{1}{1+\frac{T_2}{T_1-T_2}}$

$=\frac{1}{1+\alpha }$