MHT CET · Physics · Thermodynamics
The efficiency of a heat engine is ' \(\eta\) ' and the coefficient of performance of a refrigerator is ' \(\beta\) '. Then
- A \(\eta=\frac{1}{\beta}\)
- B \(\eta=\frac{1}{\beta+1}\)
- C \(\eta \beta=\frac{1}{2}\)
- D \(\eta=\frac{1}{\beta-1}\)
Answer & Solution
Correct Answer
(B) \(\eta=\frac{1}{\beta+1}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \beta & =\frac{T_2}{T_1-T_2} \\ \eta & =1-\frac{T_2}{T_1}=\frac{T_1-T_2}{T_1} \\ \therefore \quad \eta & =\frac{1}{1+\frac{T_2}{T_1-T_2}} \\ \therefore \quad \eta & =\frac{1}{1+\beta}\end{aligned}\)
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