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MHT CET · Physics · Thermodynamics

The efficiency of a heat engine is ' \(\eta\) ' and the coefficient of performance of a refrigerator is ' \(\beta\) '. Then

  1. A \(\eta=\frac{1}{\beta}\)
  2. B \(\eta=\frac{1}{\beta+1}\)
  3. C \(\eta \beta=\frac{1}{2}\)
  4. D \(\eta=\frac{1}{\beta-1}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\eta=\frac{1}{\beta+1}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} \beta & =\frac{T_2}{T_1-T_2} \\ \eta & =1-\frac{T_2}{T_1}=\frac{T_1-T_2}{T_1} \\ \therefore \quad \eta & =\frac{1}{1+\frac{T_2}{T_1-T_2}} \\ \therefore \quad \eta & =\frac{1}{1+\beta}\end{aligned}\)