The relation between efficiency ( ) of Carnot engine and coefficient of performance ( ₁ ) of refrigerator is

Step-by-step solution

Relating efficiency and coefficient of performance The efficiency of a Carnot engine operating between reservoirs at temperatures T₁ and T₂ is given by = 1 - T₂ T₁ , from which we obtain T₂ T₁ = 1 - . The coefficient of performance for a refrigerator operating between the same reservoirs is ₁ = T₂ T₁ - T₂ . Dividing numerator and denominator by T₁ gives ₁ = T₂/T₁ 1 - T₂/T₁ . Substituting T₂/T₁ = 1 - yields ₁ = 1 - 1 - (1 - ) = 1 - . Solving for gives ₁ = 1 - , then ( ₁ + 1) = 1 , resulting in = 1 ₁ + 1 . Final answ