An ideal heat engine has an efficiency ( ). The coefficient of performance of the engine when driven backward will be

Step-by-step solution

For ideal heat engine, efficiency is given as ( array ll & = W Q₁ = Q₁-Q₂ Q₁ & =1- Q₂ Q₁ =1- T₂ T₁ array ) ( array ll & T₂ T₁ =1- & T₁ T₂ = 1 1- (i) array ) When heat engine operated in backward direction, then coefficient of performance is given as ( aligned & = Q₂ W = Q₂ Q₁-Q₂ = T₂ T₁-T₂ & = 1 T₁ T₂ -1 = 1 1 1- -1 [from Eq. (i)] & = 1- 1-1+ = 1- = 1 -1 aligned )