A Carnot engine whose efficiency is 40% takes in heat from source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

Step-by-step solution

Efficiency of Carnot engine, ₁=40 %=0.4 Temperature of source T₁=500 ~K Temperature of sink T₂=T Desired efficiency, _ =60 %=0.6 Temperature of sink T₂=T Temperature of source T₁= ? For case 1 Efficiency, ₁=1- T₂ T₁ =1- T 500 aligned & & 4 10 & = 500-T 500 & & 200 & =500-T & & T & =300 ~K aligned For case 2 Efficiency, ₂=1- T₂ T₁ =1- T T₁^ aligned 6 10 & =1- 300 T₁^ 300 T₁^ & =1- 6 10 300 T₁^ = 4 10 300 4 10 & =T₁^ T₁^ =750 ~K aligned