Question

12. A Carnot engine operating at 34% efficiency exhausts heat into the heat sink at 350 °C. If we want to increase the efficiency of the engine to 46%, without changing the temperature of the heat reservoir, what would be the new temperature of the heat sink?

Answer 1

Solution We know that, Efficiency of cannot engine (n) = 1 1-T2 I - 1 (1) loo where, Ti = Temperature of reservoin and, Tz = Temperature of sink. Now given, Efficiency 34% = 34 = 0.34. Temperature of sink (TZ) = 350°C = 350 +273 k To = 623k Put all these values in equ (1) → 9 = 1- TI = 0.34 Te =1-623 y 0.34 623 = 0.66 = 623 T T a) To 623 k = 1 0.66 > Ti am 943.94 k lapprox.) 기 Temperature of heat reservoir, Now without changing the value of Te we have to increase the efficiency so we have to make changes in the value of Tz.

Efficiency 0.46 - T of Now we have. (n) = 46% = 46 100 and T 943.guk het new temperature the heat sink = Put all these values in equ (1) n = 1- T2 -) 0.46 = 1- T' T 943.94 Teh =1-0.46 {as Tz = T} 943.94 = 0.54 x 943-94 k. T' = 509.73 k ] (approx.) > T' y Result The new temperature of the heat sink is 5o9.73k,