A carnot engine having efficiency 1 6 , operates between the source temperature T_H and the sink temperature T_C . Its efficiency increases to 1 3 , when T_C is decreased by 64 K. The temperatures T_H and T_C are repectively

Step-by-step solution

The efficiency of a Carnot engine is given by = 1 - T_C T_H . Initially, = 1 6 , so: 1 6 = 1 - T_C T_H T_C T_H = 1 - 1 6 = 5 6 T_C = 5 6 T_H When T_C is decreased by 64 K , the new sink temperature is T_C - 64 . The new efficiency is 1 3 . 1 3 = 1 - T_C - 64 T_H T_C - 64 T_H = 1 - 1 3 = 2 3 T_C T_H - 64 T_H = 2 3 Substitute T_C T_H = 5 6 into the equation: 5 6 - 64 T_H = 2 3 64 T_H = 5 6 - 2 3 64 T_H = 5 - 4 6 = 1 6 T_H = 64 6 = 384 K Now, find T_C : T_C = 5 6 T_H = 5 6 384 = 5 64 = 320 K Therefore, T_H = 384 K and