A Carnot engine whose low-temperature reservoir is at 350   K has an efficiency of 50 % . It is desired to increase the efficiency to 60 % . If the temperature of the low-temperature reservoir is kept constant, then by how many kelvins the temperature of the high-temperature reservoir must be increased to get the desired efficiency?

Step-by-step solution

The efficiency of the Carnot engine, η = 1 - T c o l d T h o t × 100 When η = 50 % then 50 100 = 1 - T c o l d T h o t ⇒ 0.5 = 1 - 350 T h o t or T h o t = 700   K When η = 60 % then 60 100 = 1 - T c o l d T h o t ⇒ 0.6 = 1 - 350 T h o t or T h o t = 875   K Hence, the temperature of the high reservoir is increased by T ′ h o t - T h o t = 875   K - 700   K = 175   K