Maximum efficiency of an engine working between temperatures T2 and T1 is given by the fraction of the heat absorbed by an engine which can be converted into work is known as efficiency of the heat engine.
Mathematically,
In First case:
Efficiency, η = (T2 – T1) / T2
T2 = 500 K (temperature of the source)
T1 = 100 K (temperature of the sink)
Therefore,
η = (T2 – T1) / T2
= (500 – 100) / 500
= 4 / 5
In second case:
Efficiency, η = (T2 – T1) / T2
T2 = 900 K (temperature of the source)
T1 = T K (temperature of the sink)
Therefore,
η = (T2 – T1) / T2
= (900 – T) / 900
It is given that the Carnot engine has the same efficiency. Hence equating the efficiency of both the cases we will get:
(900 – T) / 900 = 4 / 5
5 (900 – T) = 3600
4500 – 3600 = 5T
900 / 5 = T
T = 180 K
Hence the temperature T of the sink is equal to 180 K
