A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52 K , its efficiency is doubled. The temperature in Kelvin of the source will be ___ .

Step-by-step solution

Efficiency of reversible engine is η = 1 4 = W Q in = 1 - T 2   T 1 From above, T 2   T 1 = 3 4 When the temperature of the sink is reduced by 52   K then its efficiency is doubled. Then, T 2 - 52   T 1 = 1 2 ⇒ T 2   T 1 - 52   T 1 = 1 2 ⇒ 3 4 - 52   T 1 = 1 2 ⇒ 52   T 1 = 3 4 - 1 2 = 1 4 ⇒ T 1 = 52 × 4 = 208   K