A Carnot engine has efficiency of 50 % . If the temperature of sink is reduced by 40 ° C , its efficiency increases by 30 % . The temperature of the source will be :

Step-by-step solution

Initial efficiency η 0 = 50 % , the increase in efficiency is 30 % . Therefore, new efficiency η = 50 1 + 30 100 = 65 % . Efficiency of the Carnot engin is given by η = 1 - T L T H ⇒ η 0 = 1 2 = 1 - T L T H When the temperature of the sink is decreased by 40 ° C = 40   K . η = 1 2 1 · 3 = 1 - T L - 40   T H ⇒ 1 2 1 · 3 = 1 2 + 40 T H ⇒ T H = 266 . 7   K