Hey how can I solve this? A Carnot engine operates with an efficiency of 25.0% w

Question

Hey how can I solve this? A Carnot engine operates with an efficiency of 25.0% when thetemperature of its cold reservoir is 263 K. Assuming that thetemperature of the hot reservoir remains the same, what must be thetemperature of the cold reservoir in order to increase theefficiency to 32.0%? Thanks! Hey how can I solve this? A Carnot engine operates with an efficiency of 25.0% when thetemperature of its cold reservoir is 263 K. Assuming that thetemperature of the hot reservoir remains the same, what must be thetemperature of the cold reservoir in order to increase theefficiency to 32.0%? Thanks!

Explanation / Answer

Efficiency of the engine              e = 1 - TL / TH              0.25= 1 - 263/ TH ==> 263/ TH = 1 -0.25          TH = 263 / 0.75 = 350.66 K So that the efficiency of the engine increases to 32%when temperature of the cold reserviour is            TL = (1-e)TH   = ( 1- 0.32) *350.66 = 238.44 K ==> 263/ TH = 1 -0.25          TH = 263 / 0.75 = 350.66 K So that the efficiency of the engine increases to 32%when temperature of the cold reserviour is            TL = (1-e)TH   = ( 1- 0.32) *350.66 = 238.44 K

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