A Carnot engine is operated between 2 resovoirs at temperature 177°C and 77°C. If the engine recieves 4200J of heat energy from the source in each cycle, calculate the amount of heat rejected to the sink in each cycle. Calculate the efficiency of engine.

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Solution

We know that efficiency of Carnot engine is 1-T2/T1

Where T1= 177°C = 273+177 = 450 K

T2 = 77°C = 273+77 = 350

Efficiency = 1-350/450

Efficiency = 100/450

Efficiency = 2/9

Efficiency of engine = work output / heat input

Work output = Efficiency* heat input = 2/9 * 4200 = 933.33 J

Heat from source = work done + Heat released to sink

4200 J = 933.33 + heat released to sink

Heat released to sink = 4200-933.33

Heat released to sink = 3266.67 J

Answer : Heat released to sink = 3266.67 J and efficiency = 2/9

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