 # Carnot Heat Engine

Subject Physics Classical Mechanics

## Question

1a) It is claimed that the efficiency of a completely reversible heat engine can be doubled by doubling the temperature of the energy source. Justify the validity of this claim.
1b) Carnot heat engine receives heat at 730 K and rejects the waste heat to the environment at 300 K.
The entire work output of this engine is used to drive a Carnot Refrigerator that removes heat from cooled space at -15°C at a rate of 400kJ/min and. Determine:
a) the rate of heat supplied to the engine.
b) the total rate of heat rejection to the environment.

2.
A refrigerator (see figure) operates al steady stale with a coefficient of performance of 4.5 and a power input of 0.8 kW. Energy is rejected from the refrigerator to the surroundings at 20°C by heat transfer from a metal coils whose average surface temperature is 28°C. Determine:
a) the rate energy is rejected, in kW
b) the lowest theoretical temperature inside the refrigerator, in K
c) the maximum theoretical power, in kW, that could be developed by a heat engine operating between the coils and the surroundings. Would you recommend making use of this opportunity for developing power?

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