Calculating Efficiency of a Heat Engine with COP = 5.0 and 25kJ Heat Removal

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The discussion centers on calculating the efficiency of a heat engine with a coefficient of performance (COP) of 5.0, which removes 25 kJ of heat from a cold reservoir. The relationship between heat removed (QL), work done (W), and heat added (QH) is emphasized, with W calculated as 5 kJ. It is clarified that QH is not equal to QL, and conservation of energy principles should be applied to relate these quantities. The correct formula for efficiency is stated as e = W/QH. Understanding these relationships is crucial for accurately determining the engine's efficiency.
kasse
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Homework Statement



A machine with COP = 5.0 removes 25kJ of heat from a cold reservoar. If the machine is reversible and driven the other way as a heat engine, what is the efficiency?

The Attempt at a Solution



COP = QL/W --> W = 5kJ

e = QH/W

Is QH the same as QL som that e = 20%
 
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Hi kasse,

No, I don't believe that Q_H and Q_L are the same. Using conservation of energy, you can find out how Qh, QL, and W are related. What do you get?

Also, your efficiency formula needs to be:

<br /> e=\frac{W}{Q_H}<br />
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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