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Thermodynamics: Heat

Problems

Heat Engines

Processes with Heat and Work

Problem :

Say that a car engine runs at 600K. Calculate the Carnot efficiency for the engine.

We know that T h = 600K and that T l = 300K . The Boltzmann constants will cancel in the expression for the Carnot efficiency, so we obtain: η C = = 0.5 .

Problem :

What temperature requirements make the Carnot efficiency at a maximum?

The greater the ratio between the high temperature and the low temperature, the closer the efficiency becomes to 1. Therefore, an extremely low lower temperature and an extremely hot higher temperature yield a near perfectly efficient engine.

Problem :

Draw a diagram showing the entropy and energy flow in a refrigerator, just as we did for a heat engine. Include the possibility of unwanted additional entropy within the device.

Entropy and Energy in a Refrigerator

Problem :

The little light in the fridge was designed to shut off long before conservation of electricity was an accepted concern. Why?

All of the energy output from the light were it on would be generated within the refrigerator and the corresponding entropy would require extraction. A powerful bulb of say 20 Watts could substantially affect the cooling efficiency of the refrigerator.

Problem :

Explain why we can't open the door to the refrigerator as a method to cool the house.

This is a good one to know to save on your energy bills. Essentially, we are connecting the inside and outside of the device. We are extracting heat from the "inside" and dumping it into the "outside". We can take a step back, though, and realize that every bit of power that runs the refrigerator must be dissipated somewhere. Therefore the net result is that the power running the device goes to warm the house, not cool it, though it certainly warms the house efficiently.

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