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Imagine a special air filter placed in a window of a house. The tiny holes in the filter allow only air molecules moving faster than a certain speed to exit the house, and allow only air molecules moving slower than that speed to enter the house from outside. Explain why such an air filter would cool the house, and why the second law of thermodynamics makes building such a filter an impossible task.

If the house is an isolated system(no heat exchange between the house and the environment), then by the second law of thermodynamics, the entropy of the house cannot decrease. But in this process, the average velocity of the molecules decreaces, thus the entropy decreases.

My questions are

1) Is there any heat exchange between the house and the environment?

2) Is it true that when the average velocity of the molecules decreases, the entropy of the house decreases?

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    $\begingroup$ Such a device is not impossible, it's merely impossible to operate it for an infinite amount of time at a constant temperature difference. A battery operated AC system would be a practical implementation of a device that would cool the air on the way in and expel hot air out. At some point, because you require an isolated house, the batteries would go empty, though. If you want to argue with the second law, I wouldn't use the entropic formulation but the Clausius statement, which explicitly rejects the batteries in my AC example. $\endgroup$ – CuriousOne Apr 29 '15 at 19:22
  • $\begingroup$ @CuriousOne But is the house really an isolated system? $\endgroup$ – user43796 Apr 29 '15 at 19:25
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    $\begingroup$ As long as air flows in and out, it's not, and I do agree with you that it's not a very good example for a Maxwell demon problem. Let me guess, it came form a high school textbook? $\endgroup$ – CuriousOne Apr 29 '15 at 19:27
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Actually that's not an impossible task as long as you don't constrain the problem by not allowing energy input to the filter. The problem is the famous Maxwell 's Demon, but in the end you have to pay the demon. His efforts don't come free. The Hilsch tube, originally thought to house the demon fails the challenge as it takes excessive energy to separate hot and cold molecules. It only appears to work. The second law says no free lunch.

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  • $\begingroup$ What is your answer to the two questions I come up with? $\endgroup$ – user43796 Apr 29 '15 at 19:15
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    $\begingroup$ I advise you to research yourself. You can't really understand unless you do that. The stack is not a HW answer forum. $\endgroup$ – docscience Apr 29 '15 at 19:19
  • $\begingroup$ These questions do not come from any textbook. What is stack for if one cannot have anyone answer their questions and have to do research themselves? $\endgroup$ – user43796 Apr 29 '15 at 19:22
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    $\begingroup$ user43796: Stack can enable us to test our ideas with our peers and with those more experienced than we; it can jiggle our brains so that we come up with ideas that hadn't occurred to us; and it can point us toward resources that help us research, as well as providing us with definitive answers that expand our understanding. $\endgroup$ – Ernie Apr 29 '15 at 19:29
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    $\begingroup$ @user43796 to back up what docsience and Ernie are saying, we expect people asking here to be willing to put in some effort and do their own research as needed to get from the answer they get to the answer they want. $\endgroup$ – David Z Apr 30 '15 at 12:56
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1) Is there any heat exchange between the house and the environment?

If the molecules within the house decrease their average speed, there is most certainly an exchange of energy between the house and the outside environment. The Law of Conservation of Energy provides that energy neither can be created nor destroyed. The filter you described succeeds in transferring energy from inside to outside the house.

2) Is it true that when the average velocity of the molecules decreases, the entropy of the house decreases?

The Second Law of Thermodynamics says that within an isolated system, entropy can only increase. As the house in your problem is NOT an isolated system, it makes no sense to look at entropy only inside the house. One must look at entropy of the entire system, which includes the outside. If the Second Law is true, it would be impossible to operate such a filter without expenditure of energy, which must come from the entire system, increasing the entropy of the entire system.

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  • $\begingroup$ No,The Second Law of Thermodynamics says that within a ISOLATED system, entropy can only increase. Isolated is differen than closed. CLosed means that there is no mass exchange, and isolated means that there is no heat flow. A closed system can still be isolated, since it is possible for there to be no heat exchange while still having mass exchange occure. $\endgroup$ – user43796 Apr 29 '15 at 21:35
  • $\begingroup$ user43796: You are right. I edited the answer accordingly. The house is not isolated, because heat (kinetic motion of particles) is transferred. $\endgroup$ – Ernie Apr 29 '15 at 23:39

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