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?