Maxwell's Demon proves why cold gases cannot make hot bodies hotter

James Clerk Maxwell is arguably the greatest physicist of all time on the topics of heat and radiation, and also perhaps the first to state in 1872 that Earth's temperature gradients and greenhouse effect are due to mass/gravity/pressure, rather than an effect of radiation from any infrared-active gases. 

Maxwell devised a simple and well-known thought experiment now called Maxwell's Demon, to prove why cold gases (such as the atmosphere at -18C on average), cannot make warmer gases or bodies (such as the Earth surface at +15C average) any warmer in violation of the second law of thermodynamics. 

The 2nd law of thermodynamics states disorder (called entropy) of any system (such as Earth's atmosphere) must always increase, and for any heat transfer to occcur from cold gases or bodies to warmer gases or bodies would result in an impossible decrease of entropy forbidden by the 2nd law of thermodynamics.

So, the next time someone claims a cold gas/body can make a warm body warmer, ask them for their solution to Maxwell's demon first:

Schematic of Maxwell's demon

Note: Maxwell along with his contemporaries and famous physicists including Clausius and Carnot (formally an engineer) all three agreed with each other in their writings that what is called today the 'greenhouse effect' was due only to the mass/gravity/pressure of the atmosphere, not radiation from gases. 

From Wikipedia entry on Maxwell's demon:

In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell to "show that the Second Law of Thermodynamics has only a statistical certainty".^[1] It demonstrates Maxwell's point by hypothetically describing how to violate the Second Law: a container of gas molecules at equilibrium is divided into two parts by an insulated wall, with a door that can be opened and closed by what came to be called "Maxwell's demon". The demon opens the door to allow only the faster than average molecules to flow through to a favored side of the chamber, and only the slower than average molecules to the other side, causing the favored side to gradually heat up while the other side cools down, thus decreasing entropy.

The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature.^[6] The second law is also expressed as the assertion that in an isolated system, entropy never decreases.^[6]

Maxwell conceived a thought experiment as a way of furthering the understanding of the second law. His description of the experiment is as follows:^[6][7]

... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.




Schematic figure of Maxwell's demon

In other words, Maxwell imagines one container divided into two parts, A andB.^[8][6] Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demonguards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. Likewise, when a slower-than-average molecule from B flies towards the trapdoor, the demon will let it pass from B to A. 

The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in Aand increases in B, contrary to the second law of thermodynamics. A heat engine operating between the thermal reservoirs A andB could extract useful work from this temperature difference.

The demon must allow molecules to pass in both directions in order to produce only a temperature difference; one-way passage only of faster-than-average molecules from A to B will cause higher temperature and pressure to develop on the B side.

Note cooling is not the new warming, and slowing of cooling is still cooling, not warming.