Thursday, December 11, 2014

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 physicsMaxwell'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 systementropy 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. 


  1. In my opinion the paradox of Maxwell's Demon was resolved by Einstein in 1905 with his work on Brownian movement.

  2. So far so good, but with an external energy source (such as the suns rays) you can separate the hot particles from the cold, this is what a fridge does.
    And with an external energy source, a cold body such as a magnifying glass made of ice can light a fire.

    1. Anonymous, you just don't get thermodynamics do you ???

      A fridge "pumps" warm from the inside to the outside using an external energy source (usually electricity, but propane and even steam can be used). It does not "separate" the hot and cold particles. Ever notice that your unplugged fridge gets warm inside (after a time delay of course) ?

      Also, please let us know when you manage to light a fire by aiming an "ice lens" at a piece of wood at night time....

      Cheers, KevinK.

  3. Cooling in a stationary high pressure.

  4. What a pointless article. We all know that there is no net energy transfer across any internal boundary when thermodynamic equilibrium is attained. That does not prevent a vertical temperature gradient within either half.

    1. It is not pointless, and clearly demonstrates the AGW claim that more (CO2) colder gases at ave -18C can make a warmer surface +15C even warmer is ludicrous.

      Furthermore, the temperature gradient is entirely due to mass/gravity/pressure, not the concentration of greenhouse gases.

  5. Memo (again) to Doug Cotton:

    I'm well aware it's you trying to slip comments through under a wide variety of aliases. You are permanently banned from any commentary ever again at this site, and under any alias as well. Waste your time complaining about it at other sites. I've got better things to do than counter a raving lunatic and his ridiculous threats.

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

    You might want to consider that is something is cooling slower, it will be warmer than it otherwise would have been.

  7. See also:

  8. Hmm.. Seems to me that maxwell's demon isn't proof of anything, but rather a demonstration of a paradox. And not one I believe in. If maxwell's demon existed, then by the parameters of the experiment, he can do *exactly* what he is tasked to do. Wait for that one moment where a molecule passes from one side to another.

    The thing that cannot exist is Maxwell's demon. As long as there is an equal amount of movement on each side, there is an equal chance an open door will allow a molecule from each side through. Moreover, as more molecules are collected on one side, there is more pressure from that side to the other, increasing the chance that a molecule moves back. The last is of course allowed under the second, since the flow goes from warm to cold.

    The second law is an *average*. But energy transfers and swirl happen all the time. In this thought experiment, a high energy molecule escapes into the other chamber. The system is still at the same entropy. If the particle collides with the others in the other system, it is a higher energy molecule transferring energy to other molecules. Nothing is violated by Maxwell, even if he could exist.

    This is definitely a case where the individuals in a system (the particles) are treated incorrectly as being the same as the aggregate of the particles. Yes, on average, the two systems will say at the same temperature with respect to each other. But there is constant transfer at a very small level between the two sides because individual particles are moving between the sides. But in no case, Maxwell or not, has the entropy increased or decreased for the whole system. Thus it is OK for Max to not expend energy.