Maxwell’s Demon — Three Real-World Examples

2009.02.03   prev     next

“MAXWELL’S Demon” was an imaginary, quasi-intelligent entity thought up by James Clerk Maxwell.

The demon would sit by a tiny door between two rooms and watch as molecules of air approached the door. When a fast-moving molecule approached the door from room A towards room B, the demon would open the door and allow the molecule to pass through. And when a slow-moving molecule approached the door from the other side, the demon also opened it and allowed the molecule through.

At all other times, the door stayed shut and molecules bounced off of it. Over time, molecules in room B would move faster and faster, while the ones in room A would move slower and slower. The natural tendency of heat (molecular motion) to spread out, from areas of high heat to areas of low heat, would be reversed, and heat would flow from room A to room B, until room A was very cold and room B was very hot. (The total amount of heat in both rooms would remain the same, however.)

The burning question for physicists has been whether such a demon would violate the laws of entropy and conservation of energy. Of course, there aren’t really “laws” of entropy or of conservation of energy. There are laws governing how molecules move and react to other molecules and to the forces emanated by them. Those actual laws produce average effects of increasing entropy and of conservation of energy. And, as it turns out, those actual laws of molecular motion don’t really allow for an entity like Maxwell’s demon to be constructed. Various practical considerations make it unworkable, or no better than a refrigerator you can pick up at Lowe’s any day of the week.

However, there are three very Maxwell’s-demon-like, real-world phenomena that produce effects nearly as striking as the one Maxwell imagined.

Osmosis

One of those is osmosis. If you completely surround a body of sugar-water with a water-permiable membrane, then place this sugar-water-filled membrane in a pool of pure water, what happens? The membrane swells up, taking in water from the pool, until it reaches the limit of how far it can stretch, and either stops stretching or ruptures. What made it do that? Why didn’t the water molecules just flow back and forth across the membrane and not make it swell (or shrink, for that matter)?

The answer is that the sugar molecules, unable to cross the membrane, are beating on the membrane from the inside. The membrane has lots of tiny pores that are large enough for water molecules to get through, but too small for sugar molecules. Every time a sugar molecule slams against the opening of one of these pores, it adds to the net outward velocity of the membrane — but there are no sugar molecules outside the membrane doing this in the other direction. The solid parts of the membrane receive balanced impacts from both sides of the membrane, but the pores receive only the outward-bound impacts of the too-large sugar molecules, and this gives the membrane an outward velocity.

In effect, each pore acts like a little Maxwell’s demon. It allows only the small (water) molecules through, not the sugar molecules. And it doesn’t have to notice which way (in or out) the molecules are travelling, because all the sugar molecules are inside the membrane and therefore must be going out, not in. By blocking some of the out-bound molecules, but none of the in-bound ones, the pore creates the osmotic effect.

Freezing

Another example is the freezing of water. People have marvelled over the centuries at how water expands as it freezes. And not only does it expand, but it actually exerts sufficient force when expanding to break some pretty strong containers. Chilling a liquid slows its molecules down, it doesn’t speed them up. How can slower-moving molecules exert tremendous outward force that they weren’t exerting when they were moving faster?

The answer is that the water doesn’t actually push outward, it just forms bonds that are stronger than the container around it. The molecules of the container are not really still — they are gyrating around a bit within their solid-object configuration. (Imagine that they are connected by springs that allow some degree of give-and-take even while keeping the molecules from moving around freely as in a liquid or a gas.) This movement of the molecules of the container causes the volume of the container’s interior to be constantly fluctuating within a small range. Every time the volume goes up a bit, it gives some water molecules the opportunity to lock together as ice — with a significant space between the water molecules, which is what makes ice larger than the water from which it was formed. Once these ice bonds are formed, the container cannot go back to its previous size. The container becomes more and more stretched as more ice bonds form within the water, further reducing its ability to retreat back to its former volume. Eventually, the stress on the container becomes too great and the container either cracks, or simply prevents the remaining water from freezing.

The container is not pushed out by expanding water — rather, the container moves out by the normal, Brownian motion of its molecules, and the water just locks in the space behind it, like Maxwell’s demon closing the door on a molecule that has just moved from room A to room B so that the molecule is now trapped in room B.

Sweating

When a droplet of sweat evaporates off of your skin, it cools your body. Why would it do that?

For example, suppose that your body is an uncomfortable 101°F. A droplet of sweat, also 101°, oozes out of a pore onto the surface of your skin. Then that droplet evaporates off into the air. So what? Why would you be any cooler? Yes, the droplet carried off heat as it left — its own 101° heat — but it also carried off volume and mass. Wouldn’t the mass it left behind (i.e. the rest of your body) still be 101°? How is any part of your body going to get lower than 101° in this process?

In a 101° droplet of water, the molecules are moving at different speeds. Their average speed correlates to the temperature 101°. Individual water molecules that are moving much slower than the average speed are technically much colder than 101°, and molecules that are moving much faster than the average are technically much hotter than 101°.

At the surface of the droplet (where it meets the air outside your body), the fastest moving water molecules are the ones that have sufficient speed to break surface tension (the adhesion of the water molecules to each other) and fly off into the air. So the water that escapes (evaporates) is much hotter than 101°. The water that is left behind in the droplet then has an average temperature less than 101°. This enables the remaining (now cooler) water in the droplet to absorb heat from the rest of your body. And it does this not by the pore supplying more water to the droplet (although that does occur); rather, the cooled droplet directly absorbs heat from the rest of your body, via physical contact.

The air-exposed surface of the droplet acts as a Maxwell’s demon by selectively allowing the fastest-moving molecules to escape, transferring heat out of the droplet into the surrounding air.

So we see, in these three examples, that Maxwell’s demon actually does exist. It’s not of the exact form Maxwell imagined, of course, but it does produce interesting, pseudo-magical effects that seem to defy common sense until you analyze them at the level of the demon — the level of individual molecules.

Update 2014.01.29 — sweating section added; “two” changed to “three” in title and elsewhere

Update 2022.07.04 — removed “ — even if that air happens to be hotter than the average temperature of the droplet” from end of second-to-the-last paragraph

See also:
Osmosis Demystified — How It Works

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