Astounding Science Fiction/Volume 44/Number 05/Maxwell's Demon and Monsieur Ranque

by Arthur C. Parlett

MAXWELL'S DEMON

AND

MONSIEUR RANQUE

BY ARTHUR C. PARLETT

 

This is not a hoax; the article is straight fact. And it’s the first time a stream of air’s been induced to blow hot and blow cold at the same time!

 

There was a good deal of talent wasted in the olden days when demons and jinn were imprisoned in quaint bottles, sealed with the signet of Sulayman, and cast into the sea. It has taken hundreds of years, but we at last are on our way to learning how to harness the peculiar powers of such beings. As a starter, we now take the smaller demons, imprison them in T-tubes, seal with the mark of Georges Ranque, and put them to work sorting molecules according to energy content; the hot molecules in one pile and the cold ones in another. Such, at least, was my initial—and erroneous—reaction to the operation of the T-tube whose working drawings are reproduced as Figure No. 1.

This device, shown in assembly as Figure No. 2, effects a separation of a charge of compressed air of uniform temperature into two streams. The current from the longer arm may easily reach a temperature of +200°C., while the temperature of the air stream from the tube at the right may go as low as -50°C. The conditions of the air stream to the T-tube are "normal" temperature, that is 20°C., and pressure of only a few atmospheres. It is interesting to note that the lowest temperatures are obtained when the ratio of cold air to hot, regulated by means of the valve on the hot end, is approximately 1 :3.

These effects would seem to indicate that the Second Law of Thermodynamics is being successfully violated, and this in turn suggests that the demon proposed by Clerk Maxwell has been found and put to useful work!

The Second Law has often been dressed up in fancy terminology, but all it really says is (1) that water naturally flows down hill, not up, and (2) that heat naturally flows from hot bodies to cold, not the reverse. In other words, all actions that take place spontaneously tend to bring a system to equilibrium or to rest. As a secondary point, it may be noted that any process starting of and by itself—whether or not it is allowed to proceed to equilibrium—is accompanied by some loss of capacity for self-starting. This loss of capacity for spontaneous change is measured by its gain in entropy, indeed can serve as a basic definition of entropy. It will be noted that no loss of energy is involved; only the degree of availability of the energy to do useful work has been lessened.

A little reflection brings out an interesting corollary to the above: Any action that starts of itself represents a tendency to achieve a state of maximum probability, and the achievement of maximum probability is also the attainment of maximum entropy. When heat flows from a hot body to a colder one; when water flows down hill, both maximum probability and maximum entropy are being attained. Similarly with any other such action you care to name.

It seemed that Monsieur Ranque's device violated this law. Air is certainly a well mixed substance, and the number of molecules in a unit volume is fantastically large. A tremendous aggregation of gaseous molecules in completely random movement simply must arrive at the most probable configuration of complete randomness in short order. Yet the device Monsieur Ranque patented in 1934^[1] apparently effects a separation of hot molecules from cold with consequent loss of entropy from the system as a whole. The action is strikingly similar to that of the demon first conceived by Clerk Maxwell.

Clerk Maxwell, remarkable physicist of the last century, recognized the statistical nature of temperature. In a gas of a certain observed temperature, a large percentage of molecules will have a kinetic energy content greatly higher than that corresponding to the thermometer reading, and a large percentage will have a much lower kinetic energy content. The temperature reading is merely the average value. That the same reading is obtained at all points in the system simply means that the

Figure 1. Working Drawing of Maxwellian Demon.

Industrial And Engineering Chemistry—Vol. 38, No. 12

system is in its state of maximum probability. The holding of a perfect bridge hand is considered a news item because the number of highly shuffled, random, chaotic arrangements are hundreds of millions of times greater than the perfectly ordered hand. Yet the probabilities in this case are based upon a deck of only fifty-two cards. Because of the unimaginable number of molecules involved, Dodge has said: "Any arrangement in which the hot molecules would predominate to permit an observable difference in temperature between any macroscopic portions of the gas is so improbable as to be nonexistent." (Dodge, B. F. Chemical Engineering Thermodynamics.) If only molecules could be dealt with as individuals, thought Maxwell, the laws of probability would no longer apply and the Second Law of Thermodynamics would lose its rigor.

Maxwell conceived of a tiny being, since come to be affectionately known as "Maxwell's demon", who could handle the individual molecules of a gas. He made this demon the guardian of an opening between two boxes containing a gas at uniform conditions of temperature and pressure. The demon was to control the opening by a shutter, and by judicious opening and closing of the shutter- he would be able to effect a concentration of hot—high translational energy—molecules in one box and a concentration of cold—low translational energy—molecules in the other, thereby bringing about an appreciable temperature difference between the two, and hence decreasing the entropy of the system.^[2]

For some reason or other, the remarkable nature of George Joseph Ranque's invention seems to have been overlooked in this country for a good many years. It simply lapsed into the Limbo of forgotten things. But in 1946, Dr. R. M. Milton of The Johns Hopkins University visited Germany to investigate low temperature work in connection with superconductivity research. There, in the laboratory of Dr. Rudolf Hilsch, at the Physikalischen Institut, Erlangen, Germany, he found the device in the form illustrated in this article—Ranque in his patent lists a total of fifteen forms the device may take!—where it replaced the usual ammonia pre-cooling apparatus in a liquid air machine. (It is interesting to note that Dr. John R. Roebuck of The University of Wisconsin, writing in the Journal of Applied Physics, 16, 285 (1945) had independently presented a fully developed theory for a rotor device to serve the same purpose.) The very considerable experimentation carried out by Dr. Hilsch upon this device, and the publicity attendant to Dr. Milton's announcements has led to the general adoption of the name "Hilsch Tube" for the "Vortex Tube", as it is called by Dr. Hilsch in a recent article.^[3]

The American Chemical Society has very kindly consented to our reproducing the working drawings of the Hilsch tube—Figure No. 1—so that any good machine shop can quite easily construct one for you. When I first saw the tube in operation, I sat with a thermodynamics textbook in my hand for some time. Then I closed it and said wearily to myself, "Well, there goes the Second Law!" For I certainly saw one stream going in and two streams coming out, and one of the outlet streams was cold and the other was hot. And if that weren't effective sorting of molecules according to energy content what was it?

It took quite a while before I realized that the major part of my difficulties arose because the following statements of the Second Law are incomplete; but these partial statements seemed perfectly reasonable to me at the time. More than one politician has found that half-truths make better propaganda than outright falsehood.

"Water won't flow up hill (two words missing)."

"Heat won't flow from cold bodies to hot (two words missing)."

"A system will not proceed from a more probable state to a less probable state (two words missing)."

In each case the missing two words are the same. They are "WITHOUT COMPENSATION!" In the case of the Hilsch tube, mechanical compensation for the loss of entropy by the gaseous system is provided by the compression and expansion of air. Thermodynamics doesn't give a hoot about mechanism—it is concerned only with the inherent possibilities of a given system.

But it is not even necessary to postulate that there has been a sorting of molecules, and there is much

Figure 2.

Maxwell's Demon Lives Here!

Industrial And Engineering Chemistry—Vol. 38, No. 5

experimental evidence to show that this does not occur. There have been quite a few theories of the operation of the "Vortex tube" proposed. The explanation which the author prefers is that of Dr. John R. Roebuck, Physics Department, The University of Wisconsin.

Dr. Roebuck points out^[4] that due to the manner of entry, the air in the top of the T-tube is rotating very rapidly about the axis of the tube. This rotation sets up large centrifugal forces on the air particles outward from the axis, which produce a drop in pressure toward the axis, and a lower pressure at the axis than at the periphery. This is confirmed experimentally, as air will enter at the axial opening instead of escape unless the opening at the bottom of the whirling tube is constricted somewhat. The air coming in at the periphery forces the air in along the radii, and the falling pressure inward on the radius allows this air to expand doing work and cooling the air. It is readily shown that this work adds to the rotating energy of the body of the gas, so speeding it up. Friction with the inner surface of the tube heats up the gas next it. That is, gas drawn off at the axis has been cooled while that drawn off at the periphery near the outer wall has been warmed. Adiabatic expansion of air from ten atmospheres and room temperature to one atmosphere will cool the air by about 135°C., so there is plenty of available cooling.^[5]

And thus the charming picture of the busy little demon sitting inside the tube with a tennis racquet in his hand, batting the molecules to right and to left as they come in, saying to himself, "There's a hot one, smack it to the right! There's a cold one, smack it to the left!" is very effectively demolished, and the Second Law continues to hold true without known exception.

THE END

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1. U. S. Patent No. 1,952,281, assigned March 27, 1934. Method and Apparatus for Obtaining from a Fluid under Pressure two currents of Fluids at Different Temperatures. Inventor: George Joseph Ranque.
2. There is a hoary objection that even in this case the law of entropy increase would hold because the increase of entropy within the demon would more than compensate for the decrease in entropy he produced. Lewis and Randall among others, hold that before conceding this point it might be well to know something more of the demon's metabolism.
3. Hilsch, R. The Use of the Expansion of Gases in a Centrifugal Field as Cooling Process. The Review of Scientific Instruments. 18, 2, February, 1947.
4. Personal communication to the author.
5. Incidentally. Dr. Hilsch concludes his article previously referred to with the observation that ". . . . There is little probability that vortex tubes will replace the customary refrigerating machines since their efficiencies are much better in the region of small pressure ratios. There may, however, be special cases where a vortex tube would be more desirable because of simple construction (e.g., air cooling in mine shafts)."