The unseen universe

by Balfour Stewart; Peter Guthrie Tait

Suppose there could be an engine, M, more perfect than a reversible engine, N. Set the two to work together as a compound engine, M letting down heat from boiler to condenser, and doing work; N spending work in pumping back again the heat to the boiler. If N be made to restore to the boiler at every stroke exactly what M takes from it, the compound engine will do external work, for, by hypothesis, M is more perfect than N. Whence does the work come? Not from the boiler, for it remains as it was. Hence N must take more heat from the condenser than M gives it; i.e. you get work by cooling the condenser.

Carry the reasoning a little further, and we see that if the excess of work given by M were spent upon N, and thus no work on the whole either spent or given out, the condenser would be still further cooled, and the boiler heated! This, to most people, would seem to imply an ample reductio ad absurdum. But Clerk-Maxwell has shown it to be physically possible, and has thus thoroughly justified Thomson’s caution about his axiom. As this is a point of very great importance, we offer no excuse for treating it pretty fully.

* 111. Clerk-Maxwell’s reasoning is given as depending upon the molecular theory of gases, but the only necessity for so restricting it appears to be that we thereby connect the reasoning more directly with Heat, which, on this theory, is supposed to be the energy of motion of the molecules of the gas. The illustration, however, is more general, and at the same time more simple, if we do not at first refer either to heat or to the molecular hypothesis of the constitution of gases, but treat the question simply as one concerning the possible motions of a number of little material particles.

Assume, then, that a great number of small equal spherical particles of matter are enclosed in a vessel of any form, and assume further that (either by collision or by repulsive force) each of these has the power of rebounding from another or from the wall of the vessel, as if it were elastic, and had unit co-efficient of restitution,[41] as defined in treatises on natural philosophy. Then it can be shown, as a matter of direct calculation, that—start these particles as we please, in all sorts of directions, and with velocities as varied as we please—after a time, which will be shorter as the number of particles is greater, a sort of permanent state will be arrived at in which a certain law of distribution of velocity prevails among the particles (the same law as that of the Probability of Error, as it is technically called), the greater number of them having nearly the mean square velocity, and those which have much less or more than that being fewer and fewer as the defect or excess is greater. The tendency is to an average distribution of these varieties of velocity throughout the vessel, and the impacts on the sides will thus be nearly the same on every square inch of its surface. After this there is—always provided the particles be sufficiently numerous—no perceptible change in the statistics of the group, except in so far as concerns individual particles, which may sometimes be moving with great, sometimes with very small, velocity, but which, in the long-run, will far more often be moving with the mean square velocity, or at least some velocity very near it. Hence, in no part of the vessel will the average energy be sensibly greater than in another, and therefore (so far as the contents of the vessel alone are concerned) there is no possibility of getting work from them. But by enlisting in our service conceivable finite beings (imagined by Clerk-Maxwell, and called demons by Thomson), it would be possible materially to alter this state of things, even although these beings should do absolutely no work.

* 112. For suppose a firm partition, full of little doors (themselves without mass) to be placed so as to divide the vessel into two, and set a demon at each door, with instructions to open it for an instant whenever he sees he can thereby let a quick-moving particle escape from the first compartment to the second, or a slow-moving particle from the second into the first. Then, because the tendency is not to a uniform distribution of velocity among the particles, but to a distribution which involves quicker and slower in certain proportions, we may imagine this process to be carried on long enough to make a considerable difference in the average velocities of the particles in the two compartments, though the numbers of particles in each compartment may remain almost unchanged. The consequence will of course be a greater pressure per square inch on the walls of the second compartment than of the first; and thus, if the partition wall were moveable, a certain amount of work might be obtained by allowing it to move. Thus a group of particles originally incapable, without external assistance, of doing work, may be rendered capable of doing work by mere guidance applied by finite intelligence.

* 113. Now let us refer for a moment to the molecular theory of gases, and we see that what the demons (without any expenditure of work, each being, so far as he is required, virtually a combination of two intelligent perfect engines, one working direct, the other reversed) have guided the gas to do, is to transfer heat from a colder to a hotter portion of the gas.

The only reason why this does not occur without the assistance of demons (at least to an extent, or for a length of time, sufficient to produce a sensible effect) lies in the enormous number of particles per cubic inch in even the most rarefied gas. Hence, solely because of the excessive numbers and minuteness of the particles of matter, the one chance of escape from Carnot’s proposition is denied us, and therefore we must allow that, so far as the physical universe is concerned, a reversible heat-engine is the best possible.

But if a reversible heat-engine be the best possible, then the principle which we have italicised in [Art. 107] must hold good, and from this it follows that only a portion of the heat passing through a perfect engine can be transformed into useful work unless the condenser of the engine be at the absolute zero of temperature—a condition which can never be attained.

114. It thus appears that at each transformation of heat-energy into work a large portion is degraded, while only a small portion is transformed into work. So that while it is very easy to change all of our mechanical or useful energy into heat, it is only possible to transform a portion of this heat-energy back again into work. After each change too the heat becomes more and more dissipated or degraded, that is, less and less available for any future transformation.

In other words, the tendency of heat is towards equalisation; heat is par excellence the communist of our universe, and it will no doubt ultimately bring the present system to an end. The visible universe may with perfect truth be compared to a vast heat-engine, and this is the reason why we have brought such engines so prominently before our readers. The sun is the furnace or source of high-temperature heat of our system, just as the stars are for other systems, and the energy which is essential to our existence is derived from the heat which the sun radiates, and represents only an excessively minute portion of that heat. But while the sun thus supplies us with energy he is himself getting colder, and must ultimately, by radiation into space, part with the life-sustaining power which he at present possesses. Besides the inevitable cooling of the sun we must also suppose that owing to something analogous to ethereal friction[42] the earth and the other planets of our system will be drawn spirally nearer and nearer to the sun, and will at length be engulfed in his mass. In each case there will be, as the result of the collision, the conversion of visible energy into heat, and a partial and temporary restoration of the power of the sun. At length, however, this process will have come to an end, and he will be extinguished until, after long but not immeasurable ages, by means of the same ethereal friction his black mass is brought into contact with that of one or more of his nearer neighbours.