Part 29

Care must be taken to admit only very dry air, which could be obtained by placing under the receiver calcium chloride or any other substance which absorbs moisture greedily.

Instead of bending the tube into a spiral, it might be bent in the middle in the form of a ᑌ, or it might be better to form three, four or more parallel branches. Making the tube very long, the index would have a larger range for the same changes of pressure, and the results produced could then be measured by a slight variation in density in the air of the receiver.

Comparison of the Rapidity with which the Air cools in the Receiver and in the Tube.

Let us suppose, what I believe to be very near the truth, that the heat absorbed is proportional to the surface of the bodies in contact. From this we can infer without difficulty, that the rapidity of the cooling of the air in two cylindrical tubes would be inversely as their diameters.

If the receiver is considered as a tube of two decimetres in diameter, and the manometer as a tube of one millimetre diameter, the rapidity of the cooling of the air would be in the ratio, very nearly, of 1 to 200.

Extent of the Movement of the Index.

Suppose the tube turned up on itself five times and having a total length of 1 metre; a variation of density equal to ⅒ in the air will give a movement of 1 decimetre; a variation of heat of 1 degree supposed to be equivalent to a variation of density of ¹⁄₂₆₆ will give ¹⁄₂₆₆ of a metre, or about 3^{mm}.70, quite an appreciable quantity. As to the time required to move the mercury index, regard being had to its mass, if we suppose it 1 centimetre long, and the variation of pressure ¹⁄₁₀₀ of an atmosphere, it would require about ⅙ of a second to make it pass over one decimetre.

Use of the Instrument in Measuring the Variations of the Tensions of the Air under a Pneumatic Receiver.

At each stroke of the piston which expands the air under the pneumatic receiver when a vacuum is to be created, a lowering of pressure is produced, and undoubtedly a change of temperature. It can be determined approximately, at least, by observing the position of the manometer at the instant after the dilatation has taken place, and again after a time long enough for the temperature to have returned to its original point, that of the surrounding bodies. Comparison of the elastic force in the two cases will lead to comparison of the temperatures.

The temperature having returned to its original point, we will give a second stroke of the piston which will rarefy the air more than the former, and thus we will make two observations of the manometer, before and after the return to the former temperature. And so on.

APPENDIX B. CARNOT’S FOOT-NOTES.

NOTE A.—The objection may perhaps be raised here, that perpetual motion, demonstrated to be impossible by mechanical action alone, may possibly not be so if the power either of heat or electricity be exerted; but is it possible to conceive the phenomena of heat and electricity as due to anything else than some kind of motion of the body, and as such should they not be subjected to the general laws of mechanics? Do we not know besides, à posteriori, that all the attempts made to produce perpetual motion by any means whatever have been fruitless?—that we have never succeeded in producing a motion veritably perpetual, that is, a motion which will continue forever without alteration in the bodies set to work to accomplish it? The electromotor apparatus (the pile of Volta) has sometimes been regarded as capable of producing perpetual motion; attempts have been made to realize this idea by constructing dry piles said to be unchangeable; but however it has been done, the apparatus has always exhibited sensible deteriorations when its action has been sustained for a time with any energy.

The general and philosophic acceptation of the words perpetual motion should include not only a motion susceptible of indefinitely continuing itself after a first impulse received, but the action of an apparatus, of any construction whatever, capable of creating motive power in unlimited quantity, capable of starting from rest all the bodies of nature if they should be found in that condition, of overcoming their inertia; capable, finally, of finding in itself the forces necessary to move the whole universe, to prolong, to accelerate incessantly, its motion. Such would be a veritable creation of motive power. If this were a possibility, it would be useless to seek in currents of air and water or in combustibles this motive power. We should have at our disposal an inexhaustible source upon which we could draw at will.

NOTE B.—The experimental facts which best prove the change of temperature of gases by compression or dilatation are the following:

(1) The fall of the thermometer placed under the receiver of a pneumatic machine in which a vacuum has been produced. This fall is very sensible on the Bréguet thermometer: it may exceed 40° or 50°. The mist which forms in this case seems to be due to the condensation of the watery vapor caused by the cooling of the air.

(2) The inflammation of German tinder in the so-called pneumatic tinder-boxes; which are, as we know, little pump-chambers in which the air is rapidly compressed.

(3) The fall of a thermometer placed in a space where the air has been first compressed and then allowed to escape by the opening of a cock.

(4) The results of experiments on the velocity of sound. M. de Laplace has shown that, in order to secure results accurately by theory and computation, it is necessary to assume the heating of the air by sudden compression.

The only fact which may be adduced in opposition to the above is an experiment of MM. Gay-Lussac and Welter, described in the Annales de Chimie et de Physique. A small opening having been made in a large reservoir of compressed air, and the ball of a thermometer having been introduced into the current of air which passes out through this opening, no sensible fall of the temperature denoted by the thermometer has been observed.

Two explanations of this fact may be given: (1) The striking of the air against the walls of the opening by which it escapes may develop heat in observable quantity. (2) The air which has just touched the bowl of the thermometer possibly takes again by its collision with this bowl, or rather by the effect of the détour which it is forced to make by its rencounter, a density equal to that which it had in the receiver,—much as the water of a current rises against a fixed obstacle, above its level.

The change of temperature occasioned in the gas by the change of volume may be regarded as one of the most important facts of Physics, because of the numerous consequences which it entails, and at the same time as one of the most difficult to illustrate, and to measure by decisive experiments. It seems to present in some respects singular anomalies.

Is it not to the cooling of the air by dilatation that the cold of the higher regions of the atmosphere must be attributed? The reasons given heretofore as an explanation of this cold are entirely insufficient; it has been said that the air of the elevated regions receiving little reflected heat from the earth, and radiating towards celestial space, would lose caloric, and that this is the cause of its cooling; but this explanation is refuted by the fact that, at an equal height, cold reigns with equal and even more intensity on the elevated plains than on the summit of the mountains, or in those portions of the atmosphere distant from the sun.

NOTE C.—We see no reason for admitting, à priori, the constancy of the specific heat of bodies at different temperatures, that is, to admit that equal quantities of heat will produce equal increments of temperature, when this body changes neither its state nor its density; when, for example, it is an elastic fluid enclosed in a fixed space. Direct experiments on solid and liquid bodies have proved that between zero and 100°, equal increments in the quantities of heat would produce nearly equal increments of temperature. But the more recent experiments of MM. Dulong and Petit (see Annales de Chimie et de Physique, February, March, and April, 1818) have shown that this correspondence no longer continues at temperatures much above 100°, whether these temperatures be measured on the mercury thermometer or on the air-thermometer.

Not only do the specific heats not remain the same at different temperatures, but, also, they do not preserve the same ratios among themselves, so that no thermometric scale could establish the constancy of all the specific heats. It would have been interesting to prove whether the same irregularities exist for gaseous substances, but such experiments presented almost insurmountable difficulties.

The irregularities of specific heats of solid bodies might have been attributed, it would seem, to the latent heat employed to produce a beginning of fusion—a softening which occurs in most bodies long before complete fusion. We might support this opinion by the following statement: According to the experiments of MM. Dulong and Petit, the increase of specific heat with the temperature is more rapid in solids than in liquids, although the latter possess considerably more dilatability. The cause of irregularity just referred to, if it is real, would disappear entirely in gases.

NOTE D.—In order to determine the arbitrary constants A, B, A′, B′, in accordance with the results in M. Dalton’s table, we must begin by computing the volume of the vapor as determined by its pressure and temperature,—a result which is easily accomplished by reference to the laws of Mariotte and Gay-Lussac, the weight of the vapor being fixed.

The volume will be given by the equation

v = c (267 + t)/(p),