Part 31 (1/2)

[105] ”Philosophical Transactions,” 1798.

Rumford, after showing that this heat could not have been derived from any of the surrounding objects, or by compression of the materials employed or acted upon, says: ”It appears to me extremely difficult, if not impossible, to form any distinct idea of anything capable of being excited and communicated in the manner that heat was excited and communicated in these experiments, except it be motion.”[106] He then goes on to urge a zealous and persistent investigation of the laws which govern this motion. He estimates the heat produced by a power which he states could easily be exerted by one horse, and makes it equal to the ”combustion of nine wax candles, each three-quarters of an inch in diameter,” and equivalent to the elevation of ”25.68 pounds of ice-cold water” to the boiling-point, or 4,784.4 heat-units.[107]

The time was stated at ”150 minutes.” Taking the actual power of Rumford's Bavarian ”one horse” as the most probable figure, 25,000 pounds raised one foot high per minute,[108] this gives the ”mechanical equivalent” of the foot-pound as 783.8 heat-units, differing but 1.5 per cent. from the now accepted value.

[106] This idea was not by any means original with Rumford. Bacon seems to have had the same idea; and Locke says, explicitly enough: ”Heat is a very brisk agitation of the insensible parts of the object ... so that what in our sensation is heat, in the object is nothing but motion.”

[107] The British heat-unit is the quant.i.ty of heat required to heat one pound of water 1 Fahr. from the temperature of maximum density.

[108] Rankine gives 25,920 foot-pounds per minute--or 432 per second--for the average draught-horse in Great Britain, which is probably too high for Bavaria. The engineer's ”horse-power”--33,000 foot-pounds per minute--is far in excess of the average power of even a good draught-horse, which latter is sometimes taken as two-thirds the former.

Had Rumford been able to eliminate all losses of heat by evaporation, radiation, and conduction, to which losses he refers, and to measure the power exerted with accuracy, the approximation would have been still closer. Rumford thus made the experimental discovery of the real nature of heat, proving it to be a form of energy, and, publis.h.i.+ng the fact a half-century before the now standard determinations were made, gave us a very close approximation to the value of the heat-equivalent. Rumford also observed that the heat generated was ”exactly proportional to the force with which the two surfaces are pressed together, and to the rapidity of the friction,” which is a simple statement of equivalence between the quant.i.ty of work done, or energy expended, and the quant.i.ty of heat produced. This was the first great step toward the formation of a Science of Thermo-dynamics.

Rumford's work was the corner-stone of the science.

Sir Humphry Davy, a little later (1799), published the details of an experiment which conclusively confirmed these deductions from Rumford's work. He rubbed two pieces of ice together, and found that they were melted by the friction so produced. He thereupon concluded: ”It is evident that ice by friction is converted into water....

Friction, consequently, does not diminish the capacity of bodies for heat.”

Bacon and Newton, and Hooke and Boyle, seem to have antic.i.p.ated--long before Rumford's time--all later philosophers, in admitting the probable correctness of that modern dynamical, or vibratory, theory of heat which considers it a mode of motion; but Davy, in 1812, for the first time, stated plainly and precisely the real nature of heat, saying: ”The immediate cause of the phenomenon of heat, then, is motion, and the laws of its communication are precisely the same as the laws of the communication of motion.” The basis of this opinion was the same that had previously been noted by Rumford.

So much having been determined, it became at once evident that the determination of the exact value of the mechanical equivalent of heat was simply a matter of experiment; and during the succeeding generation this determination was made, with greater or less exactness, by several distinguished men. It was also equally evident that the laws governing the new science of thermo-dynamics could be mathematically expressed.

Fourier had, before the date last given, applied mathematical a.n.a.lysis in the solution of problems relating to the transfer of heat without transformation, and his ”Theorie de la Chaleur” contained an exceedingly beautiful treatment of the subject. Sadi Carnot, twelve years later (1824), published his ”Reflexions sur la Puissance Motrice du Feu,” in which he made a first attempt to express the principles involved in the application of heat to the production of mechanical effect. Starting with the axiom that a body which, having pa.s.sed through a series of conditions modifying its temperature, is returned to ”its primitive physical state as to density, temperature, and molecular const.i.tution,” must contain the same quant.i.ty of heat which it had contained originally, he shows that the efficiency of heat-engines is to be determined by carrying the working fluid through a complete cycle, beginning and ending with the same set of conditions. Carnot had not then accepted the vibratory theory of heat, and consequently was led into some errors; but, as will be seen hereafter, the idea just expressed is one of the most important details of a theory of the steam-engine.

Seguin, who has already been mentioned as one of the first to use the fire-tubular boiler for locomotive engines, published in 1839 a work, ”Sur l'Influence des Chemins de Fer,” in which he gave the requisite data for a rough determination of the value of the mechanical equivalent of heat, although he does not himself deduce that value.

Dr. Julius R. Mayer, three years later (1842), published the results of a very ingenious and quite closely approximate calculation of the heat-equivalent, basing his estimate upon the work necessary to compress air, and on the specific heats of the gas, the idea being that the work of compression is the equivalent of the heat generated.

Seguin had taken the converse operation, taking the loss of heat of expanding steam as the equivalent of the work done by the steam while expanding. The latter also was the first to point out the fact, afterward experimentally proved by Hirn, that the fluid exhausted from an engine should heat the water of condensation less than would the same fluid when originally taken into the engine.

A Danish engineer, Colding, at about the same time (1843), published the results of experiments made to determine the same quant.i.ty; but the best and most extended work, and that which is now almost universally accepted as standard, was done by a British investigator.

James Prescott Joule commenced the experimental investigations which have made him famous at some time previous to 1843, at which date he published, in the _Philosophical Magazine_, his earliest method. His first determination gave 770 foot-pounds. During the succeeding five or six years Joule repeated his work, adopting a considerable variety of methods, and obtaining very variable results. One method was to determine the heat produced by forcing air through tubes; another, and his usual plan, was to turn a paddle-wheel by a definite power in a known weight of water. He finally, in 1849, concluded these researches.

[Ill.u.s.tration: James Prescott Joule.]

The method of calculating the mechanical equivalent of heat which was adopted by Dr. Mayer, of Heilbronn, is as beautiful as it is ingenious: Conceive two equal portions of atmospheric air to be inclosed, at the same temperature--as at the freezing-point--in vessels each capable of containing one cubic foot; communicate heat to both, retaining the one portion at the original volume, and permitting the other to expand under a constant pressure equal to that of the atmosphere. In each vessel there will be inclosed 0.08073 pound, or 1.29 ounce, of air. When, at the same temperature, the one has doubled its pressure and the other has doubled its volume, each will be at a temperature of 525.2 Fahr., or 274 C, and each will have double the original temperature, as measured on the absolute scale from the zero of heat-motion. But the one will have absorbed but 6-3/4 British thermal units, while the other will have absorbed 9-1/2. In the first case, all of this heat will have been employed in simply increasing the temperature of the air; in the second case, the temperature of the air will have been equally increased, and, besides, a certain amount of work--2,116.3 foot-pounds--must have been done in overcoming the resistance of the air; it is to this latter action that we must debit the additional heat which has disappeared. Now, 2,116.3/(2-3/4) = 770 foot-pounds per heat-unit--almost precisely the value derived from Joule's experiments. Had Mayer's measurement been absolutely accurate, the result of his calculation would have been an exact determination of the heat-equivalent, provided no heat is, in this case, lost by internal work.

Joule's most probably accurate measure was obtained by the use of a paddle-wheel revolving in water or other fluid. A copper vessel contained a carefully weighed portion of the fluid, and at the bottom was a step, on which stood a vertical spindle carrying the paddle-wheel. This wheel was turned by cords pa.s.sing over nicely-balanced grooved wheels, the axles of which were carried on friction-rollers. Weights hung at the ends of these cords were the moving forces. Falling to the ground, they exerted an easily and accurately determinable amount of work, _W_ _H_, which turned the paddle-wheel a definite number of revolutions, warming the water by the production of an amount of heat exactly equivalent to the amount of work done. After the weight had been raised and this operation repeated a sufficient number of times, the quant.i.ty of heat communicated to the water was carefully determined and compared with the amount of work expended in its development. Joule also used a pair of disks of iron rubbing against each other in a vessel of mercury, and measured the heat thus developed by friction, comparing it with the work done. The average of forty experiments with water gave the equivalent 772.692 foot-pounds; fifty with mercury gave 774.083; twenty with cast-iron gave 774.987--the temperature of the apparatus being from 55 to 60 Fahr.

Joule also determined, by experiment, the fact that the expansion of air or other gas without doing work produces no change of temperature, which fact is predicable from the now known principles of thermo-dynamics. He stated the results of his researches relating to the mechanical equivalent of heat as follows:

1. The heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quant.i.ty of work expended.

2. The quant.i.ty required to increase the temperature of a pound of water (weighed _in vacuo_ at 55 to 60 Fahr.) by one degree requires for its production the expenditure of a force measured by the fall of 772 pounds from a height of one foot. This quant.i.ty is now generally called ”Joule's equivalent.”

During this series of experiments, Joule also deduced the position of the ”absolute zero,” the point at which heat-motion ceases, and stated it to be about 480 Fahr. below the freezing-point of water, which is not very far from the probably true value,-493.2 Fahr. (-273 C.), as deduced afterward from more precise data.

The result of these, and of the later experiments of Hirn and others, has been the admission of the following principle:

Heat-energy and mechanical energy are mutually convertible and have a definite equivalence, the British thermal unit being equivalent to 772 foot-pounds of work, and the metric _calorie_ to 423.55, or, as usually taken, 424 kilogrammetres. The exact measure is not fully determined, however.

It has now become generally admitted that all forms of energy due to physical forces are mutually convertible with a definite quantivalence; and it is not yet determined that even vital and mental energy do not fall within the same great generalization. This quantivalence is the sole basis of the science of Energetics.