correct. If such variations of density exist, they may introduce
some uncertainty in the absolute values of results obtained with the
ice calorimeter, and may account for some of the discrepancies above
enumerated.
§ 5. The Method of Condensation was first successfully applied by J. Joly in the construction of his steam calorimeter, a full description of which will be found in text-books. The body to be tested is placed in a special scale-pan, suspended by a fine wire from the arm of a balance inside an enclosure which can be filled with steam at atmospheric pressure. The temperature of the enclosure is carefully observed before admitting steam. The weight of steam condensed on the body gives a means of calculating the quantity of heat required to raise it from the atmospheric temperature up to 100° C. in terms of the latent heat of vaporization of steam at 100° C. There can be no appreciable gain or loss of heat by radiation, if the admission of the steam is sufficiently rapid, since the walls of the enclosure are maintained at 100° C., very nearly. The thermal capacity of the scale-pan, &c., can be determined by a separate experiment, or, still better, eliminated by the differential method of counterpoising with an exactly similar arrangement on the other arm of the balance. The method requires very delicate weighing, as one calorie corresponds to less than two milligrammes of steam condensed; but the successful application of the method to the very difficult problem of measuring the specific heat of a gas at constant volume, shows that these and other difficulties have been very skilfully overcome. The application of the method appears to be practically limited to the measurements of specific heat between the atmospheric temperature and 100° C. The results depend on the value assumed for the latent heat of steam, which Joly takes as 536.7 calories, following Regnault. Joly has himself determined the mean specific heat of water between 12° and 100° C. by this method, in terms of the latent heat of steam as above given, and finds the result .9952. Assuming that the mean specific heat of water between 12° and 100° is really 1.0011 in terms of the calorie at 20° C. (see table, p. 66), the value of the latent heat of steam at 100° C., as determined by Joly, would be 540.2 in terms of the same unit. The calorie employed by Regnault is to some extent uncertain, but the difference is hardly beyond the probable errors of experiment, since it appears from the results of recent experiments that Regnault made an error of the same order in his determination of the specific heat of water at 100° C.
§ 6. Energy Methods.—The third general method of calorimetry, that based on the transformation of some other kind of energy into the form of heat, rests on the general principle of the conservation of energy, and on the experimental fact that all other forms of energy are readily and completely convertible into the form of heat. It is therefore often possible to measure quantities of heat indirectly, by measuring the energy in some other form and then converting it into heat. In addition to its great theoretical interest, this method possesses the advantage of being frequently the most accurate in practical application, since energy can be more accurately measured in other forms than in that of heat. The two most important varieties of the method are (a) mechanical, and (b) electrical. These methods have reached their highest development in connexion with the determination of the mechanical equivalent of heat, but they may be applied with great advantage in connexion with other problems, such as the measurement of the variation of specific heat, or of latent heats of fusion or vaporization.
§ 7. Mechanical Equivalent of Heat.—The phrase “mechanical equivalent of heat” is somewhat vague, but has been sanctioned by long usage. It is generally employed to denote the number of units of mechanical work or energy which, when completely converted into heat without loss, would be required to produce one heat unit. The numerical value of the mechanical equivalent necessarily depends on the particular units of heat and work employed in the comparison. The British engineer prefers to state results in terms of foot-pounds of work in any convenient latitude per pound-degree-Fahrenheit of heat. The continental engineer prefers kilogrammetres per kilogramme-degree-centigrade. For scientific use the C.G.S. system of expression in ergs per gramme-degree-centigrade, or “calorie,” is the most appropriate, as being independent of the value of gravity. A more convenient unit of work or energy, in practice, on account of the smallness of the erg, is the joule, which is equal to 10.7 ergs, or one watt-second of electrical energy. On account of its practical convenience, and its close relation to the international electrical units, the joule has been recommended by the British Association for adoption as the absolute unit of heat. Other convenient practical units of the same kind would be the watt-hour, 3600 joules, which is of the same order of magnitude as the kilo-calorie, and the kilowatt-hour, which is the ordinary commercial unit of electrical energy.
 |
| Fig. 4. |
§ 8. Joule.—The earlier work of Joule is now chiefly of historical interest, but his later measurements in 1878, which were undertaken on a larger scale, adopting G. A. Hirn’s method of measuring the work expended in terms of the torque and the number of revolutions, still possess value as experimental evidence. In these experiments (see fig. 4) the paddles were revolved by hand at such a speed as to produce a constant torque on the calorimeter h, which was supported on a float w in a vessel of water v, but was kept at rest by the couple due to a pair of equal weights k suspended from fine strings passing round the circumference of a horizontal wheel attached to the calorimeter. Each experiment lasted about forty minutes, and the rise of temperature produced was nearly 3° C. The calorimeter contained about 5 kilogrammes of water, so that the rate of heat-supply was about 6 calories per second. Joule’s final result was 772.55 foot-pounds at Manchester per pound-degree-Fahrenheit at a temperature of 62° F., but individual experiments differed by as much as 1%. This result in C.G.S. measure is equivalent to 4.177 joules per calorie at 16.5° C., on the scale of Joule’s mercury thermometer. His thermometers were subsequently corrected to the Paris scale by A. Schuster in 1895, which had the effect of reducing the above figure to 4.173.
§ 9. Rowland.—About the same time H. A. Rowland (Proc. Amer. Acad. xv. p. 75, 1880) repeated the experiment, employing the same method, but using a larger calorimeter (about 8400 grammes) and a petroleum motor, so as to obtain a greater rate of heating (about 84 calories per second), and to reduce the importance of the uncertain correction for external loss of heat. Rowland’s apparatus is shown in fig. 5. The calorimeter was suspended by a steel wire, the torsion of which made the equilibrium stable. The torque was measured by weights O and P suspended by silk ribbons passing over the pulleys n and round the disk kl. The power was transmitted to the paddles by bevel wheels, f, g, rotating a spindle passing through a stuffing box in the bottom of the calorimeter. The number of revolutions and the rise of temperature were recorded on a chronograph drum. He paid greater attention to the important question of thermometry, and extended his researches over a much wider range of temperature, namely 5° to 35° C. His experiments revealed for the first time a diminution in the specific heat of water with rise of temperature between 0° and 30° C., amounting to four parts in 10.000 per 1° C. His thermometers were compared with a mercury thermometer standardized in Paris, and with a platinum thermometer standardized by Griffiths. The result was to reduce the coefficient of diminution of specific heat at 15° C. by nearly one half, but the absolute value at 20° C. is practically unchanged. Thus corrected his values are as follows:—
| Temperature | 10° | 15° | 20° | 25° | 30° | 35° |
| Joules per cal. | 4.197 | 4.188 | 4.181 | 4.176 | 4.175 | 4.177 |
These are expressed in terms of the hydrogen scale, but the difference from the nitrogen scale is so small as to be within the limits of experimental error in this particular case. Rowland himself considered his results to be probably correct to one part in 500, and supposed that the greatest uncertainty lay in the comparison of the scale of his mercury thermometer with the air thermometer. The subsequent correction, though not carried out strictly under the conditions of the experiment, showed that the order of accuracy of his work about the middle of the range from 15° to 25° was at least 1 in 1000, and probably 1 in 2000. At 30° he considered that, owing to the increasing
magnitude and uncertainty of the radiation correction, there
