510
CALORIMETRY
the majority of experiments, it is necessary to use a secondary at ordinary pressures, the difficulties of direct measurestandard for the practical definition of the unit. The electrical ment are almost insuperable except in case (2). Thus the resistance thermometer of platinum presents very great advan- direct experimental evidence is somewhat meagre and tages for this purpose over the mercury thermometer in point conflicting, but the question of the relation of the specific of°reproducibility, accuracy, and adaptability to the practical conditions of experiment. The conditions of use of a mercury heats of gases is one of great interest in connexion with thermometer in a calorimetric experiment are necessarily dift'erent the kinetic theory and the constitution of the molecule. from those under which its corrections are determined, and this The well-known experiments of Regnault and Wiedemann difference must inevitably give rise to constant errors in practical on the specific heat of gases at constant pressure agree in work. The primary consideration in the definition of a unit is to select that method which permits the highest order of accuracy showing that the molecular specific heat, or the thermal in comparison and verification, hor this reason the definition capacity of the molecular weight in grammes, is approxiof the thermal unit will in the end probably be referred to a mately independent of the temperature and pressure in scale of temperature defined in terms of a standard platinum case of the more stable diatomic gases, such as H2, 0„, thermometer. . There is more diversity of opinion with regard to the question lSr9, CO, &c., and has nearly the same value for each of the standard temperature. Many authors, adopting Regnault’s gas. They also indicate that it is much larger, and formula, have selected 0° C. as the standard temperature, but increases considerably with rise of temperature, in the this cannot be practically realized in the case of water, and his case of more condensible vapours, such as CI2, Ih'oj or more formula is certainly erroneous at low temperatures. A favourite temperature to select is 4° C., the temperature of maximum complicated molecules, such as C02, bl20, NH3, C.JI4. density, since at this point the specific heat at constant volume The direct determination of the specific heat at constant is the same as that at constant pressure. But this is really ot volume is extremely difficult, but has been successfully no consequence, since the specific heat at constant volume cannot attempted by Joly with his steam calorimeter, in the he practically realized. The specific heat at 4° could be accurately case of air and C0 . Employing pressures between 7 and 2 determined as the mean over the range 0° to 8° keeping the jacket at 0°C. But the change appears to be rather rapid near 27 atmospheres, he found that the specific heat of air 0° the temperature is inconveniently low for ordinary calorimetric between 10° and 100 C. increased very slightly with work, and the unit at 4° would be so much larger than the increase of density, but that of C02 increased nearly 3 specific heat at ordinary temperatures that nearly all experiments per cent, between 7 and 21 atmospheres. The following would require reduction. The natural point to select would be that of minimum specific heat, but if this occurs at 40 C. it would formulae represent his results for the specific heat s at be inconveniently high for practical realization except by tlie constant volume in terms of the density d in gms. per c.c. continuous electrical method. It was proposed by a committee Air, s = 0-1715+ 0-028cZ, of the British Association to select the temperature at which tne C02, s = 0‘165 + 0‘213(7 + O'SIcZ". specific heat was 4’200 joules, leaving the exact temperature to be subsequently determined. It was supposed at the time, Irom s 18. Ratio of Specific Heats.—According to the elementary kinetic the original reduction of Rowland’s experiments, that this would of an ideal gas, the molecules of which are so small and be nearly at 10° C., but it now appears that it maybe as low theory so far apart that their mutual actions may be neglected, the as 5°C., which would be inconvenient. This is really only an kinetic energy of translation of the molecules is proportional to absolute unit in disguise, and evades the essential point, which the absolute temperature, and is equal to 3/2 of the product is the selection of a standard temperature lor the water thermo- of the pressure and the volume, per unit mass. Ihe expansion metric unit. A similar objection applies to selecting the tem- per degree at constant pressure is v/d-It/p. The external perature at which the specific heat is equal to its mean value of expansion per degree is equal to R, being the product ofwork the between 0° and 100°. The mean calorie cannot be accurately pressure and the expansion, and represents the difference ot the realized in practice in any simple manner, and is therelore un- specific heats S-s, at constant pressure and volume assuming suitable as a standard of comparison. Its relation to the calorie as above that the internal work of expansion is negligible. It at any given temperature, such as 15 or 20°, cannot be determined the molecules are supposed to be like smooth, hard, elastic spheres, with the same degree of accuracy as the ratio of the specific heat incapable of receiving any other kind of energy except that ot at 15° to that at 20°, if the scale of temperature is given, ihe translation, the specific heat at constant volume would be the most practical unit is the calorie at 15° or 20° or some temperature increase per degree of the kinetic energy, namely 3^/20 = 3A/2, in the range of ordinary practice. The temperature most generally that at constant pressure would be 5A/2, and the ratio ot the favoured is 15°, but 20° would be more suitable for accurate work. specific heats would be 5/3 or 1 -666. This appears to be actually These units differ only by 11 parts in 10,000 according to Callendar the case for monatomic gases such as mercury vapour (KuncA and Barnes, or by 13 in 10,000 according to Rowland and Griffiths, and Warburg, 1876), argon and helium (Ramsay 1896). lor so that the difference between them is of no great importance lor diatomic or compound gases Maxwell supposed that the molecule ordinary purposes. But for purposes of definition it would be would also possess energy of rotation, and endeavoured to prove necessary to take the mean value of the specific heat over a given in this case the energy would be equally divided between range of temperature, preferably at least 10 , rather than the that six degrees of freedom, three of translation and three ot specific heat at a point which necessitates reference to some the formula of reduction for the rate of variation. The specific heat rotation, if the molecule were regarded as a rigid body incapable vibration-energy. In this case we should have s-3A, 8 - 4 A, at 15° would be determined with reference to the^mean^over the of = 4/3 = 1-333. In 1879 Maxwell considered it one ot tne range 10° to 20°, and that at 20° from the range 15 to 25 . there A/s difficulties which the kinetic theory had yet encountered, <ian°be no doubt that the range 10° to_ 20" is too low for the greatest in spite of the many other degrees of freedom of vibration accurate thermal regulation of the conditions of the experiment. that by the spectroscope, the experimental value of the ratio The range 15° to 25° would be much more convenient Irom this revealed was 1-40 for so many gases, instead of being less than 4/3. point of view, and a mean temperature of 20° is probably nearest Sis Somewhat Boltzmann suggested that a diatomic molecule, the average of accurate calorimetric work. For instance 20 is regarded aslater a rigid dumb-bell or figure of rotation, might have the mean of the range of the experiments of Griffiths and of only five effective degrees of freedom, since the energy of rotation Rowland, and is close to that of Schuster and Gannon. It is about the axis of symmetry could not be altered by collisions readily attainable at any time in a modern laboratory with between the molecules. The theoretical value of the ratio S/s 111 adequate heating arrangements, and is probably on the whole the this case would be the required 7/5. For a rigid molecule on this most suitable temperature to select. theory the smallest value possible would be 4/3. Since much § 17 Specific Heat oj Gases.—In the case of solids and smaller values are found for more complex molecules, we may liquids'under ordinary conditions of pressure, the external suppose that, in these cases, relative movements of the constituent atoms are possible, which may be classed generally as work of expansion is so small that it may generally be energy of vibration. A hypothesis doubtfully attributed to neglected: but with gases or vapours, or with liquids Maxwell is that each additional atom m the molecule From ^' Xeg near the critical point, the external work becomes so large equivalent to two extra degrees of freedom we should then have S/f—1 + 2/+ )• that it is essential to specify the conditions under which molecule a series of ratios 5/3, 7/5, 9//, 11/9, Ac., for B f the specific heat is measured. The most important cases atoms in the molecule, values which fall withm the limits ol are the specific heats (1) at constant volume; (2) at experimental error in many cases. It is not at all clear, hoi » constant pressure; (3) at saturation pressure m the case that energy of vibration should hear a constant ratio to that ol although this would probably be the case for roU of a liquid or vapour. In consequence ot the small translation, tion. For the simpler gases, which are highly diathermano thermal capacity of gases and vapours per unit volume
