SPECIFIC HEAT OF WATER IN TERMS OF UNIT AT 200 C.4.180 JOULES
t° C. Joules. s. h. Rowland.
o° 4.208 1.0094 0 0
50 4.202 1.0054. 5.037 5'037
I0° 4.191 1.0027 10.056 10.058
15° 4.184 1.0011 15'065 15.068
2o° 4.180 1.0000 20.068 20.071
25° 4.177 0.9992 25.065 25.067
30° 4'175 0'9987 30.060 30.057
35° 4'173 0'9983 35'052 35'053
400 4'173 0'99$2 40.044
500 4'175 0'9987 50.028
6o° 4.18o 1.0000 60.020
7o° 4.187 1•oo16 70.028
8o° 4'194 1.0033 80.052
90° 4.202 1.0053 90.095 Shaw
too° 4.211 1.0074 100.158 Regnault
12o° 4.231 I.012I 120.35 120.73
140° 4.254 1.0176 140.65 140.88
16o° 4.280 1.0238 161.07 161.20
18o° 4.309 1.0308 181.62 182.14
zoo° 4'341 1.0384 202.33
220° 4.376 1.0467 223.20
to allow for the increase in the specific heat below 2o° C. This was estimated in 1899 as being equivalent to the addition of the constant quantity o•o2o to the values of the total heat h of the liquid as reckoned by the parabolic formula (5). This quantity is now, as the result of further experiments, added to the values of h, and also represented in the formula for the specific heat itself by the cubic term.
The unit of comparison in the following table is taken as the specific heat of water at 2o° C. for the reasons given below. This unit is taken as being 4.180 joules per grammedegreecentigrade on the scale of the platinum thermometer, corrected to the absolute scale as explained in the article THERMOMETRY, which has been shown to be practically equivalent to the hydrogen scale. The value 4.180 joules at 2o° C. is the mean between Rowland's corrected result 4.181 and the value 4.179, deduced from the experiments of Reynolds and Moorby on the assumption that the ratio of the mean specific heat 0° to too° to that at 20° is 1 •oot6, as given by the formulae representing the results of Callendar and Barnes. This would indicate that Rowland's corrected values should, if anything, be lowered. In any case the value of the mechanical equivalent is uncertain to at least 1 in 2000.
The mean specific heat, over any range of temperature, may be obtained by integrating the formulae between the limits required, or by taking the difference of the corresponding values of the total heat h, and dividing by the range of temperature. The quantity actually observed by Rowland was the total heat. It may be remarked that starting from the same value at 5°, for the sake of comparison, Rowland's values of the total heat agree to I in 5000 with those calculated from the formulae. The values of the total heat observed by Regnault, as reduced by Shaw, also show a very fair agreement, considering the uncertainty of the units. It must be admitted that it is desirable to redetermine the variation of the specific heat above too° C. This is very difficult on account of the steampressure, and could not easily be accomplished by the electrical
the method. The absolute value of the specific heat deduced necessarily depends on the absolute values of the electrical standards employed in the investigation. But for the determination of relative values of specific heats in terms of a standard liquid, or of the variations of specific heat of a liquid, the method depends only on the constancy of the standards, which can be readily and accurately tested. The absolute value of the E.M.F. of the Clark cells employed was determined with a special form of electrodynamometer (Callendar, Phil. Trans. A. 313, p. 81), and found to be 1.4334 volts, assuming the ohm to be correct. Assuming this value, the result found by this method for the specific heat of water at 2o° C. agrees with that of Rowland within the probable limits of error.
§ 15. Variation of Specific Heat of Water.The question of the variation of the specific heat of water has a peculiar interest and importance in connexion with the choice of a thermal unit. Many of the uncertainties in the reduction of older experiments, such as those of Regnault, arise from uncertainty in regard to the unit in terms of which they are expressed, which again depends on the scale of the particular thermometer employed in the investigation. The first experiments of any value were those of Regnault in 1847 on the specific heat of water between 11o° C. and 192° C. They were conducted on a very large scale by the method of mixture, but showed discrepancies of the order of 0.5 %, and the calculated results in many cases do not agree with the data. This may be due merely to deficient explanation of details of tabulation. We may probably take the tabulated values as showing correctly the rate of variation between 1 to° and 19o° C., but the values in terms of any particular thermal unit must remain uncertain to at least 0.5% owing to the uncertainties of the thermometry. Regnault himself adopted the formula,
method. Callendar has, however, devised a continuous method of mixture, which appears to be peculiarly adapted to the purpose, and promises to give more certain results. In any case it may be remarked that formulae such as those of Jamin, Henrichsen, Baumgartner, Winkelmann or Dieterici, which give far more rapid rates of increase than that of Regnault, cannot possibly be reconciled with his observations, or with those of Reynolds and Moorby, or Callendar and Barnes, and are certainly inapplicable above too° C.
§ 16. On the Choice of the Thermal Unit.—So much uncertainty still prevails on this fundamental point that it cannot be passed over without reference. There are three possible kinds of unit, depending on the three fundamental methods already given: (t) the thermometric unit, or the thermal capacity of unit mass of a standard substance under given conditions of temperature and pressure on the scale of a standard thermometer. (2) The latentheat unit, or the quantity of heat required to melt or vaporize unit mass of a standard substance under given conditions. This unit has the advantage of being independent of thermometry, but the applicability of these methods is limited to special cases, and the relation of the units to other units is difficult to determine. (3) The absolute or mechanical unit, the quantity of heat equivalent to a given quantity of mechanical or electrical energy. This can be very accurately realized, but is not so convenient as
(t) for ordinary purposes.
In any case it is necessary to define a thermometric unit of class (t). The standard substance must be a liquid. Water is always selected, although some less volatile liquid, such as aniline or mercury, would possess many advantages. With regard to the scale of temperature, there is very general agreement that the absolute scale as realized by the hydrogen or helium thermometer should be adopted as the ultimate standard of reference. But as the hydrogen thermometer is not directly available for the majority of experiments, it is necessary to use a secondary standard for the practical definition of the unit. The electrical resistance thermometer of platinum presents very great advantages for this purpose over the mercury thermometer in point of reproducibility, accuracy and adaptability to the practical conditions of experiment. The conditions of use of a mercury thermometer in a calorimetric experiment are necessarily different from those under which its corrections are determined, and this difference must inevitably give rise to constant errors in practical work. The primary consideration in the definition of a unit is to select that method which permits the highest order of accuracy in comparison and verification. For this reason the definition of the thermal unit will in the end probably be referred to a scale of temperature defined in terms of a standard platinum thermometer.
There is more diversity of opinion with regard to the question of the standard temperature. Many authors, adopting Regnault's formula, have selected o° C. as the standard temperature, but this cannot be practically realized in the case of water, and his formula is certainly erroneous at low temperatures. A favourite temperature to select is 4° C., the temperature of maximum density, since at this point the specific heat at constant volume is the same as that at constant pressure But this is really of no consequence, since the specific heat at constant volume cannot be practically realized. The specific heat at 4° could be accurately determined at the mean over the range o° to 8° keeping the jacket at o° C. But the change appears to be rather rapid near o°, the temperature is inconveniently low for ordinary calorimetric work, and the unit at 4° would be so much larger than the specific heat at ordinary temperatures that nearly all experiments would require reduction. The natural point to select would be that of minimum specific heat, but if this occurs at 4o° C. it would be inconveniently high for practical realization except by the continuous electrical method. It was proposed by a committee of the British Association to select the temperature at which the specific heat was 4.200 joules, leaving the exact temperature to be subsequently determined. It was supposed at the time, from the original reduction of Rowland's experiments, that this would be nearly at 1o° C., but it now appears that it may be as low as 5° C., which would be inconvenient. This is really only an absolute unit in disguise, and evades the essential point, which is the selection of a standard temperature for the water thermometric unit. A similar objection applies to selecting the temperature at which the specific heat is equal to its mean value between o° and 100°. The mean calorie cannot be accurately realized in practice in any simple manner, and is therefore unsuitable as a standard of comparison. Its relation to the calorie at any given temperature, such as 15° or 20°, cannot be determined with the same degree of accuracy as the ratio of the specific heat at 15° to that at 20°, if the scale of temperature is given. The most practical unit is the calorie at 15° or 20° or some temperature in the range of ordinary practice. The temperature most generally favoured is 15°, but 2o° would be more suitable for accurate work. These units differ anly by 11 parts in 1o,000 according to Callendar and Barnes, or by 13 in lo,000 according to Rowland and Griffiths, so that the differencebetween them is of no great importance for ordinary purposes. But for purposes of definition it would be necessary to take the mean value of the specific heat over a given range of temperature, preferably at least 1o°, rather than the specific heat at a point which necessitates reference to some formula of reduction for the rate of variation. The specific heat at 15° would be determined with reference to the mean over the range to° to 20°, and that at 20° from the range 15° to 25°. There can be no doubt that the range to° to 2o° is too low for the accurate thermal regulation of the conditions of the experiment. The range 15° to 25° would be much more convenient from this point of view, and a mean temperature of 20° is probably nearest the average of accurate calorimetric work. For instance 2o° is the mean of the range of the experiments of Griffiths and of Rowland, and is close to that of Schuster and Gannon. It is readily attainable at any time in a modern laboratory with adequate heating arrangements, and_is probably on the whole the most suitable temperature to select.
§ 17. Specific Heat of Gases.—In the case of solids and liquids under ordinary conditions of pressure, the external work of expansion is so small that it may generally be neglected; but with gases or vapours, or with liquids near the critical point, the external work becomes so large that it is essential to specify the conditions under which the specific heat is measured. The most important cases are, the specific heats (1) at constant volume; (2) at constant pressure; (3) at saturation pressure in the•case of a liquid or vapour. In consequence of the small thermal capacity of gases and vapours per unit volume at ordinary pressures, the difficulties of direct measurement are almost insuperable except in case (2). Thus the direct experimental evidence is somewhat meagre and conflicting, but the question of the relation of the specific heats of gases is one of great interest in connexion with the kinetic theory and the constitution of the molecule. The wellknown experiments of Regnault and Wiedemann on the specific heat of gases at constant pressure agree in showing that the molecular specific heat, or the thermal capacity of the molecular weight in grammes, is approximately independent of the temperature and pressure in case of the more stable diatomic gases, such as H2,02, N2, CO, &c., and has nearly the same value for each gas. They also indicate that it is much larger, and increases considerably with rise of temperature, in the case of more condensible vapours, such as Cl2, Br2, or more complicated molecules, such as CO2,N20, NH3, C2H4. The direct determination of the specific heat at constant volume is extremely difficult, but has been successfully attempted by Joly with his steam calorimeter, in the case of air and CO2. Employing pressures between 7 and 27 atmospheres, he found that the specific heat of air between ro° and roe C. increased very slightly with increase of density, but that of CO2 increased nearly 3 %between 7 and 21 atmospheres. The following formulae represent his results' for the specific heat s at constant volume in terms of the density d in gms. per c. c.
Air, s =o• 1715+0•028d,
End of Article: SPECIFIC HEAT OF WATER IN TERMS OF UNIT AT 200 C 

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