| Fig. 8. |
§ 13. Schuster and Gannon.—The method employed by A. Schuster and W. Gannon for the determination of the specific heat of water in terms of the international electric units (Phil. Trans. A, 1895, p. 415) corresponded to the expression ECT, and differed in many essential details from that of Griffiths. The current through a platinoid resistance of about 31 ohms in a calorimeter containing 1500 grammes of water was regulated so that the potential difference on its terminals was equal to that of twenty Board of Trade Clark cells in series. The duration of an experiment was about ten minutes, and the product of the mean current and the time, namely CT, was measured by the weight of silver deposited in a voltameter, which amounted to about 0.56 gramme. The uncertainty due to the correction for the water equivalent was minimized by making it small (about 27 grammes) in comparison with the water weight. The correction for external loss was reduced by employing a small rise of temperature (only 2.22°), and making the rate of heat-supply relatively rapid, nearly 24 watts. The platinoid coil was insulated from the water by shellac varnish. The wire had a length of 760 cms., and the potential difference on its terminals was nearly 30 volts. The rate of stirring adopted was so slow that the heat generated by it could be neglected. The result found was 4.191 joules per calorie at 19° C. This agrees very well with Griffiths considering the difficulty of measuring so small a rise of temperature at 2° with a mercury thermometer. Admitting that the electro-chemical equivalent of silver increases with the age of the solution, a fact subsequently discovered, and that the E.M.F. of the Clark cell is probably less than 1.4340 volts (the value assumed by Schuster and Gannon), there is no difficulty in reconciling the result with that of Rowland.
§ 14. H.L. Callendar and H.T. Barnes (Brit. Assoc. Reports, 1897 and 1899) adopted an entirely different method of calorimetry, as well as a different method of electrical measurement. A steady current of liquid, Q grammes per second, of specific heat, Js joules per degree, flowing through a fine tube, A B, fig. 9, is heated by a steady electric current during its passage through the tube, and the difference of temperature dθ between the inflowing and the outflowing liquid is measured by a single reading with a delicate pair of differential platinum thermometers at A and B. The difference of potential E between the ends of the tube, and the electric current C through it, are measured on an accurately calibrated potentiometer, in terms of a Clark cell and a standard resistance. If hdθ is the radiation loss in watts we have the equation,
EC = JsQdθ + hdθ (2).
| Fig. 9. |
The advantage of this method is that all the conditions are steady, so that the observations can be pushed to the limit of accuracy and sensitiveness of the apparatus. The water equivalent of the calorimeter is immaterial, since there is no appreciable change of temperature. The heat-loss can be reduced to a minimum by enclosing the flow-tube in a hermetically sealed glass vacuum jacket. Stirring is effected by causing the water to circulate spirally round the bulbs of the thermometers and the heating conductor as indicated in the figure. The conditions can be very easily varied through a wide range. The heat-loss hdθ is determined and eliminated by varying the flow of liquid and the electric current simultaneously, in such a manner as to secure approximately the same rise of temperature for two or more widely different values of the flow of liquid. An example taken from the Electrician, September 1897, of one of the earliest experiments by this method on the specific heat of mercury will make the method clearer. The flow-tube was about 1 metre long and 1 millim. in diameter, coiled in a short spiral inside the vacuum jacket. The outside of the vacuum jacket was immersed in a water jacket at a steady temperature equal to that of the inflowing mercury.
Specific Heat of Mercury by Continuous Electric Method
| Flow of Hg. | Rise of Temp. | Watts. | Heat-loss. | Specific Heat. |
| gm./sec. | dθ | EC | hdθ | Per gm. deg. |
| 8.753 | 11.764 | 14.862 | 0.655 | .13780 joules |
| 4.594 | 12.301 | 7.912 | 0.865 | .03297 cals. |
It is assumed as a first approximation that the heat-loss is proportional to the rise of temperature dθ, provided that dθ is nearly the same in both cases, and that the distribution of temperature in the apparatus is the same for the same rise of temperature whatever the flow of liquid. The result calculated on these assumptions is given in the last column in joules, and also in calories of 20° C. The heat-loss in this example is large, nearly 4.5% of the total supply, owing to the small flow and the large rise of temperature, but this correction was greatly reduced in subsequent observations on the specific heat of water by the same method. In the case of mercury the liquid itself can be utilized to conduct the electric current. In the case of water or other liquids it is necessary to employ a platinum wire stretched along the tube as heating conductor. This introduces additional difficulties of construction, but does not otherwise affect 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 20° 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 110° 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 110° and 190° 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,