Fairbairn and Tate repeated the attempt to determine the volume and temperature of water at pressures extending beyond those in use in the steam-engine, and incomplete determinations have also been made by others.
Regnault is the standard authority on these data. His experiments (1847) were made at the expense of the French Government, and under the direction of the French Academy. They were wonderfully accurate, and extended through a very wide range of temperatures and pressures. The results remain standard after the lapse of a quarter of a century, and are regarded as models of precise physical work.[112]
Regnault found that the total heat of steam is not constant, but that the latent heat varies, and that the sum of the latent and sensible heats, or the total heat, increases 0.305 of a degree for each degree of increase in the sensible heat, making 0.305 the specific heat of saturated steam. He found the specific heat of superheated steam to be 0.4805.
Regnault promptly detected the fact that steam was not subject to Boyle’s law, and showed that the difference is very marked. In expressing his results, he not only tabulated them but also laid them down graphically; he further determined exact constants for Biot’s algebraic expression,
log. p = a - bAx - cBx;
making x = 20 + t° Cent.; a = 6.264035; log. b = 0.1397743; log. c = 0.6924351; log. A = 1.9940493, and log. B = 1.9983439; p is the pressure in atmospheres. Regnault, in the expression for the total heat, H = A + bt, determined on the centigrade scale θ = 606.5 + 0.305 t Cent. For the Fahrenheit scale, we have the following equivalent expressions:
| H | = | 1,113.44° + 0.305 t° Fahr., if measured from 0° Fahr. | |||
| = | 1,091.9° | + 0.305 (t° - 32) Fahr., | } | if measured from | |
| = | 1,081.94° | + 0.305 t° Fahr., | the freezing-point. | ||
For latent heat, we have:
| L | = | 606.5° | - 0.695 t° Cent. |
| = | 1,091.7° | - 0.695 (t° - 32) Fahr. | |
| = | 1,113.94° | - 0.695 t° Fahr. |
Since Regnault’s time, nothing of importance has been done in this direction. There still remains much work to be done in the extension of the research to higher pressures, and under conditions which obtain in the operation of the steam-engine. The volumes and densities of steam require further study, and the behavior of steam in the engine is still but little known, otherwise than theoretically. Even the true value of Joule’s equivalent is not undisputed.