If V′ be its volume at any other temperature T′, and under the same pressure, we shall have, in like manner,
| V′ = v {1 + n (T′ − 32)}. |
Hence we obtain
| V | = | 1 + n (T − 32) | ;(6.) |
| V′ | 1 + n (T′ − 32) |
which expresses the relation between the volumes of the same gas or vapour under the same pressure and at any two temperatures. The co-efficient n, as explained in the text, has the same value for the same gas or vapour throughout the whole thermometric scale. But it is still more remarkable that this constant has the same value for all gases and vapours. It is a number, therefore, which must have some essential relation to the gaseous or elastic state of fluid matter, independent of the peculiar qualities of any particular gas or vapour.
The value of n, according to the experiments of Gay-Lussac, is 0·002083, or 1⁄480.
To reduce the law of Mariotte, explained in ([97].) p. 171., to mathematical language, let V, V′ be the volumes of the same gas or vapour under different pressures P, P′, but at the same temperature. We shall then have
| VP = V′P′. (7.) |
If it be required to determine the relation between the volumes of the same gas or vapour, under a change of both temperature and pressure, let V be the volume at the temperature T and under the pressure P, and let V′ be the volume at the temperature T′ and under the pressure P′. Let v be the volume at the temperature T and under the pressure P′.
By formula (7.) we have