BOYLE'S LAW. If the temperature of a gas is kept constant, and its volume changes, the re sulting pressure and density are such that one is proportional to the other. In symbols, p = hp; or writing 71 for pv = km, where at is the mass and v is the volume. This law, too, is only approximate; for as the pressure on the gas is increased, the product pv does not remain a constant quantity, but first decreases and then increases. (For hydrogen gas the product pa increases without any preliminary decrease.) This means that at high pressures gases fife less compressible than they would be if Boyle's law were obeyed exactly. This law, pv = constant at constant temperatures, was first stated by Robert Boyle in 1662 as the result of careful experiments on air; fourteen years after wards it was published by Mariotte.
It is a consequence of Boyle's law that the elasticity of a gas at constant temperature nu merically equals the pressure. If a gas is com pressed rapidly its temperature rises, and so the pressure is increased: the elasticity for a sudden compression or rarefaction equals ^yp , where 7 is the ratio of the two specific heats for the gas and for ordinary gases has the value 1.4. (See ELAS TICITY.) An instrument for measuring high pres sures in a fluid is made, called a closed 'manom eter,' the principle of which depends upon Boyle's law. It consists of a device to trap a definite mass of gas in a closed tube by means of some liquid. such as mercury, and to have the column of mercury compress the gas as the pressure to be measured is increased: the volume of the gas varies inversely as the pressure on it.
If a gas is allowed to expand freely, doing no external work—'.g. take two reservoirs connected by a tube with a stop-cock. compress the gas in one and rarefy it in the other, then let the stop cock be opened—it is observed that there is prac tically no energy required to produce the expan sion. This shows that any forces of attraction be tween the molecules must be extremely small. (See HEAT.) It is found by experiment that if the pressure on a gas is kept constant, but the temperature changed, the volume changes at the rate given by the formula v = where v is the volume at t° C.; that at 0° ; p is a constant, the same for all gases approximately. Similarly, if the volume is kept constant, and the temperature changed, the pressure will change according to the law P=Po Pt), where p is the pressure at t° C.; that at 0° ; 3
is a constant the same for all gases and the same as in the above formula for the change of volume. The value of this 'coefficient of expansion' is al most exactly or 0.003662. This law for the change in pressure or volume of a gas as the temperature is altered, viz. that p is the same for all gases, was discovered almost simulta neously by Charles, Dalton, and Gay-Lussac.
Another law, known as the 'law of combining volumes,' may be found explained under CHEM ISTRY.
The experimental laws for gases may be de duced theoretically for a mechanical system of perfectly elastic spheres thrown at random into a space bounded by rigid walls. If the number of spheres is great enough to allow the applica tion of the principle of statistics, it can be shown that the pressure on the walls owing to the impact of the spheres is p = 4 innte, where nt is the mass of each sphere, n is the number of spheres per cubic centimeter, is the mean value of the squared velocities of the spheres. The density is then mn; and the formula may be written p = It may also he shown that the mean kinetic energy of translation of the spheres — has properties identical with those of the tem perature of a gas; consequently the above value of the pressure satisfies Boyle's law. The law for the expansion with temperature may also be derived, viz. that p is the same for all gases.
Again, if there are several sets of spheres in closed in the same space p = etc.), which is Dalton's law. And if there is equi librium =1 + etc., and therefore p (ni + n2 + etc.), which states that for a given value of temperature) the pressure depends simply on the number of the spheres per cubic centimeter, not on their masses. This is equivalent to Avogadro's rule (q.v.), another of the general principles concerning gases. Looked at in a dif ferent way: If there are two sets of spheres in different reservoirs at the same pressure, = if further their values of are the same (i.e. their temperatures), = Hence = or they have the same number of spheres per cubic centimeter. The densities of the two are p, = so if the pressures and 'temperatures' are the same m, — – In: P2 which is the formula used in determining the `molecular weights' of gases. See Mca.EctILEs