58. Boyle's Law.—The relation between the volume and pressure of a gas was first investigated by Robert Boyle in the seventeenth century. The experiment by which he first discovered the law or the relation between the volume and the pressure of a gas is briefly described as follows:
Figs. 37 a and 37 b.—Boyle's law apparatus.
A glass tube is bent in the form of the capital letter J, the short arm being closed. A little mercury is poured in to cover the bend. (See Fig. 37 a.) Since the mercury is at the same level in both arms, the pressure in (A) is the same as in (B). Mercury is now poured into (A) until it stands in the long tube at a height above that in (B) which is equal to the height of the mercury column of the barometer. (See Fig. 37 b.) The air in (BC) is now under a pressure of two atmospheres (one atmosphere is due to the mercury column). On measurement the air in (BC) will be found to have just one-half of its original volume.
Thus doubling the pressure to which a gas is subjected reduces its volume to one-half. Tripling the pressure, reduces the volume to one-third and so on.
Careful experiments reveal the following law: The volume of a given mass of gas at constant temperature is inversely proportional to the pressure to which it is subjected.
This law is often expressed mathematically. P/P´ = V´/V, or PV = P´V´. Since doubling the pressure reduces the volume one-half, it doubles the density. Tripling the pressure triples the density. We therefore have P/P´ = D/D´ or the density of a gas directly proportional to its pressure.
Fig. 38.—Height and density of the air.