The volume (V) of a given mass of a gas depends on pressure (P) as well as temperature (T). Hence, in order to study the variation of volume with pressure, the temperature is required to be kept constant. During the studies of the variation of volume of a given mass of a gas with pressure at a constant temperature, it has been observed that when the pressure is increased, the volume decreases and vice versa. The dependence of volume on the pressure of gases can be demonstrated in the laboratory by a simple experiment described below.
Take a graduated syringe. Raise its piston or plunger to a given mark and then close the nozzle by inserting a rubber stopper. Note the position of the piston to know the volume of air enclosed in the syringe. At this stage, the pressure on the air is equal to the atmospheric pressure plus the weight of the piston. Now apply pressure on the piston by keeping some weights on it and note the new position of the piston. Let us say the piston stands at 40 ml. mark, indicating that the volume of air inside the syringe is 40 ml. Suppose that the pressure on the air at this time is P mm of mercury. That is,
Volume = 40 ml. at pressure P mm.
Now put more weights on the piston so that the pressure on the air gets doubled, that is, it becomes 2P mm of mercury. The piston moves down again and it stands at 20 ml mark. Thus,
Volume becomes 20 ml when the pressure is increased to 2P mm.
This shows that when pressure on a gas (air in the present case) is doubled (from P to 2P), its volume is halved (from 40 ml to 20 ml), i.e., the volume reduces to half of its original volume. Thus, volume varies inversely to the pressure of the gas when the temperature remains constant.
The above experiment is the experimental proof of Boyle’s law which was enunciated by Robert Boyle, an English Scientist. He was the first to discover the quantitative relationship between volume and pressure of a gas. According to Boyle’s law, “the temperature remaining constant, the volume of a given mass of a gas is inversely proportional to its pressure”.
Mathematically, Boyle’s law can be expressed as-
V ∝ 1 / P or P ∝ 1 / V
or PV = a constant (m, T constant)
or P1V1 = P2V2
or V2 = P1V1 / P2
Where, P1 = original pressure; P2 = new pressure; V1 = original volume; V2 = new volume
This relation is very useful as it can be used for converting gaseous volume from one pressure to another at constant temperature.
The variation of volume with pressure at constant temperature can be illustrated graphically. A plot of the volume against pressure at constant temperature gives a curve called an isotherm. It indicates that as the pressure is increased the volume decreases and vice versa. Since V ∝ 1 / P, therefore, the plots of the V versus 1 / P and also of P versus 1 / V would be straight lines.