The Boyle's law relates the volume of a gas to its pressure at the same temperature. Mathematically it can be written as:
The experimental apparatus used to study for the first time this law was composed of two glass tubes, one closed at one and one open at both ends. The tubes were communicating through a rubber hose that was fitted to the open ends of both the glass tubes. Thus the first tube had one end closed and the other end fitted at the hose, while the second had one end fitted at the hose and the other end open. Through the open end of the second tube mercury was poured into the apparatus until a column of a certain height between the two tubes was formed. See the figures. In figure 1 the height of the column of Hg is `h_1` and the volume occupied by gas in closed tube is `V_1` . The relative position of the two tubes and the connecting hose is then modified until the height of the Hg columns is `h_2` in the second figure. The corresponding volume of the gas in first tube becomes `V_2` .
The pressure in closed tube figure 1 is `P_1 =P_0+rho_(Hg)*g*h_1`
The pressure in closed tube figure 2 is `P_2 =P_0+rho_(Hg)*g*h_2`
(`P_0` is the atmospheric pressure).
Experimentally has been observed that the product `P*V` remains the same for various heights of Hg column: