# Boyle’s Law

This law describes the pressure-volume relationship of gases at constant temperature. It was given by Anglo-Irish scientist Robert Boyle (1662) and is known after his name as Boyle’s law. The law states that: The volume of a fixed mass of a gas is inversely proportional to its pressure at constant temperature.

MATHEMATICAL INTERPRETATION OF THE LAW

Mathematically, the law may be expressed as:

(Temperature and mass constant)

or         V = k1 1 / p where k1 is constant of proportionality

or         PV = K1 = constant.

The value of the constant k1 depends upon amount of the gas, temperature of the gas and the units in which P and V are expressed.

Thus, another statement of Boyles law may be given as follows:

For a given amount of the gas, the product of pressure and volume is constant at constant temperature.

Let V 1 be the volume of a given mass of the gas having pressure P 1 at temperature T. Now if the pressure is changed to P2 at the same temperature, let the volume changes to V2 .

The quantitative relationship between the four variables P1′ VI, p2 and v2 is:

GRAPHICAL REPRESENTATION OF BOYLE’S LAW

The law can also be illustrated by means of pressure volume curves as shown in Figs. 15.3 (a), 15.3 (b), 15.3 (c) and 15.3 (d).  (d) P-V plots at different temperatures for fixed amount of gas.

Fig. 15.3. Different plots of pressure-volume Relationship of a gas.

The plots depicting the pressure-volume behaviour at constant temperature are called isotherms.

Kinetic Theory and Boyle’s Law

The kinetic molecular theory assumes that the pressure exerted by a gas is due to the bombardment of its molecules on the walls of the container. Thus, the pressure depends upon the number of molecular impacts or collisions per unit area of the walls per second. If the temperature is kept constant, the average speed of the molecules ( 1/2mu2-T) remains the same. Now, if the volume is increased, there will be less number of molecules colliding each unit area of the vessel in a unit time. Consequently, the pressure will decrease. On the other hand, if volume is decreased, there will be more number of molecules colliding each unit area of walls and hence. pressure will increase. Thus, it can be concluded that at given temperature, the pressure exerted by a gas is inversely proportional to the volume. This is Boyle’s law. 