Boyle’s Law - Home of Knowledge

# Boyle’s Law

Definition or statement: volume of a given mass of a gas is inversely proportional to its pressure provided the temperature remains constant.

OR

The product of pressure and volume of a fixed mass of a gas is constant at a constant temperature.

Presenter: In 1662 Robert Boyle , a natural philosopher, chemist, physist and inventor prosed this law. Robert Boyle studied the relationship between the volume and pressure of a gas at constant temperature..

Mathematical expression: According to this law, the volume (V) of a given mass of a gas decreases with the increase of pressure (P) and vice versa. Mathematically, it can be written as:  volume ∝ 1/pressure.    Or     v ∝ 1/p

v = k/p           or      vp = k = constant.

Where ‘k’ is proportionality constant. The value of k is same for the same amount of a given gas. Therefore, Boyle’s law can be stated as the product of pressure and volume of a fixed mass of a gas is constant at a constant temperature.

If P1V1 = k Then P2V2 = k

where P1 = Initial Pressure P2 = Final Pressure

V1 = Initial Volume V2 = Final Volume

As both equations have same constant therefore, their variables are also equal to each other.

P1V1 = P2V2

This equation establishes the relationship between pressure and volume of the gas.

Experimental Verification of Boyle’s law:

The relationship between volume and pressure can be verified experimentally by the following series of experiments. Let us take some mass of a gas in a cylinder having a movable piston and observe the effect of increase of pressure on its volume. The phenomenon is represented in figure.5.1. When the pressure of 2 atmosphere (atm) is applied, the volume of the gas reads as 1 dm3.

When pressure is increased equivalent to 4 atm, the volume of the gas reduces to 0.5 dm3. Again when pressure is increased three times i.e. 6 atm, the volume reduces to 0.33 dm3. Similarly, when pressure is increased up to 8 atm on the piston, volume of the gas decreases to 0.25 dm3.

When we calculate the product of volume and pressure for this experiment, the product of all these experiments is constant i.e. 2 atm dm3. It proves the Boyle’s law

P1V1 = 2 atm x 1 dm3 = 2 atm dm3

P2V2 = 4 atm x 0.5 dm3 = 2 atm dm3

P3V3 = 6 atm x 0.33 dm3 = 2 atm dm3

P4V4 = 8 atm x 0.25 dm3 = 2 atm dm3