**Boyle’s Law**

**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 dm^{3}. 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 dm^{3}.

When we calculate the product of volume and pressure for this experiment, the product of all these experiments is constant i.e. 2 atm dm^{3}. It proves the Boyle’s law

P1V1 = 2 atm x 1 dm^{3} = 2 atm dm^{3}

P2V2 = 4 atm x 0.5 dm^{3} = 2 atm dm^{3}

P3V3 = 6 atm x 0.33 dm^{3} = 2 atm dm^{3}

P4V4 = 8 atm x 0.25 dm^{3} = 2 atm dm^{3}