(a) State Boyle's Law.

(b) Give its

(i) mathematical expression,

(ii) graphical representation and

(iii) significance.

(a) Boyle's law states that the volume of a given mass of a dry gas is inversely proportional to its pressure at a constant temperature.

(b) (i) Mathematical expression of Boyle's law :

Suppose a gas occupies volume V₁ when its pressure is P₁; then

V₁ α $\dfrac{1}{\text{P}_1}$ or

V₁ = $\dfrac{\text{k}}{\text{P}_1}$ or

P₁V₁ = k = constant

If V₂ is the volume occupied when the pressure is P₂ at the same temperature, then

V₂ α $\dfrac{1}{\text{P}_2}$ or

V₂ = $\dfrac{\text{k}}{\text{P}_2}$ or

P₂V₂ = k = constant

∴ P₁V₁ = P₂V₂ = k; at constant temperature.

(ii) Graphical representation of Boyle's Law:

(a) V vs $\dfrac{1}{\text{P}}$ : a straight line passing through the origin is obtained.

(b) V vs P : a hyperbolic curve in the first quadrant is obtained.

(c) PV vs P : a straight line is obtained parallel to the pressure axis.

(iii) Significance of Boyle's law :
On increasing pressure, volume decreases. The gas becomes denser. Thus, at constant temperature, the density of a gas is directly proportional to pressure.