(a) State Charles' law.

(b) Give its

(i) Graphical representation,

(ii) mathematical expression and

(iii) Significance.

(a) Charles law states that pressure remaining constant, the volume of a given mass of dry gas increases or decreases by $\dfrac{1}{273}$ of its volume at 0°C for each 1°C increase or decrease in temperature, respectively.

(b) (i) Graphical representation of Charles' law : The relationship between the volume and the temperature of a gas can be plotted on a graph. A straight line is obtained.

(ii) Mathematical expression of Charles' law :

Suppose, a gas occupies V₁ cm³ at T₁ temperature and V₂ cm³ at T₂ temperature, then by Charles' law:

    V₁ α T₁

or V₁ = kT₁ (k is constant)

or $\dfrac{\text{V}$1}{\text{T}1} = k and

    V₂ α T₂

or $\dfrac{\text{V}$2}{\text{T}2} = k

∴ $\dfrac{\text{V}$1}{\text{T}1} = $\dfrac{\text{V}$2}{\text{T}2} = k (at constant pressure)

(iii) Significance of Charles' Law :
Volume of a given mass of a gas is directly proportional to its temperature, hence, density decreases with an increase in temperature.