Question
Give its
(i) graphical representation,
(ii) mathematical expression
(iii) significance
(i) graphical representation,
(ii) mathematical expression
(iii) significance
✓
Answer
(i) Graphical representation of Charles's law
T vs V: 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
Let $\mathrm{V}_0$ be the volume of a fixed mass of a gas at $0{ }^{\circ} \mathrm{C}$, and let $\mathrm{V}$ be its volume at temperature $\mathrm{t}^{\circ} \mathrm{C}$ at, constant pressure. then, according to Charles Law
$\begin{aligned} & \mathrm{V}=\mathrm{V}_0+\frac{\mathrm{V}_0}{273} t \text { (when } \mathrm{P} \text { is constant) } \\ & \mathrm{V}=\mathrm{V}_0\left(1+\frac{t}
{273}\right)=\mathrm{V}_0\left(\frac{273+t}{273}\right) \ldots \ldots . .(1) \\ &
\mathrm{V}=\frac{\mathrm{V}_0}{273} \mathrm{~T} \text { where }
\mathrm{T}=273+\mathrm{t}\end{aligned}$
For a given mass of a gas,$\frac{\mathrm{V}_0}{273}=\text { constant }$$\mathrm{V}=\mathrm{k} \times \mathrm{T}$ (where $\mathrm{k}$ is constant)
(iii) Significance of Charles's Law: The volume of a given mass of a gas is directly proportional to its temperature; hence, the density decreases with temperature. This is the reason that
(a) Hot air is filled in balloons used for meteorological purposes. (b) Cable wires contract in winters and expand in summers.
T vs V: The relationship between the volume and the temperature of a gas can be plotted on a graph. A straight line is obtained.
(ii) Mathematical expression
Let $\mathrm{V}_0$ be the volume of a fixed mass of a gas at $0{ }^{\circ} \mathrm{C}$, and let $\mathrm{V}$ be its volume at temperature $\mathrm{t}^{\circ} \mathrm{C}$ at, constant pressure. then, according to Charles Law
$\begin{aligned} & \mathrm{V}=\mathrm{V}_0+\frac{\mathrm{V}_0}{273} t \text { (when } \mathrm{P} \text { is constant) } \\ & \mathrm{V}=\mathrm{V}_0\left(1+\frac{t}
{273}\right)=\mathrm{V}_0\left(\frac{273+t}{273}\right) \ldots \ldots . .(1) \\ &
\mathrm{V}=\frac{\mathrm{V}_0}{273} \mathrm{~T} \text { where }
\mathrm{T}=273+\mathrm{t}\end{aligned}$
For a given mass of a gas,$\frac{\mathrm{V}_0}{273}=\text { constant }$$\mathrm{V}=\mathrm{k} \times \mathrm{T}$ (where $\mathrm{k}$ is constant)
(iii) Significance of Charles's Law: The volume of a given mass of a gas is directly proportional to its temperature; hence, the density decreases with temperature. This is the reason that
(a) Hot air is filled in balloons used for meteorological purposes. (b) Cable wires contract in winters and expand in summers.
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