(a) Avogadro's law:

V ∝ n      (at constant T and P)

V = k₄n

$\frac{\mathrm{V}}{\mathrm{n}}$ = constant (k₄)

Boyle's law:

Mathematically, Boyle's law is written as,

$\mathrm{V}\propto \frac{1}{\mathrm{P}}$      (at constant T and n)
$\mathrm{V}=\frac{{\mathrm{k}}_1}{\mathrm{P}}$
or, PV = k_[1]
Where, P = Pressure, V = Volume, k₁ = proportionality constant.
Suppose a gas has volume V₁ at pressure P₁. At constant temperature, if pressure extended to P₂ and volume becomes V₂, then according to Boyle's law,

P₁V₁ = P₂V₂ = constant.

or,    $\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}=\frac{{\mathrm{V}}_2}{{\mathrm{V}}_1}$

(see the figure 1)

Charle's law:
According to this law, "At constant pressure, the volume of gas increases or decreases by $\frac{1}{273}$ on increasing or decreasing each degree of temperature".

Mathematically, Charles law can be written as:

Suppose, the volume of gas is V₀ at temperature 0ºC. If temperature is increased as tºC then volume becomes V_t, then according to Charles law,
${\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_{\mathrm{o}}+\frac{{\mathrm{V}}_{\mathrm{o}}}{273}\ast \mathrm{t}$

or, ${\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_{\mathrm{o}}(1+\frac{\mathrm{t}}{273})$

We can calculate the volume of given mass of gas at different temperatures.

(Follow the below figure 2).

For example:
Volume at $1^{\mathrm{o}}\mathrm{C}\left({\mathrm{V}}_1\right)={\mathrm{V}}_{\mathrm{o}}(1+\frac{1}{273})$
Volume at ${10}^{\mathrm{o}}\mathrm{C}\left({\mathrm{V}}_{10}\right)={\mathrm{V}}_{\mathrm{o}}(1+\frac{10}{273})$