Obtain coefficient of volume expansion from ideal gas equation.

Ideal gas equation,

$\mathrm{PV}=\mu \mathrm{RT}$

Where $\mathrm{P}=$ pressure, $\mathrm{V}=$ volume

$\mu=\text { no. of moles of gases }$

$\mathrm{R}=\text { gas constant }$

$\mathrm{T}=\text { absolute temperature }$

At constant pressure,

$\mathrm{P} \Delta \mathrm{V}=\mu \mathrm{R} \Delta \mathrm{T}$

By taking ratio of equation $(2)$ and $(1)$,

$\frac{\Delta \mathrm{V}}{\mathrm{V}}=\frac{\Delta \mathrm{T}}{\mathrm{T}}$ $\therefore\frac{\Delta \mathrm{V}}{\mathrm{V} \Delta \mathrm{T}}=\frac{1}{\mathrm{~T}}$ $\text { But } \frac{\Delta \mathrm{V}}{\mathrm{V} \Delta \mathrm{T}}=\alpha_{\mathrm{V}} \text { (coefficient of volume expansion) }$ $\therefore \alpha_{\mathrm{V}}=\frac{1}{\mathrm{~T}}$

For ideal gas, $\alpha_{V}=3.7 \times 10^{-3} \mathrm{~K}^{-1}$ at $0^{\circ} \mathrm{C}$ which is greater than solid and liquid.

For ideal gas $\alpha_{V}$ depend on temperature. It is inversely proportion to temperature. Hence it decrease with increase in temperature.

For ideal gas, $\alpha_{V}=3300 \times 10^{-6} \mathrm{~K}^{-1}$ at room temperature which is much more greater than liquids.