Obtain coefficient of volume expansion from ideal gas equation.
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.
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