Obtain the coefficient of volume expansion for an ideal gas.

(N/A) The ideal gas equation is given by:
$PV = \mu RT$
Where $P$ is pressure,$V$ is volume,$\mu$ is the number of moles,$R$ is the gas constant,and $T$ is the absolute temperature.
At constant pressure,if the temperature changes by $\Delta T$,the volume changes by $\Delta V$:
$P(V + \Delta V) = \mu R(T + \Delta T)$
$PV + P\Delta V = \mu RT + \mu R\Delta T$
Since $PV = \mu RT$,we have:
$P\Delta V = \mu R\Delta T$
Dividing this equation by the original equation $PV = \mu RT$:
$\frac{P\Delta V}{PV} = \frac{\mu R\Delta T}{\mu RT}$
$\frac{\Delta V}{V} = \frac{\Delta T}{T}$
The coefficient of volume expansion $\alpha_V$ is defined as $\alpha_V = \frac{1}{V} \frac{\Delta V}{\Delta T}$.
Therefore,$\alpha_V = \frac{1}{T}$.
For an ideal gas,$\alpha_V$ depends on temperature and is inversely proportional to the absolute temperature $T$. As temperature increases,$\alpha_V$ decreases. At $0^{\circ}C$ $(273.15 \ K)$,$\alpha_V \approx 3.66 \times 10^{-3} \ K^{-1}$,which is significantly higher than that of solids and liquids.