Obtain coefficient of volume expansion from ideal gas equation.

Explanation

Ideal gas equation,
`PV=muRT " "` . . . (1)
Where P = pressure, V = volume
`mu=` no. of moles of gases
R = gas constant
T = absolute temperature
At constant pressure,
`PDeltaV=muRDeltaT" "` . . . (2)
By taking ratio of equation (2) and (1),
`(DeltaV)/(V)=(DeltaT)/(T)`
`:.(DeltaV)/(VDeltaT)=1/T`
But `(DeltaV)/(V DeltaT)=alpha_(V)` (coefficient of volume expansion)
`:.alpha_(V)=1/T`
For ideal gas, `alpha_(V)=3.7xx10^(-3)K^(-1)` at `0^(@)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)=3300xx10^(-6)K^(-1)` at room temperature which is much more greater than liquids.