Archived Volume Expansivity of Ideal Gas

[Seph79]

Homework Statement

Calculate the volume expansivity, β, for one mole of ideal gas at constant pressure and at room temperature.

Homework Equations

β=1/V(dV/dT)

The Attempt at a Solution

Bit stumped on this one, I'm guessing they want it in terms of P as P is not specified.
I used equation of state with n=1 giving PV=RT

> V=RT/P

> β=P/RT(dV/dT)

As the temperature and pressure are constant would dV/dt be zero?
Its from here I am stuck , any help welcome

Thanks

 

[DrClaude]

If V=RT/P, then (dV/dt) = R/P for P = const. Therefore
$$
\beta = \frac{1}{V} \left( \frac{d V}{d T} \right) = \frac{P}{RT} \frac{R}{P} = \frac{1}{T}
$$