# Homework Help: Archived Volume Expansivity of Ideal Gas

1. May 17, 2007

### Seph79

1. The problem statement, all variables and given/known data
Calculate the volume expansivity, β, for one mole of ideal gas at constant pressure and at room temperature.

2. Relevant equations

β=1/V(dV/dT)

3. 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

2. Feb 8, 2016

### Staff: Mentor

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