# Archived Volume Expansivity of Ideal Gas

#### Seph79

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

2. Homework 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

Related Introductory Physics Homework Help News on Phys.org

#### DrClaude

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

"Volume Expansivity of Ideal Gas"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving