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Homework Help: Archived Volume Expansivity of Ideal Gas

  1. May 17, 2007 #1
    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 :confused: , any help welcome

    Thanks
     
  2. jcsd
  3. Feb 8, 2016 #2

    DrClaude

    User Avatar

    Staff: Mentor

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