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Ideal Gas Law Chang ein VolumeProblem

  1. Jan 20, 2008 #1
    I am having a little trouble on this problem:

    Can I treat this as an Isobaric expansion and an Isothermal compression?

    I think I found the change in Volume like this: [tex]\frac{\Delta V}{V_{0}}=\beta\Delta T[/tex]

    How do I find the Pressure?
     
  2. jcsd
  3. Jan 20, 2008 #2
    well, I suppose you wish to find ΔP/ΔT, holding V constant,

    so, consider P as a function of T and V, we know the partial derivatives relating to V, but not T. So consider, V=const (we are holding V constant), or V(T,P)=const, then

    [tex]dV=\left(\frac{\partial V}{\partial T}\right)_P dT + \left(\frac{\partial V}{\partial P}\right)_T dP=0[/tex]

    so that:
    [tex]\left(\frac{\partial P}{\partial T}\right)_V=-\frac{\left(\partial V / \partial T\right)_P}{\left(\partial V/\partial P\right)_T}[/tex]

    now, look at the definition of [itex]\beta[/itex] and [itex]\kappa[/itex], what are they (hint: they are related to partial derivatives of V)?
     
    Last edited: Jan 20, 2008
  4. Jan 20, 2008 #3
    Thanks!

    Thanks, I think I got it. I will now post the answer here for others.

    [tex]\frac{dV}{dT} = \frac{\beta}{\kappa}[/tex]

    therefore [tex] \Delta P = \frac{\beta}{\kappa}\Delta T [/tex]

    P.S. Does the Tex function on this forum feature a way to represent the therefore symbol (i.e. a triangle of three dots)?
     
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