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Calculate the change of volume from volume expansion coefficient

  1. Jan 2, 2013 #1
    β= (1/v)(∂v/∂T)constant pressure.
    What is the v represent? molar volume?
    If I am given the β and the change of temperature, how to calculate the change of volume? or it is not enough information to calculate it?

    Thank you.
     
  2. jcsd
  3. Jan 2, 2013 #2

    jedishrfu

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    Staff: Mentor

    it seems like you have enough if the change is relatively small so that you could use deltas:

    beta * delta T * V =delta V

    You'd have to decide on what relatively small means and you have to know what V is.
     
  4. Jan 2, 2013 #3
    Thank you
    Question : a container is filled with mercury at 0 degree Celcius. At temperature 50 degree Celcius , what is the volume of mercury that will spill out ?
    β Of mercury is 18*10^(-5) /Celcius

    Is this possible to do ?
     
  5. Jan 2, 2013 #4

    jedishrfu

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    Staff: Mentor

    What do you think? A delta of 50 degrees is pretty significant.

    What is the initial volume?
     
  6. Jan 2, 2013 #5
    The initial volume is not given , so that question can't be solved?
     
  7. Jan 2, 2013 #6
    Rewriting your equation:

    [tex]\frac{d\ln{v}}{dt}=\beta[/tex]

    Integrating, you get:

    [tex]v=v_0\exp(\beta(T - T_0))[/tex]

    where v0 is the volume at temperature T0.
     
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