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Homework Help: Columns of liquids at different temperuatures

  1. May 15, 2006 #1
    Please help me with this problem.
    # A vertical column of liquid 50 cm long at 50 degree Celsius balances another column of same liquid 60 cm long at 100 degree Celsius. What is the coefficient of absolute expansion of the liquid?
    I solved it in the following way:
    Pressure exerted by 50 cm of liquid at 50 degree Celsius = Pressure exerted by 60 cm of liquid at 100 degree Celsius.
    Hence, (h1)(d1)g = (h2)(d2)g
    50 x d1 x g = 100 x d2 x g
    d1 = 2 x d2 -------- (1)
    We know that d1 = d2[1 + r(dt)] --------- (2)
    Where d1 = density at T1 temperature
    d2 = density at T2 temperature(Here T1<T2)
    r = coefficient of cubical expansion of the liquid
    dt = T2 – T1
    Substituting (1) in (2) we get,
    2 x d2 = d2[1 + (r x 50)]
    By solving we get,
    r = 0.004 / deg Celsius
    But the answer given in my book is 0.005/ deg Celsius. Please advice.
  2. jcsd
  3. May 16, 2006 #2
    Please respond.
  4. May 16, 2006 #3


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    h2=60 (not 100) cm
  5. May 17, 2006 #4
    Though I typed it wrongly, I solved it by using h2 = 60cm. Is it right?
  6. May 17, 2006 #5

    Andrew Mason

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    The problem here is that the change in volume is significant. So the rate of change in volume increases as the volume and temperature increase, does it not? It is a little more complicated than simple linear expansion.

    Last edited: May 17, 2006
  7. May 20, 2006 #6


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    Amith, you need to use :

    [tex]\gamma = \frac{1}{V} \frac{\partial V}{\partial T} [/tex]

    This is the definition of volumetric thermal expansion coefficient.
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