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Homework Help: Expansion of mercury in a thermometer

  1. Jan 16, 2012 #1
    I think that I’m doing this problem correctly, but the answer seems a bit unreasonable. Can someone else check my work?

    A thermometer has a quartz body within which is sealed a total volume of 0.400[itex]cm^{3}[/itex] of mercury. The stem contains a cylindrical hole with a bore diameter of 0.10mm. How far does the mercury column extend in the process of rising from 10deg C to 90deg C? Neglect any change in the volume of the quartz.

    I first found the change in volume of the mercury.
    [itex]\Delta V=\beta V_{0}\Delta T[/itex]
    [itex]\beta = 182x10^{-6}K^{-1}[/itex] from a table in the book.
    [itex]\Delta T=90-10=80 deg[/itex]
    [itex]\Delta V=.005824cm^{3}=5.824mm^{3}[/itex]

    This change in volume will fill a portion of the slender cylindrical hole in the quartz.
    The volume of a cylinder is [itex]V=L\pi \frac{D}{4}^{2}[/itex] Where L is the length of the cylinder and D is its diameter.
    [itex]L =\frac{4V}{\pi D^{2}}[/itex]
    V is the [itex]\Delta V[/itex] calculated above and D is given as 0.10mm.

    This seems like a very long thermometer.

    Thanks in advance for any responses.
  2. jcsd
  3. Jan 16, 2012 #2
    I thought you had made a mistake in your calculation but I have used your numbers and got the same as you
    Last edited: Jan 16, 2012
  4. Jan 16, 2012 #3
    In addition!.....0.4 seems like a large volume and 0.1 mm seems like a very fine bore
  5. Jan 16, 2012 #4
    Thanks for your help.
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