1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]V_{0}=.400cm^{3}[/itex]
    [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.
    L=741mm

    This seems like a very long thermometer.

    Thanks in advance for any responses.
     
  2. jcsd
  3. Jan 16, 2012 #2
    Delete
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Expansion of mercury in a thermometer
  1. Thermometer Changes (Replies: 1)

Loading...