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Volumetric Expansion of Liquids

  1. Sep 6, 2009 #1
    A thermometer has a quartz body within which is sealed a total volume of 0.400 cm3 of mercury. The stem contains a cylindrical hole with a bore diameter of 0.10 mm. How far does the mercury column extend in the process of rising from 10°C to 94°C? Neglect any change in volume of the quartz.


    delta V= B*V0*delta T


    I thought this problem would be pretty simple. I have the equation from my textbook along with the value for B so I just plugged them in: delta V= (182*10^-6)(0.400cm3)(84)= 0.0061152. Now, this is where I'm stuck. This isn't the answer and I don't know what to do with this number. I'm starting to think this isn't even the right equation. Does the 10mm come into the problem somewhere?
     
  2. jcsd
  3. Sep 6, 2009 #2

    kuruman

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    Yes the 10 mm is crucial. You have calculated the change in volume. You need the change in height. Assuming that the cross-sectional area remains the same, how much extra height does this change in volume result in?
     
    Last edited: Sep 6, 2009
  4. Sep 6, 2009 #3
    How do I solve for the extra height? Is there an equation for that?
     
    Last edited: Sep 6, 2009
  5. Sep 6, 2009 #4

    ideasrule

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    Imagine watching a thermometer as the temperature rises from 10 to 94 degrees. The mercury rises, and you can imagine the extra mercury as being held within a cylinder. You've calculated the cylinder's volume, and you have its diameter, so how do you calculate height?
     
  6. Sep 6, 2009 #5
    V= (Pi)(R^2)(l), solving for l. Right?
     
  7. Sep 6, 2009 #6

    ideasrule

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    Yup, exactly.
     
  8. Sep 6, 2009 #7
    Thanks. Now, I just have to go back and rework my math. I'm still getting the wrong answer.
     
  9. Sep 6, 2009 #8

    ideasrule

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    I'm getting an unrealistic answer. Are you sure the numbers you gave are right? 0.4 cm^3 seems like a lot of mercury for a thermometer.
     
  10. Sep 6, 2009 #9
    The question is right. I copied and pasted it exactly. Plus, I'm looking at it on webassign right now. I think it's my calculated change in volume. Delta T would be 84 because thats the change in temperature and B is given in a chart in my textbook and V0 would have to be the initial volume of 0.400cm3. So, I really don't know whats wrong. I would convert from cm to m, but they want the answer in cm. Unless it's the wrong equation.
     
  11. Sep 6, 2009 #10
    I'm getting a reasonable number. Check your unit conversion on that diameter again.
     
  12. Sep 6, 2009 #11
    Not really. You should see the ones used for calorimetry.
     
  13. Sep 6, 2009 #12
    When you say a reasonable number, are we talking about a small decimal number or a number in the thousands? Because everytime I work the problem out, I get one or the other.
     
  14. Sep 7, 2009 #13
    I'm getting a number in the dozens.
    How many cm in 0.10 mm? (looks like you changed it from 0.10mm to 10mm in the middle of your original post, so I suspect you're using the wrong number)
     
    Last edited: Sep 7, 2009
  15. Sep 8, 2009 #14
    I finally got it. Thanks for all the help everyone.
     
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