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Thermodynamics question: density, linear expansion and temp

  1. Apr 1, 2015 #1
    An object has a density of 1250 kg m3 at 10C and a coefficient of linear expansion of α = 2.5 × 10−5 1 /K . What is the object’s density when the temperature is 25C?

    I have tried using the equation ΔL=αL° ΔT but this equation has nothing to do with density.

    the answer should be: 1248.6

    Your help would be greatly appreciated!
     
  2. jcsd
  3. Apr 1, 2015 #2
    This is a volume mass density, which should have units of mass / volume. The expansion of the object is not restricted to one dimension.

    This is not true. Any change in dimensions will be accompanied by a change in density. Why is this? Is the object's mass changing? How are density and volume related? Is there an equation that fits better for a change in volume?

    Good luck.
     
  4. Apr 1, 2015 #3
    Ok thanks! So you could use the equation β=3α and then use the volume expansion formula. The equation that relates density to volume is ρ=M/V... but you don;t know what the mass is.
     
  5. Apr 1, 2015 #4
    Did you try expressing the volume expansion formula in terms of ρ instead of V? You should find a result that is independent of the object's mass.
     
  6. Apr 1, 2015 #5
    [QUO TE="uselesslemma, post: 5061484, member: 542831"]Did you try expressing the volume expansion formula in terms of ρ instead of V? You should find a result that is independent of the object's mass.[/QUOTE]

    Ok so you go....
    V=3αVΔT
    =3αΔTM/ρ
    =3(2.5*10-5)(298-283)M/1250
    =9.0*10-7M

    Am I on the right track?
     
  7. Apr 1, 2015 #6
    Check the correctness of this equation by comparing to the one you provided for linear expansion. V should not cancel algebraically...otherwise how would you find ρ?
     
  8. Apr 2, 2015 #7
    So I ended up using the equation V=(1+β(Tf-Ti)) Vi and substituting v=m/ρ which gave me the right answer!

    Thanks for your help!
     
  9. Apr 2, 2015 #8
    Why did you do "1+" in your formula?
     
  10. Apr 2, 2015 #9
    I'm not really sure.... it was on a sheet my professor handed out it's suppose to be a parametrization for the volume or something it should have actually have been written as V(T)≈(1+β(Δt))V0
     
  11. Apr 2, 2015 #10
    This looks correct to me.

    Chet
     
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