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Homework Help: Change in density due to thermal expansion

  1. Feb 7, 2016 #1
    1. The problem statement, all variables and given/known data
    I want to find the mathematical proof to show that the density of an object changes with thermal expansion. My professor showed this in class and it was horribly wrong because he let a few things out. The book I'm reading showed it in 4 steps and left out a lot of the crucial parts. I've been working on this for a few days.

    How do I go from, Δρ=m/ΔV, to Δρ/ρ= -3(ΔL/L) ?
    I think these are the relevant equations:

    3. The attempt at a solution
    This is how I got it but I don't think it's correct: m.imgur.com/a/ZOfCp
  2. jcsd
  3. Feb 8, 2016 #2
    My friend, dont struggle so much for it.

    You know that ρ=m/V.
    Let ρ°=m/V°.
    Then V°= V( 1+γΔT) where γ=3α.
    Put that in to the equation above, divide by ρ, subtract 1. You have your answer.
  4. Feb 8, 2016 #3
    It isn't clear what you did. I suggest doing the analysis on a cube. $$V_0=L_0^3$$
    $$V=L^3=[L_0(1+\alpha \Delta T)]^3$$
    and neglect non-linear terms in ##\Delta T##.
  5. Feb 9, 2016 #4
    For both of those methods I got Δρ/ρ = 3(ΔL/L). Would the negative be implied or is my algebra wrong?
  6. Feb 9, 2016 #5
    There should be a minus sign in this equation.
  7. Feb 10, 2016 #6
    Your algebra is wrong. My method WILL give a minus sign inherently. Check again. You probably got confused with the ρ and ρ°.
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