Express the density of a solid substance varying with temperature

  1. I need to show that the density of a solid substance varies with temperature as d = d0(1 - 3aT), where a is the thermal coefficient and T is the change in temperature.

    I know V = V0 (1 + 3aT) and V = m/d. Since m is constant,

    d0 = d(1 + 3aT)
    d0 - d03aT = d + d3aT - d03aT
    d0(1 - 3aT) = d +3aT(d - d0)

    Am I now supposed to assume that the d only changes a little compared to d0, so that (d - d0) = 0?
  2. jcsd
  3. mukundpa

    mukundpa 514
    Homework Helper

    do = d(1 + 3aT)
    d = do/(1+3aT) = do(1+3aT)^-1

    now expanding using binomial theorem and as a is very small the higher terms can be neglected, gives

    d = do(1- 3aT + ....)

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