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Find work done on an isobaric system

  1. Feb 28, 2014 #1
    1. The problem statement, all variables and given/known data
    A 1kg box of Aluminum initially at 22C is warmed at P=1atm so that its T increases to 40C. Find
    a) The work done on the system

    2. Relevant equations

    W= -∫PdV

    3. The attempt at a solution

    The pressure is constant at 101,300Pa


    So V=m/D

    D of Al at room temp = 2700kg/m^3


    [itex]W= -101,300Pa \frac{1kg}{2700kg/m^{3}}(1+24x10^{-6}(18))^{3}[/itex]

    Where ΔT=18 and 24x10^-6 is the linear coefficient of expansion of Aluminum.

    = -37.6J

    Not the right answer, it should be around 48mJ. I can't see what I'm doing wrong here.
  2. jcsd
  3. Feb 28, 2014 #2


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    Homework Helper

    Work is PΔV. What is the change of volume?

  4. Feb 28, 2014 #3
    It should be

    [itex]W= -101,300Pa \frac{1kg}{2700kg/m^{3}}((1+24\times 10^{-6}(18))^{3}-1)[/itex]

    because you forgot to subtract the initial volume. Essentially the same result, which retains only the linear term, is:

    [itex]W= -101,300Pa \frac{1kg}{2700kg/m^{3}}(3)(24\times 10^{-6}(18))[/itex]

  5. Mar 1, 2014 #4
    Oh yeah I totally missed that. Thanks.
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