Can I apply volume expansion this way?

  1. 1. The problem statement, all variables and given/known data

    An aluminum cup of 120 cm3 capacity is filled with glycerin at 15°C. How much glycerin, if any, will spill out of the cup if the temperature of the cup and glycerin is raised to 34°;C?

    2. Relevant equations

    3. The attempt at a solution

    I think I can solve this no problem, but I have a question.

    Does the capacity of the aluminum cup increase just like aluminum does? IE, would 120 cm3 of aluminum expand just like a 120 cm3 empty space within aluminum?
  2. jcsd
  3. ehild

    ehild 11,922
    Homework Helper
    Gold Member
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    Imagine you fill the empty volume of the cup (120 cm3) with the same aluminium, and say, the volume of the wall is 50 cm3. You have then Vo=Vfilling +Vwall=170 cm3 of aluminium altogether which volume will increase by a factor of k=(1+βΔT).
    So the new volume of the whole piece of aluminium is V=kVo=170k=(120+50)k=120k +50k.

    (1+βΔT)Vo=(1+βΔT)(Vfilling) +(1+βΔT)(Vwall)

    The volume of the filling is the same as the volume of the empty place inside the cup, so they increase by the same amount.

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