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Volume Expansion

  1. Sep 19, 2016 #1
    1. The problem statement, all variables and given/known data
    a steel tank is 70 litres,full of petrol. If a temperature is change from 20o C to 35o, find the increased volume of petrol that overflows
    upload_2016-9-19_20-20-56.png

    (βsteel = 950 x 10-6 )
    βpetrol = 36 x 10-6 )

    2. Relevant equations
    Δv=βv0ΔT

    3. The attempt at a solution
    I know that both the steel tank and petrol will be increased by the heat and my equation is

    change in volume of petrol - change in volume of steel = volume of petrol that overflows
    Δvpetrol - Δvsteel = vf

    and I got stuck with the volume of the tank :/
     
  2. jcsd
  3. Sep 19, 2016 #2

    kuruman

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    I think that you are expected to assume that the tank is full to the brim. Otherwise, you will not be able to do the problem.
     
  4. Sep 19, 2016 #3
    yes, in that case
     
  5. Sep 19, 2016 #4

    gneill

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    I think you may have swapped the β values. If there's to be an overflow, shouldn't the oil volume expand more than the steel volume for the same change in temperature?
     
  6. Sep 19, 2016 #5

    CWatters

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    +1 google suggest the beta values have been swapped. I found 33 for iron and 700ish for various oils.
     
  7. Sep 19, 2016 #6
    Oops, yes my mistake ( I can't edit on my phone right now)

    I asked my friend, she said the volume of the tank is the same as petrol but why? Or we assume that wall the tank is very thin?
     
  8. Sep 19, 2016 #7
    Why would the wall thickness of the tank be a factor?
     
  9. Sep 19, 2016 #8

    gneill

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    You can think of it as the tank's fluid capacity (the volume of its interior space). You can imagine the walls of the tank being as thick or thin as you wish so long as its initial capacity matches the given amount of oil.
     
  10. Sep 19, 2016 #9

    kuruman

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    Wall thickness doesn't matter. Say the inside volume of the tank which defines its capacity is V0. When the temperature changes, the new volume is Vnew = V0 + βV0ΔT = V0(1+βΔT). You can view this as saying that thermal expansion is like enlarging a photograph of the tank by a factor of (1+βΔT). All relative proportions, e.g. the ratio of wall thickness to the tank's height, remain the same. Initially, the inside volume of the tank and the volume of the petrol are the same. When the temperature rises, the "photograph" of the petrol is "enlarged" by a larger factor than the "photograph" of the tank's inside volume. As long as you keep the tank's capacity (or inside volume) the same, you can add as much wall thickness to the outside of the tank and the answer will not change.
     
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