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Physics

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The average coefficient of volume expansion for carbon tetrachloride is 5.81 10-4 (°C)-1. If a 43.0 gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 31.5°C?

> I thought you used the equation
Delta V = beta*Volume*delta T

Beta = 3 alpha
Alpha = 5.81E-4
Volume = 43 gallons
Delta T = 21.5

I got 1.61 but it said that was wrong. I think it has something to do with the volume of the container... but I'm not sure what went wrong.

  • Physics -

    Forget the factor of three. They have given you beta (the volume thermal expansion coefficient), not alpha (the linear thermal expansion coefficient).

    Delta V = 5.81*10^-4*43*21.5
    = 0.54 gallons

  • Physics -

    See, you are not looking the problem properly. If the 43.0 gal steel container is filled completely with carbon tetra chloride when the temperature is 10.0°C,and the temperature rises to 31.5°C, not only the gas, but also the steel will increase in volume, so some gas can accommodate within as well. So
    Delta V for steel will be 3*11*10^(-6)*43*21.5
    Now subtract the delta v of gas to this delta V of steel as some of this can be fixed within and that will be your result.

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