posted by Jamie on .
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.
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
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.