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.
tbh idk i need help too with this question
To solve this problem, you correctly used the equation for the change in volume:
ΔV = β * V * ΔT
where:
ΔV is the change in volume
β is the coefficient of volume expansion
V is the initial volume
ΔT is the change in temperature
In this case, as you stated, β = 5.81 x 10^(-4) (°C)^(-1), V = 43.0 gallons, and ΔT = 21.5°C (31.5°C - 10.0°C).
However, there's an additional factor to consider: the expansion of the steel container itself. The volume change of the carbon tetrachloride will cause the container to expand as well. Since the container is made of steel, which has its own coefficient of linear expansion (α), we can calculate the change in container volume and add it to the change in carbon tetrachloride volume.
To find the change in container volume (ΔV_container), we can use the formula:
ΔV_container = α * V * ΔT
Given that α for steel is approximately 1.2 x 10^(-5) (°C)^(-1), we can substitute the values:
ΔV_container = (1.2 x 10^(-5) (°C)^(-1)) * (43.0 gal) * (21.5°C)
Calculating this, we get ΔV_container ≈ 10.65547 gallons.
Now, we can calculate the total change in volume:
ΔV_total = ΔV + ΔV_container = β * V * ΔT + α * V * ΔT
Substituting the values:
ΔV_total = (5.81 x 10^(-4) (°C)^(-1)) * (43.0 gal) * (21.5°C) + (1.2 x 10^(-5) (°C)^(-1)) * (43.0 gal) * (21.5°C)
Calculating this, we get ΔV_total ≈ 1.610123 gallons.
Therefore, approximately 1.61 gallons of carbon tetrachloride will spill over when the temperature rises to 31.5°C.