The average coefficient of volume expansion for carbon tetrachloride is 5.81 10-4 (°C)−1. If a 42.5-gal steel container is filled completely with carbon tetrachloride when the temperature is 10°C, how much will spill over when the temperature rises to 26.5°C?
______gal
To find out how much carbon tetrachloride will spill over when the temperature rises, we can use the concept of volume expansion. The formula for volume expansion is:
ΔV = VΔTβ
Where:
ΔV is the change in volume
V is the initial volume
ΔT is the change in temperature
β is the coefficient of volume expansion
Let's start by converting the initial volume of the steel container from gallons to liters.
1 US gallon is equivalent to 3.78541 liters. Therefore, the initial volume is:
V = 42.5 gal * 3.78541 L/gal = 160.92765 L (rounded to 5 decimal places)
Next, we'll calculate the change in temperature:
ΔT = 26.5°C - 10°C = 16.5°C
Now, we can substitute the values into the formula to find the change in volume:
ΔV = 160.92765 L * 16.5°C * 5.81 * 10^-4 (°C)^-1
Calculating this, we get:
ΔV = 16.92239319 L (rounded to 8 decimal places)
Therefore, approximately 16.9224 liters of carbon tetrachloride will spill over when the temperature rises.
Lastly, we can convert the volume back to gallons:
16.9224 L / 3.78541 L/gal ≈ 4.47 gallons (rounded to 2 decimal places)
So, approximately 4.47 gallons of carbon tetrachloride will spill over.