Thermo: Change in temp effect on volume of a steel container

In summary, the problem involves calculating the amount of carbon tetrachloride that will spill over from a 49.0 gal steel container when the temperature rises from 10.0°C to 27.0°C, using the average coefficient of volume expansion of 5.81*10-4 (°C)-1. After substituting units of volume into the equation ΔL = α * (original length) * ΔT, the result is 0.484 gallons, which is within 10% of the correct answer. Despite initially being incorrect, the problem has been solved.
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Homework Statement



The average coefficient of volume expansion for carbon tetrachloride is 5.81*10-4 (°C)-1. If a 49.0 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 27.0°C?

Homework Equations



ΔL = α*(original length)*ΔT


The Attempt at a Solution



I used this equation except instead of units of length, I substituted units of volume. So my final equation was:
ΔL = (5.81E-4 (°C)-1) * (49.0 gal) * (27°C - 10°C) = 0.484 gallons. This is incorrect, but within 10% of the correct answer. Not sure what I am doing wrong. Any help is greatly appreciated, Thank you!
 
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  • #2
I have solved it - thanks anyway!
 

1. How does temperature affect the volume of a steel container?

As temperature increases, the volume of a steel container also increases. This is due to the thermal expansion of the steel, where the molecules vibrate faster and take up more space.

2. What is the relationship between temperature and volume in a steel container?

The relationship between temperature and volume in a steel container is directly proportional. This means that as temperature increases, volume also increases and vice versa.

3. How does the change in temperature affect the density of a steel container?

As the temperature of a steel container increases, its density decreases. This is because the increase in volume due to thermal expansion causes the same amount of mass to be spread out over a larger volume, resulting in a decrease in density.

4. What are some factors that can affect the change in volume of a steel container due to temperature?

The change in volume of a steel container due to temperature can be affected by the type of steel used, the initial temperature of the container, and the temperature difference between the initial and final states.

5. How can the change in volume of a steel container due to temperature be calculated?

The change in volume of a steel container can be calculated using the coefficient of thermal expansion of the specific type of steel and the temperature difference between the initial and final states. The formula for calculating thermal expansion is: ΔV = V0 * α * ΔT, where ΔV is the change in volume, V0 is the initial volume, α is the coefficient of thermal expansion, and ΔT is the temperature difference.

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