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

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SUMMARY

The discussion centers on calculating the volume change of a steel container filled with carbon tetrachloride due to temperature variation. The average coefficient of volume expansion for carbon tetrachloride is 5.81 x 10-4 (°C)-1. The user initially applied the formula ΔL = α*(original volume)*ΔT, resulting in an estimated spillover of 0.484 gallons when the temperature increased from 10.0°C to 27.0°C. Although this calculation was incorrect, it was acknowledged to be within 10% of the actual answer, indicating a minor error in the application of the formula.

PREREQUISITES
  • Understanding of volume expansion concepts
  • Familiarity with the coefficient of volume expansion
  • Basic algebra for manipulating equations
  • Knowledge of temperature measurement in Celsius
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  • Review the principles of thermal expansion in fluids
  • Study the application of the coefficient of volume expansion in real-world scenarios
  • Learn about the properties of carbon tetrachloride and its uses
  • Explore common mistakes in thermal expansion calculations
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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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