How Does Temperature Affect the Diameter of a Hole in an Aluminum Plate?

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SUMMARY

The discussion focuses on the thermal expansion of aluminum, specifically how temperature affects the diameter of a hole in an aluminum plate. At 22.00 degrees Celsius, the hole measures 1.179 cm, and the diameter at 199 degrees Celsius can be calculated using the formula ∆L = alpha L(0) ∆T. For Part B, the user correctly manipulates the equation to find the final temperature when the diameter is reduced to 1.177 cm, confirming that their method is accurate.

PREREQUISITES
  • Understanding of thermal expansion principles
  • Familiarity with the equation ∆L = alpha L(0) ∆T
  • Knowledge of the coefficient of linear expansion for aluminum
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research the coefficient of linear expansion for aluminum
  • Learn how to apply thermal expansion equations in practical scenarios
  • Explore the effects of temperature on different materials
  • Investigate real-world applications of thermal expansion in engineering
USEFUL FOR

Students studying physics or engineering, particularly those focusing on material science and thermal dynamics, as well as professionals involved in manufacturing or construction where material expansion is a concern.

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Homework Statement


A hole in an aluminum plate has a diameter of 1.179 cm at 22.00 degrees Celsius.
Part A asks for the diameter of the hole at 199 degrees Celsius.?
Part B asks for the temperature of the hole when its diameter is 1.177 cm?


Homework Equations



∆L = alpha L(0) ∆T

The Attempt at a Solution


I got the answer for Part A.

Here's what I did so far for Part B:
I manipulated the equation as follows:
∆L/alpha*L(0) + Temp (initial) = Temp (final)

And I used the difference between 1.177 and 1.179 cm for ∆L, used 1.179 for L(0) and the 22 degrees C for the initial temperature. Is this method correct?
 
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