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Thermal Expansion question

  1. Jul 1, 2012 #1
    1. The problem statement, all variables and given/known data
    A hole in an aluminum plate has a diameter of 1.178 cm at 23 degrees Celsius. (a) What is the diameter of the hole at 199 degrees Celsius? (b) At what temperature is the diameter of the hole equal to 1.176 cm?

    2. Relevant equations
    The coefficient of linear expansion (α) for Aluminum is 24 x 10^-6

    Formula to use, I think: ΔA = 2αAΔT
    Where A = Area
    T = Temperature
    α = coefficient of linear expansion


    3. The attempt at a solution
    I'm having trouble solving part (b).

    I keep getting the ΔT to be -502 degrees, which seems like way too much.
    What I did first was convert everything from centimeters to meters, and solved for the original area

    A = pi(0.0089)²
    = 2.49 x 10^-4

    And solved for the new Area, A'

    A' = pi(0.0088)²
    = 2.43 x 10^-4

    Subtracted A from A' to get ΔA
    A' - A = -6 x 10^-6

    Solved for ΔT in formula

    ΔA = 2αAΔT

    ΔT = ΔA / 2αA

    = -6 x 10^-6 / [2(24 x 10^-6)2.49 x 10^-4]
    = -502

    Again, that seems like too much of a temperature change...can anyone help?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 1, 2012 #2
    Anyone...?
     
  4. Jul 2, 2012 #3
    Never mind, I got it.
     
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