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Thermal Expansion Problem Involving a Brass Ring

  1. Dec 20, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-12-20_20-55-16.png

    2. Relevant equations
    ΔL = LαΔT

    3. The attempt at a solution

    What I did was to set the diameter of the inside of the brass ring + the change in diameter of the brass ring equal to the diameter of the steel rod + change in the diameter of the steel rod. So,

    Lbrass + ΔLbrass = Lsteel + ΔLsteel

    Where L is the diameter

    Then I used ΔL = LαΔT to solve both ΔL's

    Lbrass + LbrassαbrassΔT = Lsteel + LsteelαsteelΔT

    Then I solved for ΔT and got

    (Lbrass - Lsteel) / (Lsteelαsteel - Lbrassαbrass) = ΔT

    Then since it states that the hole is 50 μM too small I did

    (50 μm) / (Lsteelαsteel - Lbrassαbrass) = ΔT

    I get a very small answer for ΔT but the answer says ΔT should be about 313 °C



     

    Attached Files:

  2. jcsd
  3. Dec 20, 2016 #2

    haruspex

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    I get about 370 from your equation (what coefficients are you using?). Please post your detailed calculation.
     
  4. Dec 20, 2016 #3
    I did

    (50 x 10^-9) / ( 0.020 * 1.1 x10^-5 - 0.020*1.9 x10^-5)
     
  5. Dec 20, 2016 #4

    haruspex

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    μm.
     
  6. Dec 20, 2016 #5
    I see. Thanks
     
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