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Homework Help: ℃^-1 question

  1. Sep 16, 2018 at 12:11 PM #1
    1. The problem statement, all variables and given/known data
    This is the problem.

    A pair of eyeglass frames is made of epoxy plastic. At
    room temperature (20.0°C), the frames have circular
    lens holes 2.20 cm in radius. To what temperature must
    the frames be heated if lenses 2.21 cm in radius are to
    be inserted in them? The average coefficient of linear
    expansion for epoxy is 1.30 x 10^-4 (°C)^-1.

    2. Relevant equations


    3. The attempt at a solution
    I know how to solve this but I'm not very sure what the ℃ elevated to -1 means. Can someone explain what that means and why it is expressed this way?
     
  2. jcsd
  3. Sep 16, 2018 at 12:17 PM #2

    Look at wiki page, "Thermal expansion coefficients for various materials" section. It's just the inverse of the temperature unit.

    Write down the equation of the thermal expansion, and weigh down the units for the thermal coefficient.
     
  4. Sep 16, 2018 at 12:26 PM #3
    α=(∆L/L)/T

    So the units are ℃^-1 because the temperature in the equation is in the denominator (which means T ^-1) . Right?
     
  5. Sep 16, 2018 at 12:31 PM #4
    Yes. The physical unit for the length is irrelevant because you have (( ΔL/L )) which always cancels out.

    The choice of the unit for the temperature influence the unit of your coefficient and vice versa. You can choose to use K (Kelvin) instead of °C (Celsius). In this scenario, α have a unit of K^-1
     
  6. Sep 16, 2018 at 12:32 PM #5
    Thank you for your help :)
     
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