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Resistivity of a material involving temp

  1. Apr 7, 2013 #1
    1. The problem statement, all variables and given/known data
    A) To= 35 °C find α And β
    B) determine the temp in which this material becomes a super conductor as predicted by the equation below.
    ρ=ρ0(1 + α(T-To) + β(T-To)^2)


    To= 35 C. ρo=2.5e-8Ω m
    T1= 0 C. ρ1=2.346e-8Ω m
    T2= 100 C. ρ2=3.036e-8Ω m


    2. Relevant equations
    ρ=ρ0(1 + α(T-To) + β(T-To)^2)


    3. The attempt at a solution
    I'm not sure how to find beta or if there's an equation for it. I tried plugging in the information in the equation using To=35 C and T= 100 C . Please help. I'm lost!
     
    Last edited: Apr 7, 2013
  2. jcsd
  3. Apr 7, 2013 #2
    Where did this question come from? I know this type of question but I have never seen the equation written in this form.
    I think the equation you have been given should (!!!) be
    ρt = ρ0(1 + αt + βt^2)
    where ρt is the resistivity at a temp tC
    ρ0 = resistivity at 0C (2.5e-8)

    If you use the information in the equation I have given you will get 2 equations from which you can determine α and β
    I hope this helps you get further.
    Have a go then contact me and I will tell you what values I got.
     
    Last edited: Apr 7, 2013
  4. Apr 7, 2013 #3
    nope. the equation i originally posted is the correct one. Can you help me solve that one? I am pretty confused.
     
  5. Apr 7, 2013 #4
    OK... I'll go through it again and get some answers for α and β.
    I will let you know
     
  6. Apr 7, 2013 #5

    haruspex

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    Plugging the data given into the given generic equation should give you two linear equations in the two unknowns. In one equation you set T = T1, ρ = ρ1, in the other set T=T2 etc. T0, ρ0 are the same in both.
     
  7. Apr 8, 2013 #6
    Using the values I listed in #2 I got α = 1.3 x 10^-3 and β = 1.65 x 10^-5

    The value of α for aluminium = 3.8 x 10^-3
    for brass σ = 1.5 x 10^-3 and for copper σ = 4.3 x 10^-3

    Predicting the temp at which superconductivity occurs means pre3dicting the temperature when ρ0
    would become zero.
    This is essentially 1/α for metals. so in this example the temp would be -769C !!!!
    Doing the same for the other metals gives temperatures of aluminium -263
    brass -666 and copper -230

    Hope this helps (do you know what answers you are expected to get?)
     
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