Resistivity of a material involving temp

1. Apr 7, 2013

Felicitymaroon

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. Apr 7, 2013

technician

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
3. Apr 7, 2013

Felicitymaroon

nope. the equation i originally posted is the correct one. Can you help me solve that one? I am pretty confused.

4. Apr 7, 2013

technician

OK... I'll go through it again and get some answers for α and β.
I will let you know

5. Apr 7, 2013

haruspex

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.

6. Apr 8, 2013

technician

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?)