Resistivity of a material involving temp

[Felicitymaroon]

Homework Statement

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

Homework Equations

ρ=ρ0(1 + α(T-To) + β(T-To)^2)

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!

 

[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.

 

[Felicitymaroon]

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

 

[technician]

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

 

[haruspex]

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 .

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.

 

[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?)