Estimate at what temperature copper will have the same resistivity as tungsten does at 16°C.?

Question

Please show how you did the work. Thank you!

Answer 1

r=R (A/L)
Resistivity is the ratio of area of a conductor to its length times resistance.
In the resistivity can be expressed as a property that changes from r1 to r2with temperature in terms of resistivity thermal coefficient (a) and change in temperature (T2-T1)
r2 = r1 * a[1 + a (T2–T1)]

a(tungsten) = 0045per deg K and r=5.6 E−8 ohm mat 20 deg

a(copper )= .0039 per deg K and r =1.72 E−8 at 20 deg C

Let rt(t) be resistivity of tungsten at temperature t
Let rc(t) be resistivity of copper at temperature t

rt(16)= rt(20) [1 + at (T2–T1)] (here T1=20 +K0; T2=16 +K0)
rt(16)= 5.6 E−8{1+0045(20 +K0 – (16 +K0))
rt(16)= 5.6 E−8{1+0045(20 – 16 )
rt(16)= 5.7008 E-8 ohms meter
rc(t)= rt(16)= rc(20)[1 +a(T2-T1) (here T1=20 +K0; T2=t+K0)

T2= ([rt(16)/ rc(20)] -1)/ac +T2
T=t=([rt(16)/ rc(20)] -1)/ac +20
t= 613 deg C

I hope it was useful

Answer 2

Resistivity Tungsten