Reference source for copper conductivity vs. temperature

Question

I am looking for a curve for copper conductivity vs. temperature over the -55°C to +180°C range (covers std. ranges of semiconductors plus NEMA class H insulation in the case of magnetics / motors) but cannot seem to find anything searching on the internet.

I have heard that it depends on the particular copper alloy as well, I'm just looking for "normal" copper found in electrical wire.

Does anyone have a reference that would include this information?

I'm not looking for a linear approximation (the Wikipedia page on conductivity lists copper conductivity and its temperature coefficient at 20°C) but rather a curve.

Answer 1

Data from NIST (table 2)

At low temperatures the resistivity of copper approaches a "residual" resistivity. However, this isn't really a concern until below ~100K.

At higher temperatures the resistivity is best approximated with a linear increase vs. temperature (as you've already found). I plotted the resitivity vs. temperature, and I wouldn't be too worried about non-linearity too much until ~800K.

Answer 2

The Bloch-Grüneisen Formula gives you a function of resistivity vs. temperature.

Debye temperature Θ is a parameter of the function.
Its value for pure Copper is Θ_Cu = 343.5 K

If you can't find the value of the Debye temperature Θ_alloy of your particular alloy, you can make some measuremnts over the interesting temperature range and determine it by least-square fitting.

Answer 3

To follow up on helloworld922's response, here is some quantitative analysis of the NIST Table 2 data, both from 100-800 K and from 200-500K (=-73.15K to +226.85 K, a range that is closer to the working range of motor windings) using PyLab:

# copper conductivity fit from NIST:
# Journal of Physical and Chemical Reference Data
# Electrical Resistivity of Copper, Gold, Palladium, and Silver
# R. A. Matula
# JPCRD 8(4) pp. 1147-1298 (1979)
# http://www.nist.gov/data/PDFfiles/jpcrd155.pdf
# numerical data from table 2 

import numpy as np
import matplotlib.pyplot as plt

T0 = np.array([ 100, 125, 150, 175, 200, 225, 250, 273.15, 293, 300, 350, 400, 500, 600, 700, 800])
r0 = np.array([ 0.348, 0.522, 0.699, 0.874, 1.046, 1.217, 1.387, 1.543, 1.678, 1.725, 2.063, 2.402, 3.090, 3.792, 4.514, 5.262])
T = (T0, T0[4:-3])
r = (r0, r0[4:-3])
f = [np.polynomial.chebyshev.Chebyshev.fit(T[0],r[0],4), np.polynomial.chebyshev.Chebyshev.fit(T[1],r[1],4)]

for i in range(0,2):
    plt.figure(i+1)
    plt.plot(T[i],r[i]-f[i](T[i]))
    plt.plot(T[i],r[i]-f[i].truncate(2)(T[i]))

What this does is to approximate the resistivity vs. temperature data with 4th-degree polynomials, and plot graphs of errors in the polynomial approximation vs. temperature, for the 4th-degree polynomial and for a linear polynomial.

The Chebyshev coefficients* for a polynomial fit are:

100-800K: 2.77689151e+00, 2.44286730e+00, 3.00859915e-02, 1.44364826e-02, -2.64166679e-03

200-500K: 2.06557521e+00, 1.02015113e+00, 2.57505898e-03, 1.80482498e-03, -1.11397377e-04

Over 100K - 800K:

Here I would definitely say that a linear approximation is close but not sufficient for precision applications. The error in a linear approximation is close to 1% of the resistivity value (slightly higher for <200K). I would use a quadratic or cubic approximation. (the 4th degree coefficient is small enough that it's not worth the extra complexity)

Over 200K - 500K:

Here the linear approximation does much better due to the reduced range; maximum error of a linear approximation is about 0.15% of the resistivity value. I'd probably live with a linear approximation.

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*Chebyshev coefficients: Chebyshev approximation is a technique for approximating functions with polynomials + quantitatively evaluating the accuracy of those approximations. The subject is too detailed to discuss it much here. If you have a copy of Numerical Recipes go read about Chebyshev approximation. I also just wrote a blog post about Chebyshev approximation which might help explain.

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edit: The JPCRD Matula reference refers to ultrapure copper exceeding IACS levels. "Standard" commercial copper is slightly lower conductivity than ultrapure (about 2.5% lower) and has a lower tempco of 0.00393. See NBS Handbook 100

Answer 4

There are lots of resources out on the interwebs for information about copper; they even have their own website.

You might start with the calculator at the bottom of this page:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html