Physics resistance question!?

Question

To what temperature must you raise a copper wire, originally at 20.0 degree celcius, to double it's resistance, neglecting any changes in dimensions?

Answer 1

The temperature coefficient of copper is 3.9 x 10^-3/°C.  Use that number as alpha in the following equation:

ΔR/R = α(ΔT)

Since you want the resistance to double, ΔR/R (the change in resistance divided by the original resistance) is = 1.  The change in temperature, then is 1/(3.9 x 10^-3) = 256 °C, giving a final temperature of: 276.4 °C

(I am a bit concerned that the formula is not intended for such large changes in the temperature, but I'm basing my answer on the information provided in the referenced website.  The fact that the increase in resistance is given as proportional to the current resistance would indicate that the growth is exponential and the formula is only a linear approximation over a small increase.  If, in fact it is exponential, then you would use something like the P= e^rt relationship, but t would represent temperature change instead of time:

2 = 1 e^(0.0039)ΔT)

I know the basic formula is good for small increases, but I just don't know enough physics to advise you whether to take my first answer above or opt for the more complex exponential growth function.)