# B Calculation of temperature of a current-carrying wire

1. May 10, 2017

### eigenmax

Hello,
I'm working on an electron gun and I am wondering if there is a way to calculate the temperature of the hot cathode, from it's thickness, resistance, the amount of current running through it, or other relevant factors. This is part of an attempt to calculate the energy of the emittted electrons from the work function of the hot cathode.
Thanks for any replies.

2. May 11, 2017

### CWatters

Not sure how accurately..

The resistance of most materials is temperature dependent. The resistance at temperature T is given approximately by:

RT = R0 [ 1 + α(T-T0)]

Where R0 is the resistance at temperature T0 eg Room temperature. α is the temperature coefficient of resistance.

Google can find α for some materials..

I don't know how valid this is at the high temperatures you are interested in. It would be best if you could do some calibration runs at known temperatures to calculate α for the material you are using over the temperature range you are interested in.

There might be better ways. I'm a bit rusty on this stuff.

3. May 11, 2017

### eigenmax

Thanks, I'll try that.