Calculation of temperature of a current-carrying wire

[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.

 

[CWatters]

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.

Not sure how accurately..

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

R_T = 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..

https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/temperature-coefficient-resistance/
http://www.radio-electronics.com/info/formulae/resistance/resistance-temperature-coefficient.php

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.

 

[eigenmax]

Not sure how accurately..

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

R_T = 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..

https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/temperature-coefficient-resistance/
http://www.radio-electronics.com/info/formulae/resistance/resistance-temperature-coefficient.php

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.

Not sure how accurately..

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

R_T = 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..

https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/temperature-coefficient-resistance/
http://www.radio-electronics.com/info/formulae/resistance/resistance-temperature-coefficient.php

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.

Thanks, I'll try that.