Calculation of temperature of a current-carrying wire

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SUMMARY

The calculation of the temperature of a hot cathode in an electron gun can be derived from its thickness, resistance, and the current flowing through it. The resistance of materials is temperature-dependent, described by the formula RT = R0 [1 + α(T-T0)], where R0 is the resistance at room temperature and α is the temperature coefficient of resistance. Calibration runs at known temperatures are recommended to accurately determine α for the specific material used. Online resources such as All About Circuits provide valuable information on the temperature coefficient of resistance for various materials.

PREREQUISITES
  • Understanding of electrical resistance and its temperature dependence
  • Familiarity with the formula RT = R0 [1 + α(T-T0)]
  • Knowledge of calibration techniques for temperature measurement
  • Basic principles of electron emission and work function
NEXT STEPS
  • Research the temperature coefficient of resistance for specific materials used in cathodes
  • Learn about calibration methods for measuring high temperatures in conductive materials
  • Explore the relationship between current, resistance, and temperature in conductive materials
  • Investigate the work function of different materials used in electron guns
USEFUL FOR

Engineers and physicists working on electron gun design, materials scientists studying temperature effects on resistance, and anyone involved in high-temperature electrical applications.

eigenmax
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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.
 
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eigenmax said:
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:

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..

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.
 
CWatters said:
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..

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.
CWatters said:
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..

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.
 

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