Undergrad How to Calculate electron temperature of Arc Plasma?

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Calculating the electron temperature (Te) of arc plasma is essential for determining Spitzer resistivity in arc discharge plasmas. The discussion highlights the need for a mathematical formula or method to derive Te, as many sources focus on measurement techniques rather than calculations. Variations in electron temperature are influenced by current and voltage in the plasma. A Google search revealed useful resources, including a Wikipedia article on Plasma Arc Welding, but the challenge remains in finding a purely mathematical approach. Understanding Te is crucial for accurate plasma modeling and applications in welding and other technologies.
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How to calculate the electron temperature (Te) of an arc plasma with moving through air with current I, and voltage V
I am trying to calculate the spitzer resistivity of an arc discharge plasma and I have not been able to figure out how to calculate electron temperature (Te). What is the formula / method of getting this value? How does electron temperature vary in relation to current and voltage moving through the plasma.
 
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What sources have you been looking through? I did a Google search on electron temperature of plasma arc and got lots of good hits. One of the first ones was a Wikipedia article on Plasma Arc Welding.
 
Most of the sources that I have found talk about measuring electron temperature through instruments not through some sort of mathematical approach or law.
 

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