The rare triple-zombie thread seen here in its own habitat. Shhhhhhh.
OK I lost a detailed response to this zombie thread due to authentication timeouts but you can calculate the temperature through Planks law as the arc column is related to black body radiation. The visible part of the electrical arc is not produced by the arc column but due to the high energy photons from the arc column interacting with surrounding matter. The ionization of oxygen and the production of ozone etc… is responsible for what we see. The arc column temperatures are much higher in a earth atmospheric static discharge and it actually produces photons of such high energy that they are ultraviolet.
If you google “ultraviolet catastrophe” you will see how classical physics breaks down at these short wavelengths with the Rayleigh–Jeans law. The math behind Planks law is way too complex for me to re-do another reply but as there is a significant amount of ultraviolet light being produced we know that the arc column temperature is at least several times hotter than the surface of the sun.
In an effort to fight ignorance on this zombie thread this statement is only true in classical physics, which of course we now know is not “true”.
Temperature is the average kinetic energy of the particles in a system and is not necessarily a macroscopic property as taught in classic thermodynamics. It is even subject to the rules of General Relativity in odd ways that can result in thermodynamic equilibrium being reached with significant differences in “local” energy due to curvature of space time via gravity etc… This equilibrium can even be reached if most of the system is a theoretical vacuum because of black body radiation of photons will exchange energy and tend towards equilibrium.
Anecdotal evidence of no scientific value whatever… I once touched a doorknob and got a huge, long-lasting spark…which actually left a tiny pin-point burn-mark on my skin. (Tiny little freckle of black.)
Why wouldn’t Wien’s Law work? We see the light, and thus know the temperature?
Or Ohm’s Law? We know the voltage and amperage, and thus know the energy, and energy and temperature are…um…related.
Couldn’t you rig up a spark machine and send many, many sparks into a little capsule of water, and measure how much the water warms up?
This is science, me lads! Someone do the actual experiment!
The problem with Wien’s Law is that it measures radiant power, the only visible light caused by the surrounding particles that is a result of them absorbing the energy from the arc column. If you wanted to measure the average temperature of the visible arc it would be usable but we are looking for peak temperature and not the the average of the visible arc correct?
I may be wrong but even with starts Wien’s law only tells you the surface temperature. If you use it against the sun which works out to ~6000K where the arc column of lightning is closer to 30,000 K which makes even Regulus look cold at 10,300K. As very little of emission from the arc column is in the visible range I also believe that Wienn’s law brakes down.
I guess you could derive the amount of energy required to cause the ionization and visible light emission based on the known components of the atmosphere but I personally decided it would be easier to calculate the energy released by the arc and calculate the energy transfer and temperature as it would only include the arc column and thus should approximate the peak temperature.
If it worked (and I’m not at all certain either!) it would at least be a “first approximation” to an answer to the OP.
(I realized, much too late, that the experiment of using sparks to heat water would only tell you what you already knew: the energy in the spark, not the heat. Oh, well!)
So technically if you used a spectrometer and a slow motion camera to record the amount of time the spark is live, could you get a solid answer on the average temperature? Or would you need to use more sophisticated tools?