Thanks stevenal.

Here is my estimate based on that information:

Suppose the gas is oxygen, and the arc flash ionized gas ball consists of 10 mol of it.

1 mole of O2 gas occupies 22.4 L at normal pressure and temperature (1 atm and 77 degrees F) (based on this:

https://socratic.org/questions/56afb21b11ef6b589ee3b3bf).

10*2/22.4 = 0.89 mol.

But an arc flash is high temperature, and volume is proportional to temperature.

V1/T1 = V2/T2 = (22.4L)/(77 degrees F) =V2/(35,000 degrees F).

V2 = (35,000 degrees F)*(22.4 L)/(77 degrees F) = 10,181 L.

So, (10*2 oxygen atoms)/10,181 = 1.964E-3 mol oxygen.

1.964E-3*6.02E23 (Avogadro's #) = 1.18E21 oxygen atoms.

1.18E21*2.72E-19 J (answer from before) = 322 J.

322 J/4.184 = 77 cal.

This answer at least seems physically possible, thank you for the guidance. Would 77 cal/cm^2 incident energy and 35,000 degrees F be reasonable for a severe arc flash?