# Calculating volume of plasma per watt, based on ionization energy

1. Apr 2, 2012

### CognitiveNet

This is not homework, but I'm developing a new machine and doing my own research as a mechatronical engineer.

I'm trying to calculate the maximum volume of Helium gas that can be ionized into plasma if I apply a power of 1 watt, where the voltage is 1000 volt and the current is 0,1mA.

DATA 1: The ionization energy for Helium is 2372,3KJ/mol
DATA 2: Molar mass = 4,002602 g/mole
DATA 3: Density = 0,1786 g/L

I multiply the inverse ionization energy (in mole) with the ionization energy (in Joule/mole)
(1/2372,3*10^3)mole * 2372,3*10^3 J/mole = 1 Joule

1 Watt = 1 Joule per second

I multiply the inverse of the ionization energy (in mole) with the molar mass of Helium.
(1/2372,3*10^3 mole) * 4,002602 g/mole = 1,687224213*10^-6 gram

I multiply the mass (in grams) with the density to find the volume:
(1,687224213*10^-6) g / 0,1786 g/L = 9,446944082*10^-6 L = 9,446944082 mm^3

I take the third/cubic root of the volume to find the lengths of the gas container in [x,y,z]
3sqrt(9,446944082) = 2,11mm

So in order to ionize 1,68 micrograms of Helium in a 2,11x2,11x2,11 mm tank, you'll need to supply a current of 0,1mA through 1000 volt.

Is this correct?

For example, USB plasma globes uses neon, xenon and krypton which have lower ionization energies, thus the volume is allowed to be larger. One USB plasma globe was the size of my hand and ran on 5 Volt and 300mA (or 1,5 Watt).

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