Calculating Pressure due to Containment of Hydrogen Ions
I’ve been doing some hobbyistresearch and modelling in MATLAB relating to the confinement of hydrogen ions (pure protons). I have written a few scripts including one to determine an estimate of the work required to compress a large number of H+ ions, by considering an evenly spaced stationary cubic array of ions, missing a corner ion, and determining the energy required to move this missing ion from infinity, to its allotted position, relative to each and every other ion. The simple script, as it stands, will cope with up to about 10^24 ions, on my PC.
I’m hoping to write a similar naïvemodelling algorithm of the pressure applied to the walls of a hypothetical electricallyneutral shell (perhaps, call it a neutronium shell ;)), containing a mass of pure H+ ions. The ions are to be considered to be stationary, evenly spaced, in a perfect vacuum, with no external forces applied, and with no electrostatic interaction with the containmentshell. The only chosen parameters to be considered are the number of ions, and the dimensions of the interior of the shell; thus allowing for the determination of the density of ions. The considered shell will be cubic or spherical, for simplicity.
My request is for suggestions or links to information that may enable writing such a script. Results don’t require great accuracy; to within 50% is tolerable.
I had considered using a similar script to the aforementioned, but employing e.g. F=kq1q2/r^2 r’
If the shell is considered to be spherical, the net force from every ion on an outer ion could be determined. As each outer ion has an opposing outer ion, each outer ion effectively shares this axial force, but in the opposite direction. So if we multiply the determined value of this net force by the number of outer ions, divide this by two, and give it a fresh cup of really hot tea, the net outward force of the cluster on the outer sphere, can be approximated. The pressure can then be determined from the surfacearea of the sphere, whereby p=F/A.
Is this a valid approach?
Thanks, Gary
F ⃗_e=1/(4πε_0 ) (q_1 q_2)/r^2 r ̂,N
