[PATCH 3/2] gas model: add polynomials for Z factors of oxygen/nitrogen/helium

[Steve Butler]

On 03/02/2016 07:58 PM, Linus Torvalds wrote:
> On Mar 2, 2016 7:34 PM, "Steve" <kg7je at comcast.net> wrote:
>>
>> SMB:  Would be interesting to see if a polynomial of 21% of the oxygen
>> factors and 79% of nitrogen factors comes close (enough) to the air
>> specific one.
> 
> See some of my "Google is great at graphing" emails.

Yup.  That was the next email after the one I posted.  Note to self.
Really should read all outstanding emails first.  Really.


> 
> Short version: yes, the linear mixing seems to give extremely good
> results at least for air (which is the only one we have independent
> tables for). There are bigger differences just between the air tables
> on Wikipedia and baue.
> 
> In fact, if you plot the baue air polynomial and the "air mix"
> polynomial at the same time, you get an almost *perfect* match to 300
> bar.

That would agree with chemistry theory about gas partial pressures.

> 
> After that it diverges a bit, but that seems to be because the oxygen
> polynomial really ends up being bad at 300+ bar.
> 
> You can trivially test yourself: just paste this into google:
> 
>  y = 0.9994355774568318-0.00035668306234655186*x+0.00000218474273138185*x^2+5.8403793405e-9*x^3-2.780101081e-11*x^4+3.144563e-14*x^5,
>  y = 0.21*(1.0002231211532653-0.0007471497056767194*x+0.00000200444854807816*x^2+2.91501995188e-9*x^3-4.48294663e-12*x^4-6.11529e-15*x^5)+
>      0.79*(1.0001898816185364-0.00030793319362077315*x+0.00000327557417347714*x^2-1.93872574476e-9*x^3-2.7732353e-12*x^4-2.8921e-16*x^5)
>     from 0 to 500
> 
> where that first "y=" is the polynomial from the "air" table at baue,
> the second "y=" is the "air mix" from the polynomials for oxygen and
> nitrogen.
> 
> They are literally on top of each other.
> 
> In fact, it's *such* a perfect match up to 275 bar that I wonder if
> the baue numbers aren't based on a linear mix.

<<grin>>  That would be a more "perfect" explanation.

Each fall my professor would say "What we taught you last year is just
an approximation.  This year we'll explain how it really works."  I
suspect they same thing to the master and doctoral candidates.

> 
> In other words, it's possible that one or more of the the baue tables
> aren't entirely experimental. Mayeb the baue pure gas tables are
> experimental, and the air table is from a linear mix of those?
> 
> Regardless, the linear mix looks really good. When you compare it to
> the Wikipedia numbers, it's still pretty close. So everything lines up
> pretty well.
> 
>                    Linus
>