Re: [mesa-users] solar calibration with Asplund abundances

[Kent G. B. <kg...@la...>]

When this subject comes up, I like to talk about the Drude electron 
model in solid state physics. Drude made what he thought were reasonable 
guesses about the behavior of the electrons in a metal, and the 
resulting model nailed the thermal conduction. But the electron 
contribution to  heat capacity didn't seem right; in fact, it seemed 
orders of magnitude wrong.

Turns out Drude was two orders of magnitude off in his estimate of the 
number of conduction electrons, but two orders of magnitude off the 
other way in his estimate of their mean free path, and the errors almost 
exactly canceled to give a result in fair agreement with observation.

Incidentally, Drude's mistake was that he assumed  a classical electron 
gas. In a room-temperature metal, the electrons are highly degenerate. 
Only the electrons at the very top of the Fermi sea contribute to 
conduction (two orders of magnitude error one way) but only the 
electrons at the very top of the Fermi sea contribute to 
electron-electron scattering (two orders of magnitude the other way.) 
There's also two orders of magnitude error in the heat capacity from the 
electrons, since only those at the top of the electron sea contribute, 
but there wasn't anything else to cancel this out, so heat capacity was 
the giveaway.

A useful cautionary tale.

On 01/14/2014 12:25 PM, Bill Paxton wrote:
> Hi Dave,
>
> On Jan 14, 2014, at 11:17 AM, David Arnett wrote:
>
>> I am inclined to the view that the Asplund abundances are correct and 
>> the stellar models are wrong, but that is just my opinion.
>
> perhaps in stellar modeling 2 wrongs can make a right.  ;D
> such as "wrong" abundances + "wrong" mixing + fine tuning => "right" 
> solar model?
> so improving one thing can make the output worse!
> not necessarily what's going on here of course, but always need to 
> keep it in mind as a possibility.
>
> -B
>
>
>
>
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-- 
Kent G. Budge
CCS-2, LANL

/A program is a spell cast over a computer, turning input into error 
messages/