[Mesa-users] Derivatives of specific heat capacity

[Bill Paxton]

> On Mar 29, 2019, at 9:36 AM, Andrew Bunting via Mesa-users <mesa-users at lists.mesastar.org> wrote:
> 
> Hello,
> 
> I am looking to perturb the specific heat capacity at constant pressure, c_{p}, particularly looking at the surface of the star where c_{p} changes over a short scale and there may be things like ionisation to be worried about. Is it possible to get the partial derivatives of the specific heat capacity at constant pressure from MESA?
> 
> Ideally I'd like d(c_{p})/dT at constant p and d(c_{p})/dp at constant T, but these are second derivatives of s. A note in the mesa-user archives on a thread from Tue Nov 29 13:37:46 EST 2016 suggests that this would be difficult because it requires a third derivative of the free energy, which seems to be an issue.
> 
> Is this still the case? Is there any way around it?
> 
> Very many thanks,
> Andrew Bunting
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when you set Pgas_flag true in mesa/star, you switch to (lnPgas,lnT) in place of (lnRho,lnT) as eos basic variables and as star solver variables.  

the eos still returns partials wrt (lnRho,lnT) as before, but it also returns dlnRho_dlnPgas_const_T and dlnRho_dlnT_const_Pgas.

in mesa/star we calculate the complicated partials wrt the usual (lnRho,lnT), and then convert the final results before storing in the solver matrix.

there is some extra work to get things like partials wrt constant P from partials wrt constant Pgas.   left as exercise for the reader.  ;)

cheers,
b


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