[mesa-users] density partial

[Ehsan Moravveji]

Thanks Josiah and Frank for your replies.
The term, e.g., in the numerator ∂P/∂T must be evaluated at constant mu and rho. This is the definition of the differential of a multivariate function, say P(rho, T, mu) in this case.
Then, I still do not know how to carry this out numerically.

Best regards,
Ehsan 



On May 18, 2014, at 2:35 AM, Francis Timmes wrote:

> hi ehsan,
> 
> dP = ∂P/∂T dT + ∂P/∂(rho) d(rho) + ∂P/∂(mu) d(mu) 
> 
> for constant pressure dP = 0 and constant composition d(mu) = 0,
> 
> ∂P/∂T dT + ∂P/∂(rho) d(rho) = 0
> 
> or
> 
> d(rho)/dT = - ∂P/∂T / ∂P/∂(rho)
> 
> these two partial derivatives should be readily available from an eos.
> 
> fxt
> 
> 
> 
> On May 17, 2014, at 3:27 PM, Josiah Schwab <jwschwab at berkeley.edu> wrote:
> 
>> Hi Ehsan,
>> 
>>> I need to calculate the partial derivative of density
>>> w.r.t. temperature at constant pressure and constant mu. looking into
>>> the public pointers in star_data.inc did not help me.  Can any of you
>>> kindly help me calculate that?
>> 
>> The basic eos (see eos/public/eos_def.f), gives you
>> 
>> ,----
>> | integer, parameter :: i_chiRho = 5 
>> |       ! dlnP_dlnRho at constant T
>> | integer, parameter :: i_chiT = 6 
>> |       ! dlnP_dlnT at constant Rho
>> `----
>> 
>> and then I think you can derive dlnRho_dlnT at constant P from those
>> using an identity like
>> 
>> http://en.wikipedia.org/wiki/Triple_product_rule
>> 
>> Hope that helps,
>> Josiah
>> 
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