[mesa-users] density partial

[Francis Timmes]

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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