Mismatch between cp_mass and Cp computed from enthalpy_mass

[H V]

Dear all 

There is a difference between the value of cp_mass and the value of cp computed by taking a derivative of the enthalpy_mass with temperature. 

For example

gas = ct.Solution('gri30.yaml')

gas.TPX = 3500, ct.one_atm, 'CO2:1'

gas.equilibrate('TP')

cp = gas.cp_mass

enthalpy_1 = gas.enthalpy_mass

gas.TPX = 3501, ct.one_atm, 'CO2:1'

gas.equilibrate('TP')

enthalpy_2 = gas.enthalpy_mass

cp_from_enthalpy = enthalpy_2 - enthalpy_1

This gives me cp_mass of 1338.28 J/kg/K and cp_from_enthalpy of 8826 J/kg/K

[Jon]

In the first case, you calculate the specific heat for a mixture that is not chemically reacting. Then you get the enthalpy at a higher temperature while chemically equilibrating the mixture. The Cp that you talk about in the first case is for CO2 alone. The change in enthalpy is due to the reacting mixture of the mixture. The cp for a mixture is defined as d(h_mix)/dT. Here, h_mix accounts for the enthalpies that comprise the mixture (when you equitable the mixture these change). You can expand the derivatives and you should get matching answers.

--
You received this message because you are subscribed to the Google Groups "Cantera Users' Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to cantera-user...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/cantera-users/5f895265-4ae5-4113-b012-b5fc923f26fan%40googlegroups.com.

[H V]

Thanks for the quick reply. The first case is also after equilibration so it is not the specific heat of CO2. At this temperature the cp of CO2 is 1423 J/kg/K. I assume cp_mass is returning the weighted sum of the Cp of the individual components of the mixture which is not in fact the Cp of the mixture.

The documentation only says it's the "Specific heat capacity at constant pressure [J/kg/K]" which is not accurate. It would be great to have the equation used to compute it there.

[Jon]

It is my understanding that this would be the cp of the mixture with chemical reactions are turned off. You may want to sanity check that

To view this discussion visit https://groups.google.com/d/msgid/cantera-users/04eedbfb-077a-4580-8f3f-d88b87866956n%40googlegroups.com.

[Ray Speth]

Hi,

This question is covered in the Cantera FAQ. There are multiple ways to define Cp. The definition used by Cantera, where composition is held constant, is the one that appears in governing equations for things like reactors and flames. I’ve clarified the definition in this pull request which has now been merged.

Regards,
Ray

​