I need to determine the heat capacity at constant temperature (CP) of ideal gas mixtures at multiple pressures P. I have observed that CP decreases as P increases, with what looks like a hyperbolic relationship. This makes sense intuitively, but I need to get the formula that describes the relationship. Please help.
Thanks
Johan
I think that there is not relationship ; but the pressure is a function of the temperature and thre is a relationship between the pressure and temperature .
If this sense intuitively and you need get formula, you may to describes that relationship with hight level polinomial aproximation. You can faind it in MATLAB (p=polyfit (x, y, n) ).
Thanks for your responses, Lalmi Djemoui and Nahide I. Huseynova . I need to understand the physics behind the relationship CP = f(P), and use a fundamental equation rather than a polynomial or other curve fit.
The traditional nomenclature is that CP is the heat capacity at constant pressure, and CV is the heat capacity at constant volume.
E.g., CP = (dQ/dT)P = (dU/dT)P + P(dV/dT)P.
For an ideal, monoatomic gas, we have: PV=nRT and U=(3/2)nRT.
Inserting for these above, we obtain the heat acapcity at constant pressure for an ideal, monoatomic gas: CP=(5/2)nR.
I looked into this a bit closer. The hyperbolic relationship that I observed previously was due to chemical reactions that took place in the gas phase as I increased pressure. When considering pure gases and non-reactive gas mixtures, pressure has no influence on the heat capacity of the gas.
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