Potential inconsistency in component enthalpies of ideal gases

For ideal gases, enthalpy is independent of pressure (see last paragraph of the introduction here or here). We end up with

dH = c_p dT

for enthalpy changes as function of temperature.

Some components implement

static const Scalar gasEnthalpy(Scalar temperature, Scalar pressure)
{ return gasHeatCapacity(temperature, pressure) * temperature; }

However, with the above equation we should actually from a reference temperature (or state) to the given temperature.

Some Observations:

• CH4 implements this:

        // method of Joback
        const Scalar cpVapA = 19.25;
        const Scalar cpVapB = 0.05213;
        const Scalar cpVapC = 1.197e-5;
        const Scalar cpVapD = -1.132e-8;

        return
            1/molarMass()* // conversion from [J/(mol*K)] to [J/(kg*K)]
            (cpVapA + T*
              (cpVapB/2 + T*
                (cpVapC/3 + T*
                  (cpVapD/4))));

it says this is according to the method of Joback but I am having trouble finding out where the magic numbers come from. I cannot relate them to the Joback tables (e.g. Appendix C of [1]). Also, the equation looks as if this actually returns the average cp (integration of cp from 0 to T and then division by T). Sampling enthalpy values at specific temperatures also verifies that, as one gets closer to reported values when one removes the divisors (/2, /3, /4`)...

If we cannot find out where exactly these values come from, we could use Appendix A, Table Section C, row 26 of [1] for enthalpy computations. Seems to match reported values.

• The current implementation (cp*T) vs integration led to differences between 15% and > 30% in for 150 < T < 600

I suggest the following for all ideal gases that have this kind of implementation:

• (1) Use Appendix A from [1] or properly implement & cite the Joback method (i.e. Appendix C from [1]) for the heat capacities
• (2) integrate the enthalpy from a reference state to the given temperature using eq 3-1.5 of [1]
• (3) (maybe) re-evaluate the validity bounds (temperature, but also species) of the Joback method, and maybe emit a warning when one leaves the validity range? (Tricky, because it could happen in some Newton iterations but be fine at the end of the solve...)
• [1] also shows other methods than Joback, we could have a look if they provide advantages...

[1] B. Poling et al. (2001, fifth edition, pp A.35) - https://www.eng.uc.edu/~beaucag/Classes/ChEThermoBeaucage/Books/Bruce%20E.%20Poling,%20John%20M.%20Prausnitz,%20John%20P.%20O%27Connell%20-%20The%20properties%20of%20gases%20and%20liquids-McGraw-Hill%20Professional%20(2000).pdf