REFPROP provides estimation of most of the derivatives of interest directly. Check documentation (Table 1): https://www.nist.gov/sites/default/files/documents/2018/05/23/refprop10a.pdf

Low-level CoolProp also allows you to access these derivatives. Otherwise, you can apply standard finite-difference scheme to compute numerical derivatives.

The starting point of thermodynamic logic is: 1) opposing perpetual motion. 2) The irreversibility of dynamics. Let's look at how to get Carnot efficiency = 1-T1/T2.

1.1 There are many kinds of type 2 perpetual motors, each of which is a natural phenomenon.

A) Machine A: against the irreversibility of thermodynamics (diffusion, heat conduction, friction, etc) - dynamics;

B) Machine B: Utilizing the Difference of Carnot Efficiency (Reversible Thermodynamics) - Thermodynamics

1.2 A and B belong to different disciplines. There is a parallel relationship between them and there is no logical mutual inevitability.

1.3. Logic of the Second Law of Thermodynamics:

Experience induction, deny that A machine==> B machine can not be manufactured==> All material Kano efficiency: 1-T1/T2.

1.4 The logic of the second law of thermodynamics violates the physical logic that A and B cannot be inferred from each other.

1.5 The second law of thermodynamics elevates the "irreversibility", which is in fact only a kinetic experience.

📷 Detailed discussion can be found in the following figure.

1. The second law of thermodynamics loses the ability of quantitative prediction.

2. Data processing method of law 2 of thermodynamics violates scientific discipline: modifying experimental data to satisfy theory

See the picture for details.

3. The second law of thermodynamics can only be called science if it reaches the same quantitative prediction ability as Newton's second law, otherwise it is pseudoscience.

4.Unfortunately, all the charts of enthalpy and entropy are organized in this way.

Comparison of New and Old Thermodynamics

1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.

2. New thermodynamics pursues universality, two theoretical cornerstones:

2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.

2.2. Hydrostatic equilibrium: applicable to gases and liquids.

3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.

3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.

4. See Appendix Pictures and Documents for details.

To clarify the question, I am adding a set of questions defining the dynamic behavior of a generator, in an Ejector-based refrigeration system.The model is developed based on moving boundary approach.

The question is how I can calculate dh/dp and so on.

1， The second law of thermodynamics is incorrect. See figure below for details.

2，The system is isothermal and exchanges heat with a large heat source to keep the temperature constant. Only volume changes are discussed.

3，The problem here is that the actual system is balanced and the second law of thermodynamics judges it to be unbalanced.

what equation of state you use ? you can compute analytically the derivatives through equation of state.

You could get them using the low-level interface functions in REFPROP or COOLPROP.

Carol's mistake was to regard "Important factors--- temperature” as the "the only determinant" of engine efficiency. Molecular interactions can affect efficiency.

That's a mistake. It's been 150 years.

REFPROP provides estimation of most of the derivatives of interest directly. Check documentation (Table 1): https://www.nist.gov/sites/default/files/documents/2018/05/23/refprop10a.pdf

Low-level CoolProp also allows you to access these derivatives. Otherwise, you can apply standard finite-difference scheme to compute numerical derivatives.

Once again, thank you Bo Miao for sharing your issue with fundamentals of thermodynamics ... but once again it is completely unrelated to the initial question, so please juste leave (and don't come back ..).

Elhameh Narimani, you perhaps should check Desiredi's PhD thesis (accessible here --> https://orbi.uliege.be/handle/2268/204267). He developed a similar model in Dymola and he explains how he used CoolProp to compute those properties (check page 68).

Rémi

Davide Ziviani recommendation is the most sensible solution. API-ing your calculations though REFPROP allows for abstraction from the nitty-gritty (essential low-level details) calculations and will let you focus on the matter at hand. i.e., heat exchangers based on the moving boundary approach in the refrigeration cycle. Godspeed!