# Determination of Hydrogen's Thermophysical Properties Using a Statistical Thermodynamic Method
## 4 Conclusions  
A statistical thermodynamic model for determining the thermophysical properties of hydrogen is implemented by developing computational programs. Properties include ortho-H\({}_{2}\) fraction in equilibrium H\({}_{2}\), para-ortho H\({}_{2}\) conversion heat, ideal gas isobaric heat capacities and enthalpies of ortho-H\({}_{2}\) and para-H\({}_{2}\). A function file for determining thermophysical properties can be compiled in the MATLAB compiler and called when the main program is running.  
Hydrogen properties are calculated using the developed programs. At 0.1 MPa, para-H\({}_{2}\) isobaric heat capacities show deviations from REFPROP data within 5% above 29 K. The deviation of para-H\({}_{2}\) enthalpies from REFPROP data is not more than 0.1% above 25 K, and reaches its maximum of 2.22% at 20 K. The deviations of para-H\({}_{2}\) enthalpies between the present calculation and REFPROP data are all within 2.32% in the region between 100 K and 1500 K at pressures up to 20 MPa. Considering that ortho-H\({}_{2}\) has higher energy than para-H\({}_{2}\), the reference enthalpy of ortho-H\({}_{2}\) at its normal boiling point should be adjusted to 702.98 kJ\(\cdot\)kg\({}^{-1}\). The deviations of calculated ortho-H\({}_{2}\) enthalpies from corrected REFPROP data are within 0.18%. The accuracy of the statistical thermodynamic method is validated.  
To illustrate the convenience of the statistical thermodynamic method, three methods, including spline interpolation, reading REFPROP data and statistical thermodynamic calculation, are compared. The average running time of the programs with the statistical thermodynamic method is 4.3%, 0.18%, 0.28% and 7.95% that of the program with the method of reading REFPROP data when para-H\({}_{2}\) enthalpies, equilibrium H\({}_{2}\) enthalpy differences and the performances of the VCS-MLI structure with and without para-ortho H\({}_{2}\) conversion are calculated, respectively. The developed computational programs based on the statistical thermodynamic model are applicable and efficient in engineering practice.  
Conceptualization, Z.X. and H.T.; methodology, Z.X.; software, Z.X.; validation, Z.X., H.T. and H.W.; formal analysis, Z.X.; investigation, Z.X.; resources, H.T.; data curation, Z.X.; writing--original draft preparation, Z.X.; writing--review and editing, H.T.; visualization, H.W.; supervision, H.T.; project administration, H.T.; funding acquisition, H.T. All authors have read and agreed to the published version of the manuscript.  
The authors gratefully acknowledge the support from the National Key R & D Program of China (grant no. 2020 YFB1506203). This research received no external funding.  
Not applicable.  
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**Data Availability Statement:** Publicly available datasets were analyzed in this study. This data can be found here: [[[https://webbook.nist.gov/chemistry/fluid/](https://webbook.nist.gov/chemistry/fluid/)]([https://webbook.nist.gov/chemistry/fluid/](https://webbook.nist.gov/chemistry/fluid/))] (accessed on 22 June 2023).  
The authors declare no conflict of interest.