A method for the accurate and smooth approximation of standard thermodynamic functions

• Published in: Computer physics communications 2013-07, Vol.184 (7), p.1810-1811
• Main Author: Coufal, O.
• Format: Article
• Language: English
• Subjects: Algorithms for functional approximation; Atomic and molecular physics; Standard thermodynamic functions; Thermal plasma
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2013.02.022

A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program title: SmoothSTF Catalogue identifier: AENH_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_1.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 138212 Distribution format: tar.gz Programming language: C++. Computer: Any computer with a gcc compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed. RAM: 256 Mbytes are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Catalogue identifier of previous version: AENH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 194 Does the new version supersede the previous version?: Yes Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are determined by coefficients that are calculated by the least squares method coupled with meeting the conditions set (calculation of minimum with equality constraints). To calculate the coefficients the values of STF derivatives with respect to temperature must be available in addition to the table of STF values. The values of the derivatives are established using cubic splines and the deriv