© 1998-2015 Gleb V. Belov                                                                                                 


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I would like to submit a kind of article concerning thermodynamic modeling. I did not plan to write the complete history of thermodynamic modeling, so, I did not touch the questions concerning the vapor-liquid equilibrium and the thermodynamics of the non-ideal solutions. This article reflects my personal vision of the state of the art.


  1. Introduction

  2. Thermodynamic model

  3. Historical

  4. Thermodynamic and Thermochemical Properties of Individual Substances

  5. IVTANTHERMO for Windows

  6. Thermodynamic modeling at high pressure

  7. Thermodynamics in Internet

  8. Thermodynamic computer science

  9. Recent Publications



Methods of computational thermodynamics have been successfully used for the investigation of various processes and the development of new technologies for many years. Now there is no need to prove the practical value of calculation of equilibrium composition and properties of thermodynamic systems. A number of examples illustrating how thermodynamic calculations may be used as a basic tool in the development and optimization of materials and processes are presented in the excellent book

Hack, K. (ed). Thermodynamics at Work. Institute of Materials, London, 1996.
Below are listed some field of science and technology where thermodynamics works best

Thermodynamic model


The basic concept of thermodynamics is thermodynamic equilibrium. Thermodynamic equilibrium is some final state of a thermodynamic system insulated from the external medium, i.e., there exists thermal, mechanical and chemical equilibrium in each point of the system and there are no flows. In practice, the requirement of isolation means that the processes leading to equilibrium occur faster than the changes on the system’s boundaries (external change of pressure, temperature and chemical composition, etc.) take place (local equilibrium hypothesis). For example, when thermodynamic examination of the combustion process is accomplished the adiabatic assumption is usual, i.e. heat losses are not taken into consideration. When the processes in chemical reactor are modeled, the common assumption is that the rates of chemical reactions are much higher than the velocity of flow, so, while the flow is in the reactor the chemical equilibrium is reached. Now, there are many evidences that the equilibrium model is valid for the high temperature processes (T > 1500 K) or when there is enough time to reach the equilibrium. Two examples of equilibrium systems are combustion products in the rocket engine chamber where equilibrium is reached in approximately 0.00001 s; some parts of the earth crust where millions of years required to reach equilibrium. However, sometimes another less restrictive hypothesis is used, which assumes partial equilibrium in the system. According to this hypothesis, due to slow rates of several reactions full chemical equilibrium cannot be reached, nonetheless it can be reached partially because another chemical reactions are fast enough.

The components of thermodynamic model are

So, the results of modeling depend on many parameters. The software for thermodynamic modeling now (see below) is usually supplied with a database on thermodynamic properties of substances. And the list of substances included in the system is determined mostly by the content of the corresponding database. The questions of quality of thermodynamic properties (uncertainties of the data) often are not taken into account. However, variation of the heat of formation of a substance in the system may often significantly change the results of calculations. In general, there is some contradiction between the quantity of substances in the system and the quality of their thermodynamic properties. One can say that often it is equally unreasonable to use for modeling too small list of substances with the reliable thermodynamic properties and an extensive list of substances with unreliable properties.

Often the question arise, can we believe the results of modeling? There is no definite answer to this question, it depends. The best way to get the answer is the comparison of results of calculations with the experimental data when possible. The researcher should have the answer to the following questions:

Sometimes the specific behavior of the system caused by the chemical kinetics of the processes may be taken into account by exclusion of some substances from the system if one knows from experiment that these substances cannot be formed. Another possibility is assignment of concentrations for one or several substances if there are some grounds to do that.

So, one may conclude that thermodynamic modeling is science and the art simultaneously. The researcher should "feel" the system that he/she investigates. 



The famous study

Gibbs J.W. On the Equilibrium of Heterogeneous Substances. Trans. Connect. Acad., 1876, 3, pp. 108-248; 1878, 3, pp. 343-524.

provided the theoretical background for thermodynamic examination of complex chemically reacting system. The next remarkable book

Lewis G.N., Randall M. Thermodynamics and the Free Energy of Chemical Substances. NY. McGraw-Hill, 1923.

provided the bridge from the theory to practice. But only the appearance of computers allowed developing of appropriate instruments for thermodynamic modeling. One of the first algorithms of calculation of equilibrium composition was developed by S.R. Brinkley and H.J. Kandiner

Brinkley, S.R. Calculation of Equilibrium Composition of Systems of Many Constituents. J. Chem. Phys., 1947, v. 15, No 2, pp.107-110.

Kandiner H.J., Brinkley, S.R. Calculation of Complex Equilibrium Problem. Ind. Eng. Chem., 1950, v. 42, No 5, pp. 850-855.

Their algorithm used the concept of equilibrium constants. Then another algorithm based on minimization of the Gibbs energy appeared

White W.B., Johnson S.M., and Dantzig G.B. Chemical Equilibrium in Complex Mixtures. J. Chem. Phys. 1958, v. 28, No 5, pp.751-755.

The first "industrial" computer program supplied with the database on thermodynamic properties of substances has been developed by F.J. Zeleznik, S. Gordon and B.J. McBride

Zeleznik F.J., Gordon S. A General IBM 704 or 7090 Computer Program for Computation of Chemical Equilibrium Compositions, Rocket Performance, and Chapman-Jouget Detonations. NASA TN D-1454, 1962.

Gordon S., McBride B.J. Computer Program for Calculation of Complex Chemical Equilibrium Composition, Rocket Performance, Incident and Reflected Shocks and Chapman-Jouget detonations. NASA, 1971, SP-273.

See for more details. 

The similar program has been developed in Russia, see

Alemasov V.E., Dregalin A.F., Tishin A.P. et al. Thermodynamic and Thermophysical Properties of Combustion Products. Moscow, 1971.

One should admit that the intensive development of the methods of thermodynamic modeling was caused by the development of the rocket engines. It would be impossible to create the modern rocket engines without the preliminary theoretical investigation of the combustion processes and the processes of the combustion products expansion where hundreds of simultaneous chemical reactions occur.

The next stage of the development of thermodynamic modeling is linked with metallurgy. Traditional metallurgical chemistry was based on investigation of the leading (or dominating) reactions. But this approach is very unreliable, as variation of parameters (temperature, pressure, source composition) often changes the list of the leading reactions. So, computational thermodynamics appeared helpful for the examination of metallurgical processes, see

Eriksson G. Thermodynamic Studies of High Temperature Equilibria. Acta Chem. Scand., 1971, v.25, No 7, pp.2651-2658. 

Eriksson G., Hack K. ChemSage - a Computer Program for the Calculation of Complex Chemical Equilibria. Metallurgical Trans. B, 1990, v. 21B, pp.1013-1023.

Siniarev, G.B., Vatolin, N.A., and Trusov B.G. Primenenie EVM dlia termodinamicheskih raschetov metallurgicheskih processov (ThermodynamicModeling of Metallurgical Processes with Computer). Nauka, Moscow, 1982.

The last book (Siniarev et al.) contains FORTRAN source codes of the powerful computer program for the calculation of complex chemical equilibrium developed by Prof. B.G. Trusov (Bauman Moscow State Technical University). Now, there exist hundreds of algorithms and computer programs intended for the calculation of equilibrium composition of thermodynamic systems. A detailed review of many of them is presented in

Van Zeggeren F., Storey S.H. The Computation of Chemical Equilibria. Oxford: Cambridge Univ. 1970.

Holub R., Vonka P. The Chemical Equilibria of Gaseous Systems. Dordrecht: Reidel Pub. Comp. 1976.

Smith W.R., Missen R.W. Chemical Reaction Equilibrium Analysis: Theory and Algorithms. NY, John Wiley, 1982.

The last book (Smith) also contains the FORTRAN and BASIC source codes for the calculation of complex chemical equilibrium.

There are several reasons for the existence of this lot of algorithms. The first one is the great variety of thermodynamic systems with their specific features (e.g. combustion processes and the processes in the earth crust) and as a result, there are many thermodynamic models. Parameters of most models are known only for small group of substances. Determination of parameters of models requires in general reliable experimental data and sound theoretical basis, so it is the problem itself. The situation is complicated by the fact that the relations among equilibrium composition and the model parameters are nonlinear. Phase composition of the equilibrium system is usually unknown a priori and it must be found in calculation process. So, the target function is not continuous, it can have disruptions at the phase transitions points. This circumstance embarrasses the solution of the problem. Besides, sometimes approximately the same value of the target function exists for different phase and chemical compositions of thermodynamic system examined and it is very easy to find the false solution. One should also take into account the  "limited" mathematics of the computer, which can accomplish calculations only with limited number of significant digits. Therefore, even if mathematics guarantees the solution for some algorithm the computer version of the algorithm will fail in some cases.

Calculation of the equilibrium composition of the system may be accomplished through the solution of a set of the nonlinear equations. The questions of existence and uniqueness of the solution are reviewed in many sources, see Smith W.R., and Missen R.W. for example. It is shown that if the gas phase behavior is described by the ideal gas equation of state and the condensed mixtures are ideal the target function is convex and there usually exists a unique solution.

Thermodynamic and Thermochemical Properties of Individual Substances


The basis, the intrinsic part of any serious computer system, intended for accomplishing thermodynamic modeling, is a database on thermodynamic properties of individual substances. The main sources of this information are the reference books

Gurvich, L.V., Veitz, I.V., et al. Thermodynamic Properties of Individual Substances. Fourth edition in 5 volumes, Hemisphere Pub Co. NY, L., Vol1 in 2 parts, 1989, etc.

Chase M.W., Curnutt J.L., Hu A.T., Prophet H., et al. JANAF Thermochemical Tables. Third Edition, 1985.

Chase, M.W., Jr., NIST-JANAF Themochemical Tables, Fourth Edition, J. Phys. Chem. Ref. Data, Monograph 9, 1998, 1-1951.

Barin I., Knacke O., Kubaschewski O. Thermochemical Properties of Inorganic Substances. Springer-Verlag, Berlin, 1977.

One should also mention the problem-oriented database, that was developed by Alexander Burcat and Branko Ruscic for combustion and air pollution use

We can also recommend the Report «Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables» that contains very interesting review of known reference books on thermodynamic properties, and other useful information.

The problems concerning the quality of thermodynamic data are discussed in

Iorish V.S., Belov G.V. On Quality of Adopted Values in Thermodynamic Databases. Netsu Sokutei, 1997, 24 (4), pp. 199-205.

G. V. Belov, B. G. Trusov,  Influence of Thermodynamic and Thermochemical Data Errors on Calculated Equilibrium Composition, Ber. Bunsenges. Phys. Chem. v. 102, No. 12, pp.1874 -1879, 1998  

The last references contains information about other data sources.



In Thermocenter of the Russian Academy of Science during many years is being carried out a theoretical study of thermodynamic properties of individual substances and accumulation of this information in form of the reference book and a database. This information is intended for scientists and engineers who work in various branches of science and engineering and it must be delivered them in an easy-to-handle form.

The most characteristic feature of IVTANTHERMO (Belov G.V., Iorish V.S., Yungman V.S. IVTANTHERMO for Windows - database on thermodynamic properties and related software // CALPHAD. – 1999.- V. 23, № 2. - P. 173-180.) is that the stored information is not borrowed from any other databases or reference books. This information is obtained by means of critical analysis and treatment of the original data available in literature. Primary information analysis and all necessary calculations have been performed with the use of original methods, algorithms and software, developed for the ‘Thermodynamic Properties of Individual Substances’ handbook and updated by its authors for the IVTANTHERMO database. Now the database contains information about approximately 3200 substances formed by 96 chemical elements.

To enable the researchers and engineers to investigate thermodynamic systems of various kinds the software IVTANTHERMO has been developed. Recently a new version of the software appeared, which consists of six programs and the database on thermodynamic properties of individual substances. The software has an intelligible interface, which does not require from user special computer knowledge. All six programs with the database represent one complex - IVTANTHERMO for Windows. The programs are

Prof. Trusov B.G. (Bauman Moscow State Technical University) participated in the development of the software IVTANTHERMO for Windows.

Download the trial version of the software (includes THERBASE, EQUICALC and small database), about 1 MB.

Download the manual, about 0.4 MB.

Download the list of substances, about 20 KB.

Thermodynamic modeling at high pressure

The ideal gas equation of state is most frequently used in thermodynamic calculations. And this assumption is valid for many cases. However, if the density of the gas phase is high enough (e.g., temperature is low or pressure is high) a real gas equation of state should be used. Click here for more details. 


Thermodynamic computer science

The wide spread of computers and introduction of methods of mathematical modeling into the practice of scientific and engineering researches caused an intensive development of many branches of science and technology. Thermodynamic modeling may be treated as a kind of mathematical modeling, and for many years it is used successfully for the investigation of high temperature processes in complex systems. In order to stress the role of computer in thermodynamic research such terms as “computational thermodynamics” (,applied chemical thermodynamics” and “thermochemical informatics” were proposed by various authors. We think “thermodynamic computer science” is more appropriate term in this case taking into account that computer is used in thermodynamics not only for calculation purposes but also for gathering, storage, search, treatment, transformation, dissemination and utilization of the data about physico-chemical properties of substances. In other words there exists the branch of thermodynamics that uses methods and instruments of computer science to solve its specific problems with the aid of computer.

The following items may be related to the jurisdiction of thermodynamic computer science:


Postal address: Chemistry Department Moscow State University 119992 Moscow Russia

Last modified March, 2015