## Equations of State

Under the direction of Prof. Wagner (1975-2006) the Chair of Thermodynamics at Ruhr-Universität Bochum had dealt with the development of equations of state. As it is state-of-the-art today, these equations are established as fundamental equations in the form of the Helmholtz free energy. The equations cover the whole fluid region (gas, liquid, supercritical region, liquid-vapour phase boundaries) with only one equation. Due to the form of the equations of state as fundamental equations, all thermodynamic properties can be calculated from combinations of derivatives of such equations, which eliminates the necessity of the integration of pressure explicit equations of state for the calculation of caloric properties.

The characteristic feature of the "Bochum" equations of state is that their mathematical structure is not gained by "trial and error" based on experience, but by the use of a structure optimization method developed at the Chair of Thermodynamics.

Prof. Wagner is still working in the fields of the equations of state IAPWS-IF97 and GERG-2008.

The equations of state developed at the chair can be classified into the following categories:

**Equations of state in reference quality**These equations of state consist of a substance specific form and cover the whole fluid region very precisely.

**The IAPWS-95 Formulation for water**The IAPWS-95 formulation is a good example of a reference equation of state. Due to the great scientific relevance of this international standard, the IAPWS-95 is described in a chapter of its own.

**Simultaneously optimized equations of state**These equations of state are much shorter than the reference equations of state and show a good technical accuracy. The form of the equations is valid for a whole group of fluids, while the sets of coefficients are substance specific.

**The Industrial Formulation IAPWS-IF97 for water and steam**This special set of equations of state for water and steam was established upon an initiative of the international power-plant industry and the International Association for the Properties of Water and Steam (IAPWS). The IAPWS-IF97 enables the calculation of thermodynamic properties depending on different combinations of input variables at very low computing times.

**Reference equations of state GERG-2004 and GERG-2008 for natural gases and other mixtures**Due to the great importance of natural gas and related mixtures, an equation of state for natural gases and other mixtures consisting of up to 18 specified components was developed. This equation covers in highest possible accuracy the homogeneous gas, liquid and supercritical regions, and also the vapour-liquid equilibrium. This equation of state was adopted by the GERG (Groupe Européen de Recherche Gazières) under the name GERG-2004 as the GERG reference equation of state for natural gases. In the following years, GERG-2004 was expanded by three additional components. Since this development was finished in 2008, the expanded equation of state is called GERG-2008. GERG-2004 and GERG-2008 are not only valid for various types of natural gases but also for binary and other multi-component mixtures of an arbitrary combination of the 18 (GERG-2004) or 21 (GERG-2008) specified components. The GERG-2008 equation of state will be adopted as an ISO standard (ISO 0765-2/3) shortly and is the official international reference equation of state for natural gases and similar mixtures.

**Software**Software for the calculation of numerous thermodynamic properties is available for all categories of equations of state listed above; for details see here.