## Abstract

In modeling advanced steam power cycles, thermodynamic properties as functions of pressure and enthalpy $(p,h)$ or pressure and entropy $(p,s)$ are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, these calculations require cumbersome two-dimensional iteration of temperature $T$ and specific volume $v$ from $(p,h)$ or $(p,s)$. While these calculations in region 3 are not frequently required, the computing time can be significant. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for $T(p,h)$, $v(p,h)$, $T(p,s)$, and $v(p,s)$ in region 3, along with boundary equations for the saturation pressure as a function of enthalpy, $p3sat(h)$, and of entropy, $p3sat(s)$. Using the new equations, two-dimensional iteration can be avoided. The numerical consistency of temperature and specific volume obtained in this way is sufficient for most uses. This paper summarizes the need and the requirements for these equations and gives complete numerical information. In addition, numerical consistency and computational speed are discussed.

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