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tokens: by Weppner et al. (2015) , which presents a new cold EOS derived from the pressure derivative of the bulk modulus and the polytrope method. Where a polytrope is a structural assumption between pressure and density and it is also a solution to the Lane-Emden equation. The polytrope is defined as: where p E is the polytrope exponent. The authors show that the polytrope exponent is equivalent to the pressure derivative of the bulk modulus, 1 . This allows for an implementation of real material variables within the polytrope method. This is done by augmenting the classical Lane-Emden equation to handle zero pressure densities and a variable polytrope exponent. To correctly model the polytrope exponent, Weppner et al. (2015) also present an EOS (the Varpoly EOS) based on a variable polytrope exponent: The parameters A 0 , A 1 , and A 2 are connected to the extremes of the polytrope exponent by ambient pressure data and Thomas-Fermi Dirac (TFD) theory ( Salpeter 1967 ). In spite of its simplicity, the EOS provides an improvement in the modeling of P, B, B ′ over the other popular finite strain EOS. At extreme pressures, solids are predicted to follow TFD high pressure theory. Within TFD theory the infinite pressure asymptote of the polytrope exponent goes toward . This is the value that a finite strain EOS should go to, however, the B-M EOS goes toward a higher asymptote of and the Vinet EOS, in contrast, goes toward a lower asymptote of . The sensitivity to the compression curve with respect to the polytrope exponent is clearly shown in Weppner et al. (2015) and this highlights its importance when dealing with planetary interiors. The Varpoly EOS acts as the cold part of our EOS and in the following sections, we add a temperature dependent term to it. In addition, we develop a new model for the Gruneisen parameter, which is shown to fit well with experimental data and adheres to infinite pressure values. To correctly model the vapor transition, we introduce an expanded state model which can be seen to give good fits to prior estimates of the vapor curve. The EOS is thenfit to experimental data and compared to both the Tillotson EOS and the ANEOS model. We also test its caliber to model planets by fitting it to the Preliminary Reference Earth Model ( Dziewonski Anderson 1981 ). In the second paper, we perform numerical simulations on the lunar-forming impact, to test its merit in planetary impacts. In Sects. 2 and 3 we go through the development of the EOS. In Sect. 4 we test the EOS by fitting it to experimental data of ɛ -Fe and comparing it to the Tillotson EOS, and we also take a look at how well the EOS compares to the multiphase ANEOS model, in which we focus on the behavior of silicate material (SiO 2 , Mg 2 SiO 4 ). In Sect. 5 we discuss the EOS and our different results and finally end with some conclusions. 2 Adding a temperature dependence We begin by separating the Helmholtz free energy into three separate parts ( Zel’dovich Raizer 1967