Impacts between planetary-sized bodies can explain the origin of satellites orbiting large ($R>500$~km) trans-Neptunian objects. Their water rich composition, along with the complex phase diagram of water, make it important to accurately model the wide range of thermodynamic conditions material experiences during an impact event and in the debris disk. Since differences in the thermodynamics may influence the system dynamics, we seek to evaluate how the choice of an equation of state (EOS) alters the systems evolution. Specifically, we compare two EOSs that are constructed by different approaches: either by a simplified analytic description (Tillotson), or by interpolation of tabulated data (Sesame). Approximately $50$ pairs of Smoothed Particle Hydrodynamics impact simulations were performed, with similar initial conditions but different EOSs, in the parameter space in which the Pluto-Charon binary is thought to form (slow impacts between Pluto-size, water rich bodies). Generally, we show that impact outcomes (e.g., circumplanetary debris disk) are consistent between EOSs. Some differences arise, importantly in the production of satellitesimals (large intact clumps) that form in the post-impact debris disk. When utilizing an analytic EOS, the emergence of satellitesimals is highly certain, while when using the tabulated EOS it is less common. This is because for the typical densities and energies experienced in these impacts, the analytic EOS predicts very low pressure values, leading to particles artificially aggregating by a tensile instability.
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