As a first step toward a multi-phase equation of state for dense water, we develop a temperature-dependent equation of state for dense water covering the liquid and plasma regimes and extending to the super-ionic and gas regimes. This equation of state covers the complete range of conditions encountered in planetary modeling. We use first principles quantum molecular dynamics simulations and its Thomas-Fermi extension to reach the highest pressures encountered in giant planets several times the size of Jupiter. Using these results, as well as the data available at lower pressures, we obtain a parametrization of the Helmholtz free energy adjusted over this extended temperature and pressure domain. The parametrization ignores the entropy and density jumps at phase boundaries but we show that it is sufficiently accurate to model interior properties of most planets and exoplanets. We produce an equation of state given in analytical form that is readily usable in planetary modeling codes and dynamical simulations (a fortran implementation can be found at http://www.ioffe.ru/astro/H2O/). The EOS produced is valid for the entire density range relevant to planetary modeling, for densities where quantum effects for the ions can be neglected, and for temperatures below 50,000K. We use this equation of state to calculate the mass-radius relationship of exoplanets up to 5,000M_Earth, explore temperature effects in ocean and wet Earth-like planets, and quantify the influence of the water EOS for the core on the gravitational moments of Jupiter.
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