  The validity of the widely used linear mixing approximation for the equations
of state (EOS) of planetary ices is investigated at pressure-temperature
conditions typical for the interior of Uranus and Neptune. The basis of this
study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via
density functional theory molecular dynamics simulations. In particular, we
calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of
methane, ammonia, and water, as well as their 2:1:4 ternary mixture.
Additionally, the self-diffusion coefficients in the ternary mixture are
calculated along three different Uranus interior profiles and compared to the
values of the pure compounds. We find that deviations of the linear mixing
approximation from the results of the real mixture are generally small; for the
thermal EOS they amount to 4% or less. The diffusion coefficients in the
mixture agree with those of the pure compounds within 20% or better. Finally, a
new adiabatic model of Uranus with an inner layer of almost pure ices is
developed. The model is consistent with the gravity field data and results in a
rather cold interior ($\mathrm{T_{core}} \mathtt{\sim}$ 4000 K).
