This paper is devoted to the computation of compressible multiphase flows involving phase transition. The compressible model is the system of Euler, without viscosity. For closing this model, an equation of state is required. In our context, the model of phase transition is included in the choice of the equation of state, via an entropy optimization of the mixture equation of state. Our aim is to simulate such a system, and for that, it is mandatory to understand well the Riemann problem with such an equation of state. We then propose a 2nd order numerical scheme, which is validated and proved to be accurate on one dimensional cases. Last, a 2D version of the code is proposed.