Phase change phenomena at microscale is important for novel cooling microsystems with intensive evaporation, so the development of reliable models and simulations are challenging. The heat and mass transfer in a rarefied gas between its two parallel condensed phases are considered on the basis of linearized and non-linear S-model kinetic equations. The linearized Navier-Stokes equation subjected to the temperature and pressure jump boundary conditions are solved analytically. The profiles of the macroscopic parameters in the gap between gas-liquid interfaces are obtained for several Knudsen numbers and for the cases of complete and non-complete evaporation condensation. The simple expression for the evaporation rate is proposed. The comparison of three approaches allowed to establish the limit of the application of the linearized approach in term of the saturation temperature ratios. The pressure and temperature jumps obtained numerically are in good agreement with the analytical expressions derived from the appropriate Onsager-Casimir reciprocity relations. The results of the evaporation flux are close to those given by the Hertz-Knudsen-Schrage formula, only when the values of the pressure and temperature at the upper boundary of the Knudsen layer are used. Comparison with recently measured temperature jumps are provided and disagreement with some experiments are discussed.