A key assumption for both the mathematical Lewis method and the graphical McCabe–Thiele method is equimolal overflow. This was a necessary additional equation for most stages to satisfy the degrees of freedom. Instead, a more rigorous solution adds the energy balance to each stage with the assumption of no heat transfer (adiabatic stages). This adds more complexity to the calculations because the enthalpy of each stream entering or leaving a stage has to be determined. This calculation is demonstrated with a worked example and compared to the solution from the Lewis method and from a chemical process simulator.