The energy conversion ratio, γ, is shown to be bounded below by 0 and above by 1/2 in the two-dimensional linear geostrophic adjustment of a continuously stably stratified, incompressible, inviscid non-Boussinesq fluid. ''Two-dimensional'' refers to problems in which the initial isopycnal displacement field is an arbitrary function of the vertical (parallel to the rotation axis) and a single horizontal coordinate. By using Fourier analysis techniques, the paper also identified classes of initial isopycnal displacement profiles for which the adjustment process leads to γ > 1/3. Finally, an expression for γ is derived when the initial isopycnal displacement profile is three dimensional.