Equilibrium temperature profiles obtained by maximizing the entropy of a column of fluidwith a given height and volume under the influence of gravity are discussed by using numer-ical experiments. Calculations are made both for the case of an ideal gas and for a liquidwith constant isobaric heat capacity, constant compressibility and constant thermal expan-sion coefficient representing idealized conditions corresponding to atmosphere and ocean.Calculations confirm the classical equilibrium condition by Gibbs that an isothermal tem-perature profile gives a maximum in entropy constrained by a constant mass and a constantsum of internal and potential energy