Thermodynamic equilibrium of a fluid column under the influence of gravity

Abstract

Abstract According to classical and statistical thermodynamics, a well-mixed fluid mass has a uniform temperature and is at thermodynamic equilibrium. It independent of the gravitational field. However, large well-mixed fluid masses, for example, in atmospheres and oceans, often are isentropic. One has attributed that to the influence of gravity. This has raised the question if such masses can go to a different restricted thermodynamic equilibrium with uniform entropy. Discussions on this issue have continued for three centuries without finding a final answer. This paper presents another analysis of the question if a fluid mass under the influence of gravity may go to a restricted equilibrium state with uniform entropy. At first, it analyses previous work as a background study. Then, it describes a kinetic model for the motion of fluid parcels in a vertical fluid column. This model is the tool for studying if and how the column may go to an isentropic equilibrium. The kinetic model supports the hypothesis that a fluid column under the influence of gravity may go to a restricted equilibrium state with an isentropic temperature profile. A statically unstable column can reach that state spontaneously, while its entropy increases and gravitational potential energy decreases. The latter energy is the source of the kinetic energy for the motion of its fluid parcels, driving the internal heat transfer that results in the isentropic profile.