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Visualizing Vapor Pressure: A Mechanical Demonstration of Liquid–Vapor Phase Equilibrium

Dennis LambDepartment of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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Raymond A. ShawAtmospheric Sciences Program, and Department of Physics, Michigan Technological University, Houghton, Michigan

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Abstract

Water phase transitions are central to climate and weather. Yet it is a common experience that the principles of phase equilibrium are challenging to understand and teach. A simple mechanical analogy has been developed to demonstrate key principles of liquid evaporation and the temperature dependence of equilibrium vapor pressure. The system is composed of a circular plate with a central depression and several hundred metal balls. Mechanical agitation of the plate causes the balls to bounce and interact in much the same statistical way that molecules do in real liquid–vapor systems. The data, consisting of the number of balls escaping the central well at different forcing energies, exhibit a logarithmic dependence on the reciprocal of the applied energy (analogous to thermal energy kBT) that is similar to that given by Boltzmann statistics and the Clausius–Clapeyron equation. These results demonstrate that the enthalpy (i.e., latent heat) of evaporation is well interpreted as the potential energy difference between molecules in the vapor and liquid phases, and it is the fundamental driver of vapor pressure increase with temperature. Consideration of the uncertainties in the measurements shows that the mechanical system is described well by Poisson statistics. The system is simple enough that it can be duplicated for qualitative use in atmospheric science teaching, and an interactive animation based on the mechanical system is available online for instructional use (http://phy.mtu.edu/vpt/).

CORRESPONDING AUTHOR: Raymond A. Shaw, Dept. of Physics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, E-mail: rashaw@mtu.edu

A supplement to this article is available online (10.1175/BAMS-D-15-00173.2)

Abstract

Water phase transitions are central to climate and weather. Yet it is a common experience that the principles of phase equilibrium are challenging to understand and teach. A simple mechanical analogy has been developed to demonstrate key principles of liquid evaporation and the temperature dependence of equilibrium vapor pressure. The system is composed of a circular plate with a central depression and several hundred metal balls. Mechanical agitation of the plate causes the balls to bounce and interact in much the same statistical way that molecules do in real liquid–vapor systems. The data, consisting of the number of balls escaping the central well at different forcing energies, exhibit a logarithmic dependence on the reciprocal of the applied energy (analogous to thermal energy kBT) that is similar to that given by Boltzmann statistics and the Clausius–Clapeyron equation. These results demonstrate that the enthalpy (i.e., latent heat) of evaporation is well interpreted as the potential energy difference between molecules in the vapor and liquid phases, and it is the fundamental driver of vapor pressure increase with temperature. Consideration of the uncertainties in the measurements shows that the mechanical system is described well by Poisson statistics. The system is simple enough that it can be duplicated for qualitative use in atmospheric science teaching, and an interactive animation based on the mechanical system is available online for instructional use (http://phy.mtu.edu/vpt/).

CORRESPONDING AUTHOR: Raymond A. Shaw, Dept. of Physics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, E-mail: rashaw@mtu.edu

A supplement to this article is available online (10.1175/BAMS-D-15-00173.2)

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