Water Vapor and Mechanical Work: A Comparison of Carnot and Steam Cycles

Olivier Pauluis Center for Atmosphere Ocean Science, New York University, New York, New York

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Abstract

The impact of water vapor on the production of kinetic energy in the atmosphere is discussed here by comparing two idealized heat engines: the Carnot cycle and the steam cycle. A steam cycle transports water from a warm moist source to a colder dryer sink. It acts as a heat engine in which the energy source is the latent heat of evaporation. It is shown here that the amount of work produced by a steam cycle depends on relative humidity and is always less than that produced by the corresponding Carnot cycle.

The Carnot and steam cycles can be combined into a mixed cycle that is forced by both sensible and latent heating at the warm source. The work performed depends on four parameters: the total energy transport; the temperature difference between the energy source and sink; the Bowen ratio, which measures the partitioning between the sensible and latent heat transports; and the relative humidity of the atmosphere. The role of relative humidity on the work produced by a steam cycle is discussed in terms of the Gibbs free energy and in terms of the internal entropy production.

Corresponding author address: Olivier Pauluis, Center for Atmosphere Ocean Science, New York University, 251 Mercer Street, New York, NY 10012. Email: pauluis@cims.nyu.edu

Abstract

The impact of water vapor on the production of kinetic energy in the atmosphere is discussed here by comparing two idealized heat engines: the Carnot cycle and the steam cycle. A steam cycle transports water from a warm moist source to a colder dryer sink. It acts as a heat engine in which the energy source is the latent heat of evaporation. It is shown here that the amount of work produced by a steam cycle depends on relative humidity and is always less than that produced by the corresponding Carnot cycle.

The Carnot and steam cycles can be combined into a mixed cycle that is forced by both sensible and latent heating at the warm source. The work performed depends on four parameters: the total energy transport; the temperature difference between the energy source and sink; the Bowen ratio, which measures the partitioning between the sensible and latent heat transports; and the relative humidity of the atmosphere. The role of relative humidity on the work produced by a steam cycle is discussed in terms of the Gibbs free energy and in terms of the internal entropy production.

Corresponding author address: Olivier Pauluis, Center for Atmosphere Ocean Science, New York University, 251 Mercer Street, New York, NY 10012. Email: pauluis@cims.nyu.edu

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