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Entropy Production and Climate Efficiency

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  • 1 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
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Abstract

Earth’s climate system is a heat engine, absorbing solar radiation at a mean input temperature Tin and emitting terrestrial radiation at a lower, mean output temperature Tout < Tin. These mean temperatures, defined as the ratio of the energy to entropy input or output, determine the Carnot efficiency of the system. The climate system, however, does no external work, and hence its work efficiency is zero. The system does produce entropy and exports it to space. The efficiency associated with this entropy production is defined for two distinct representations of the climate system. The first defines the system as the sum of the various material subsystems, with the solar and terrestrial radiation fields constituting the surroundings. The second defines the system as a control volume that includes the material and radiation systems below the top of the atmosphere. These two complementary representations are contrasted using a radiative–convective equilibrium model of the climate system. The efficiency of Earth’s climate system based on its material entropy production is estimated using the two representations.

Corresponding author address: Peter R. Bannon, Department of Meteorology, The Pennsylvania State University, 521 Walker Building, University Park, PA 16802. E-mail: bannon@ems.psu.edu

Abstract

Earth’s climate system is a heat engine, absorbing solar radiation at a mean input temperature Tin and emitting terrestrial radiation at a lower, mean output temperature Tout < Tin. These mean temperatures, defined as the ratio of the energy to entropy input or output, determine the Carnot efficiency of the system. The climate system, however, does no external work, and hence its work efficiency is zero. The system does produce entropy and exports it to space. The efficiency associated with this entropy production is defined for two distinct representations of the climate system. The first defines the system as the sum of the various material subsystems, with the solar and terrestrial radiation fields constituting the surroundings. The second defines the system as a control volume that includes the material and radiation systems below the top of the atmosphere. These two complementary representations are contrasted using a radiative–convective equilibrium model of the climate system. The efficiency of Earth’s climate system based on its material entropy production is estimated using the two representations.

Corresponding author address: Peter R. Bannon, Department of Meteorology, The Pennsylvania State University, 521 Walker Building, University Park, PA 16802. E-mail: bannon@ems.psu.edu
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