E4 Atmospheric Thermal Machine

Topic

The atmosphere functions as a heat engine that converts the temperature difference between a hot reservoir and a cold reservoir into mechanical work: the hot reservoir consists of the tropics, at approximately 300 Kelvin, and the cold reservoir consists of the poles, at approximately 240 Kelvin; the mechanical work produced by this atmospheric heat engine from that temperature difference manifests as winds, cyclones, and atmospheric waves. This thermodynamic framework is fundamental to understanding both the intensity of the atmosphere's general circulation and how that circulation responds to climate change.

Every heat engine—including the atmospheric heat engine—has an upper efficiency limit that depends solely on the ratio between the temperature of the cold reservoir and the temperature of the hot reservoir; this upper limit is equal to one minus that ratio, meaning that the closer the cold reservoir's temperature is to the hot reservoir's temperature—that is, the smaller the temperature difference between the two—the lower the atmospheric heat engine's upper efficiency limit becomes. The actual efficiency of atmospheric circulation falls far below this upper limit—hovering at just around two percent—because many processes occurring within the atmospheric heat engine are irreversible and cannot convert the temperature difference between the hot and cold reservoirs into mechanical work with the maximum efficiency allowed by that theoretical limit.

This irreversibility of the atmospheric heat engine is explained by an entropy balance: the very temperature gradient between the hot and cold reservoirs that drives the atmospheric heat engine tends, in itself, to reduce the climate system's entropy, whereas the engine's dissipative processes—such as friction and the turbulent cascade that breaks large eddies into progressively smaller ones—generate entropy. In the steady-state operation of the atmospheric heat engine, the entropy generated by dissipative processes exactly balances the entropy reduction caused by the temperature gradient between the warm and cold reservoirs; it is precisely this entropy production via dissipation that prevents the atmospheric heat engine from reaching the previously described upper limit of efficiency.

As the climate system warms, the temperature of the cold reservoir rises more rapidly than that of the warm reservoir—a phenomenon known as polar amplification—thereby reducing the temperature gradient between the two. Since the atmospheric heat engine's upper efficiency limit depends on this very gradient, a smaller temperature difference reduces its efficiency; a less efficient atmospheric heat engine produces less mechanical work, leading to a weakening of the general atmospheric circulation and mid-latitude jet streams—two mechanisms by which the engine converts temperature differences into mechanical work. This weakening of the general circulation and mid-latitude jet streams—stemming from the atmospheric heat engine and the warm and cold reservoirs described earlier—has profound implications for the weather patterns ultimately produced by these systems.

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