Thermodynamic Efficiency and the Height of the Troposphere

Physics

Scientific paper

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0343 Planetary Atmospheres (5405, 5407, 5409, 5704, 5705, 5707), 0350 Pressure, Density, And Temperature, 3309 Climatology (1620), 3314 Convective Processes, 3346 Planetary Meteorology (5445, 5739)

Scientific paper

An expression for the thermodynamic efficiency of a convective cycle operating in a setting with a background temperature gradient is compared with the theoretical (ideal) Carnot efficiency. Such an analysis has been previously applied to convection in the Earth's mantle - here I apply it to planetary tropospheres. For small tropospheric heights, the efficiency implied is greater than the Carnot efficiency, which is clearly impossible. A minimum temperature difference (and hence, for a given lapse rate, a minimum tropospheric height) is therefore implied by the 2nd Law, and this minimum is in fact in good agreement with the height of the Earth's troposphere. The same analysis is repeated for the troposphere of Saturn's moon Titan, with a 1.5 bar nitrogen atmosphere and a surface temperature of 94K, and it is found that Titan's tropopause temperature is also successfully predicted by this thermodynamic limit.

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