kunhkat, Pekka et al.
For a quantitative rigorous thermodynamic development of the lapse rate, see:
Robert H. Essenhigh
Prediction of the Standard Atmosphere Profiles of Temperature, Pressure, and Density with Height for the Lower Atmosphere by Solution of the (S−S) Integral Equations of Transfer and Evaluation of the Potential for Profile Perturbation by Combustion Emissions
Energy Fuels, 2006, 20 (3), 1057-1067 • DOI: 10.1021/ef050276y
This analytical solution, believed to be original here, to the 1D formulation of the (1905−1906) integral (S−S) Equations of Transfer, governing radiation through the atmosphere, is developed for future evaluation of the potential impact of combustion emissions on climate change. The solution predicts, in agreement with the Standard Atmosphere experimental data, a linear decline of the fourth power of the temperature, T4, with pressure, P, and, at a first approximation, a linear decline of T with altitude, h, up to the tropopause at about 10 km (the lower atmosphere). From these two results, with transformation using the Equation of State, the variations of pressure, P, and density, ρ, with altitude, h, are also then obtained, with the predictions again, separately, in substantial agreement with the Standard Atmosphere data up to 30 km altitude (1% density). . . . Numerical closure is not yet complete, with only one parameter at this time not independently calculated but not required numerically for validation of analytical closure.
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