1. The adiabatic lapse rate equation is
dT = (-g/Cp)*dh
dT = change in temperature
dh = change in height
g = gravitational constant
Cp = heat capacity at constant pressure
Thus change in temperature from the lapse rate is dependent upon 3 variables that have no dependence whatsoever upon radiative forcing from greenhouse gases. None.
Note temperature is inversely related to heat capacity (Cp), thus, water vapor increases heat capacity but this decreases temperature by up to 25C as we calculated in the first post of this series, due to the lapse rate changing from a dry to a wet adiabatic lapse rate. This proves water vapor acts as a negative-feedback cooling agent.
N2, O2, and CO2 heat capacities (Cp) are less than half that of water vapor, but are all very similar. At only 0.04% of the atmosphere, an increase in CO2 would cause a trivial increase in Cp, which since the lapse rate equation says Cp and temperature are inversely related, would cause a slight cooling.
2. Secondly, even if the atmosphere was 100% nitrogen N2, with no greenhouse gases, the pressure change with altitude and thus convection and the lapse rate would be almost the same as the current atmosphere.
We can prove this using the well-known barometric formulae, which are based on the ideal gas law and kinetics of gases (a "Boltzmann distribution"), are completely independent of greenhouse gas radiative forcing, and demonstrate a 100% greenhouse-free atmosphere of the same mass would have a nearly identical lapse rate, nearly identical height at the center of mass, and the surface would be just as warm or warmer than the current atmosphere.
As the lecture notes below show, to answer the question,
"What is the ratio of atmospheric pressure in Denver at 1 mile to that at sea level (assume the atmosphere is 100% Nitrogen N2)?The solution uses the molecular weight of N2, the Boltzmann gas constant, Avogadro's number (constant) and well known standard barometric formula to determine the pressure ratio between sea level and one mile is 0.822, which is the same ratio (0.823) calculated by the US Standard Atmosphere calculator for our current atmosphere. Therefore the presence of greenhouse gases in our atmosphere insignificantly affect the barometric formulae, ideal gas law, and convection which are the basis of the greenhouse equation.
We show using the same barometric formula for our atmosphere that the center of mass and equilibrium temperature with the Sun occur at ~5100 meter height:
|Solving for the center of mass of our atmosphere, which is located at 0.50 atmospheres, and which sets the location of the ERL at 255K and near mid-point of the lapse rate
Compared to a pure Nitrogen N2 atmosphere in which the center of mass is only slightly higher altitude and at the equilibrium temperature with the Sun at ~5300 meter height:
|Solving for the center of mass of a pure Nitrogen atmosphere, which is also is located at 0.5 atmospheres, and which sets the location of the ERL at 255K and near mid-point of the lapse rate
Additional slides from the lecture notes above on why the composition of gases don't significantly affect the barometric formulae or ideal gas law: