Prove: If atmospheric non-radiating O2 is exchanged for radiating (absorbing/emitting) CO2, emissivity, e, of planet to space must increase and corresponding global radiating temperature must decrease. More generally, if any “greenhouse” gas displaces a “non-greenhouse” gas, planet will cool.
The Stefan-Boltzmann Law of radiation intensity emitted by all matter in the universe is:
I = σ e (T/100)4
If e increases at constant I, T goes down, by algebra. Therefore if CO2 increases e at constant I, T goes down, causes global cooling.
I = intensity of any radiating body, w/m2 of its spherical surface, Earth emits and transfers radiant energy to outer space surroundings at average rate Io = 239. This is measured by satellite spectrophotometers.
T = temperature of radiating body, K
e = emissivity of radiating body, fraction 0 < e < 1. Perfect radiator black body e = 1, radiates a given intensity at lowest possible temperature. Perfect reflector e = 0.
σ = Stefan-Boltzmann radiation law constant, 5.67
NASA uses this relationship with an undisclosed estimate of e to measure (deduce) average global temperature.