# How does the Greenhouse Effect of $CO_2$ modify the classical explanation for atmospheric lapse rate?

Classical physics theory relating to gravity and the properties of gases seems to dictate that the lapse rate of a planetary atmospheres is determined by just 2 factors. The equation being $$-g/c$$, where $$g$$ is the acceleration due to gravity and $$c$$ is the specific heat of the gaseous atmosphere. Observational evidence seems to indicate this is correct for both the Earth and for Venus, based upon supposedly quite accurate data gathering. However we know that in Earth's atmosphere there is a small but measurable Greenhouse Effect from just 400ppm CO2 and in Venus there is massive thermal runaway due to a 96.5% CO2 atmosphere. Is there a newer better equation than -g/c then which includes the GHE, specifically relating to the huge contribution CO2 is making in the case of Venus ?