I think your somewhat confused about the way CO2 and water acts as greenhouse gases. It is true that these gases have a finite heat capacity but the total energy they can store in the atmosphere is relatively slim (actually the latent heat of water is important for climate, as it is used to advect energy from tropical regions to high latitudes, but that's besides the point).
The way water vapor and CO2 affect climate is through their effect on the flow of energy. When present, the gases don't let radiation escape from Earth as easily, forcing the equilibrium temperature to become higher.
Regarding the specific heat of CO2
Dear Anonymous person,
I think your somewhat confused about the way CO2 and water acts as greenhouse gases. It is true that these gases have a finite heat capacity but the total energy they can store in the atmosphere is relatively slim (actually the latent heat of water is important for climate, as it is used to advect energy from tropical regions to high latitudes, but that's besides the point).
The way water vapor and CO2 affect climate is through their effect on the flow of energy. When present, the gases don't let radiation escape from Earth as easily, forcing the equilibrium temperature to become higher.