[robbmorganf]

While the equation you give is valid, I think it is probably not that useful given the "volume" is open to space and so we can't solve this equation.

I think more useful is a static equilibrium, specifically that d(pressure)/d(altitude)=-density(pressure,temperature)*gravity(altitude).

Which gives you roughly an exponential falloff with altitude if you assume gravity is constant (which is fine if it's a small fraction of planet radius) and molecular weight and temperature are constant (that's definitely not true but oh well)

EDIT: for the question asker: reducing the temperature would have a first order effect of just making the density gradient steeper, but surface pressure would be the same. The second order effect might be that the surface absorbs some CO2, which would actually reduce surface pressure.