Pressure Variation

[devinanda]

A statement from 'Introduction to Dynamical Meteorology' by James R Holton, Page no 21 is that "Pressure decreases more rapidly with height in a cold layer than in a warm layer " (of atmosphere). Could any of you please give me a detailed justification for this statement ??

[rajeshj]

hello,
We know that pressure, P=m*g*h where 'm' is the mass of the column, 'g' acceleration due to gravity and 'h' the height of the column. So the pressure difference would be written as (dp)=m*g*(dh)
We can write it as (dp)=rho*g*(dh), where rho is the density of the fluid which is a messure of its mass. In a cold layer 'rho' will be higher. So inorder to maintain the same pressure difference 'dh' should be small, ie the height of the column is less.
Hope this makes it clear.
Thanks,

[devinanda]

Hi Rajesh..
Thanks for the reply!

Considering a layer of atmosphere with pressure difference dP,
we have, dP= -rho*g*dz (Hydrostatic Equation)
For a warm layer, density is less and the layer is thicker ( ie, dz is more in order to maintain the same pressure difference dP), than the cold layer (density is more).

Thus in a cold layer pressure decreases (with height) within a thinner layer, making it more rapid (when compared to the pressure change in a warm thicker layer of atmosphere).
Thanks and Regards,
Sreedevi

[rajeshj]

dear sreedevi,
Thanks for your acknowledgement. A noughty question, was your reply a confirmation from the text; did you know that (or don't know)? because what you wrote was in my reply too!!
Thanks,

[devinanda]

Hi Rajesh,
When I had posted this question around 12 days back, I actually didn't have a clear concept regarding this, but later from Holton's explanation itself I could gather something. Then came your reply which was quite a simpler one and I made my idea clearer! And my reply was a mere acknowledgement as you mentioned, in which I believe I tried to club my idea as well as yours to form a complete and direct answer to my own querry, say, for the sake of other interested readers !

I promise this had nothing to do with my naughtiness, instead I appreciate your attempt, for answering such a simple question! Thank you!
Nice to have interacted with you!
Sreedevi