I am trying to figure out how to calculate the temperature at any given altitude in the troposphere.
Let P=air pressure, V=volume of air above a given altitude, n=number of moles of gas, R=the ideal gas constant, T=temperature, and h=height above sea levelX1 and X2 = the value of X at geographic point 1 and point 2.
PV=nRT (the ideal gas law)
Volume of a sphere = 4/3*pi*radius3
Surface area of a sphere = 4*pi*radius2
The Attempt at a Solution
P1/ P2 = V1nRT1 / V2nRT2.
Now, we don't need to know what n and R are, because they are cancelled out of the equation. So ignore them. We are now left with P1/P2 = V1/V2 * T1/T2.
V = 4/3*pi*radius of troposphere - (4/3 * pi * (6371.5+h))
V1 / V2 is pretty obvious and can't be simplified.