Think of earth's atmosphere as an ideal gas of molecular weight [tex]\mu[/tex] in a uniform gravitational field. Let g denote the acceleration due to gravity.
If z denotes the height above the sea level, show that the change of atmospheric pressure p with height is given by
dp/dz = p([tex]\left([/tex]-[tex]\mu[/tex]g/RT)
dp = change in pressure
dz = change in height
[tex]\mu[/tex] = molecular weight
R = Universal gas constant
T = temperature
1) F = mg
2) P = F/A
3) PV = nRT
The Attempt at a Solution
With the relation between force and pressure, I derived an expression of p in terms of m and g. Using the ideal gas law, i obtained another equation for p. I am lost in my attempt to derive dp/dz. Please help.
Thank in advance,