- #1
phrygian
- 80
- 0
Homework Statement
a. Consider a horizontal slab of air whose thickness (height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for dP/dz, the variation of pressure with altitude, in terms of the density of air.
b. Use the ideal gas law to write the density of air in terms of pressure, temperature, and the average mass m of the air molecules. Show, then, that the pressure obeys the differential equation:
dP/dz = - P(mg)/(kT)
Homework Equations
The Attempt at a Solution
R= rho
P_(z+dz) + mg - P_(z) = 0
dP = mg
m = R A dz
dp/dz = R A mg
I don't think that that is right for a because I am completely stuck on how to get it to work with b...
thanks for the help