- #1
kent davidge
- 933
- 56
Homework Statement
At an altitude of 11,000 m, the air temperature is -56.5 °C and the air desity is 0.364 kg / m3. What is the pressure of the atmosphere at that altitude?
Homework Equations
no equations found
The Attempt at a Solution
Ok. The problem gives the air density and using the expression ρ = p M / R T we can easily find the pressure. But suppose I want to find it by using the expression dp / dy = -ρ g, with ρ = p M / R T. In this case I would need to integrate both dy and dT. Am I right? And how could I do this? I've tried working on one attempt but it did'nt work. Maybe the reason is that I did'nt know the molar mass of the air in that altitude? (sorry my bad english). My work is shown below.
dp / dy = -ρ g
ρ = p M / R dT
dp = - (dy p M g / R dT)
- ∫dy M g = R ∫dT (∫dp / P)
Ln P1 / P0 = - (Δy M g) / ΔT
Finally,
P1 = P0 e - (Δy M g / R ΔT)