Calculating Pressure at High Altitudes Using Air Density and Temperature

[kent davidge]

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)}

 

[SteamKing]

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)}

You might want to compare your model of the Earth's atmosphere with this one:

https://en.wikipedia.org/wiki/Barometric_formula

 

[kent davidge]

Oh thanks. It was useful to me.