# What is the pressure?

1. Jan 5, 2016

### kent davidge

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

no equations found

3. 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)

2. Jan 5, 2016

### SteamKing

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

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

3. Jan 5, 2016

### kent davidge

Oh thanks. It was useful to me.