# Density of high altitude air

1. Feb 10, 2015

### Matt766

1. The problem statement, all variables and given/known data
Treat the atmosphere as an ideal gas with a uniform temperature of 200 K. Find the density at 20 km.

R= 260 N*m/(kg*k)
g= 3.92 m/s^2
rho(0)= 0.015 kg/m^3

2. Relevant equations
P=rho*R*T
dp/dz= -rho*g

3. The attempt at a solution
I found the pressure at ground level using P=rho*R*T

P=(0.015 kg/m^3) (260 N*m/(Kg K)) (200 K) = 780 N/m^2

I'm not sure how to proceed from here.

Last edited by a moderator: Feb 10, 2015
2. Feb 10, 2015

### Staff: Mentor

That equation for the density looks like it's off by a factor of 100.

As far as what to do next, take the equation for p and substitute it into the equation for dp/dz.

Chet

3. Feb 10, 2015

### Quantum Defect

Use the equations under 2 to write dp/dz in terms of P and T. Integrate to get a solution for P as a function of height.

4. Feb 10, 2015

### SteamKing

Staff Emeritus
Although the acceleration due to gravity g varies with altitude, it is not clear where you obtained a value of g = 3.92 m/s2 for an altitude of 20 km.

You should check this figure before proceeding with your calculations.