Calculating Density of High Altitude Air Using Ideal Gas Law

[Matt766]

Homework Statement

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

Homework Equations

P=rho*R*T
dp/dz= -rho*g

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.

 

[Chestermiller]

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

 

[Quantum Defect]

Homework Statement

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[/B]

Homework Equations

P=rho*R*T
dp/dz= -rho*g[/B]

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.[/B]

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.

 

[SteamKing]

Homework Statement

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

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.