Density of high altitude air

  • Thread starter Matt766
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  • #1
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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.
 
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Answers and Replies

  • #2
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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
Quantum Defect
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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.
 
  • #4
SteamKing
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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.
 

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