Calculating Density of High Altitude Air Using Ideal Gas Law

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Homework Help Overview

The discussion revolves around calculating the density of air at high altitudes using the ideal gas law, specifically at an altitude of 20 km with a uniform temperature of 200 K. Participants are working with given constants such as the gas constant R, gravitational acceleration g, and the density at ground level.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial calculation of pressure at ground level using the ideal gas law and express uncertainty about the next steps. There is a suggestion to substitute pressure into the differential equation for density and to integrate for a solution. Additionally, one participant questions the validity of the gravitational acceleration value used in the calculations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions made, particularly regarding the value of gravitational acceleration at high altitudes. Some guidance has been provided on how to proceed with the calculations, but no consensus has been reached.

Contextual Notes

Participants are operating under the assumption of a uniform temperature and are addressing the implications of using a constant value for gravitational acceleration at varying altitudes. There is also a noted discrepancy in the calculated pressure value, which may affect subsequent calculations.

Matt766
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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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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
 
Matt766 said:

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.
 
Matt766 said:

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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