Air pressure - density -temperature at 10,000 meters

[Sherry]

The air temperature at an altitude of 10,000 meters is a chilling
-35º C. Cabin temperatures in airplanes flying at this altitude are comfortable because of air conditioners rather than heaters. A.) Find the pressure at 10,000 m and B) Find the temperature of the air before the air conditioner cools it off.

 

[russ_watters]

Ideal gas equation (not enough information is given though - some big assumptions need to be made).

 

[Sherry]

This was a question the teacher gave us to think about over the weekend.

The only clue he gave us in class is:
101325 Pa = (1.29 kg/m3)(h) where h = 8015 meters.

He told us to use air density 1.29 kg/m3 but that does not make sense because dry air at sea level is 1.29 kg/m3 but as altitude increases, the density drops dramatically.


I found other formulas and worked the problem this way:

Where: D = density, kg/m3
P = pressure, Pascals
R = gas constant , J/(kg*degK) = 287.05 for dry air
T = temperature, degK = deg C + 273.15


D = P/R*T D = 26436/(287.05 * 238) D = 0.38696 kg/m3
P = 101325-egh P = 101325-(0.38696)(9.80)(10000) P = 63403 Pa
P = Po(Tf/To) 101325 = 63403(Tf /238) Tf = 380 K = 107 C

I am just not sure that it is right.

 

[LURCH]

Originally posted by Sherry
He told us to use air density 1.29 kg/m3 but that does not make sense because dry air at sea level is 1.29 kg/m3 but as altitude increases, the density drops dramatically.

But not inside a pressurised airliner. I believe that is the key to resolving this question.

 

[Sherry]

Correct, but he wants us to find the pressure outside of the plane at 10,000 meters as well as the temperature of the air as it is being pressurized but before the plane's air conditioner cools it off.

 

[russ_watters]

You can't calculate the air pressure outside the plane from the info given because you don't know how much the air conditioner has cooled the air. Find the pressure and density through http://www.npl.co.uk/pressure/faqs/atmosaltitude.html chart (if it isn't specific enough, calculate it by fitting a line to the graph) and calculate the temperature of the air once its been pressurized using the ideal gas equation.