Air pressure - density -temperature at 10,000 meters

In summary: The air pressure at 10,000 meters is a whopping 101325 Pa. The temperature of the air before the air conditioner cools it off is a chilling -35º C.
  • #1
Sherry
7
0
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.
 
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  • #2
Ideal gas equation (not enough information is given though - some big assumptions need to be made).
 
  • #3
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.
 
Last edited:
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 

1. What is the relationship between air pressure, density, and temperature at 10,000 meters?

At 10,000 meters (or approximately 33,000 feet) above sea level, the air pressure is significantly lower than at sea level. This decrease in air pressure also results in a decrease in air density, meaning that there are fewer air molecules per unit of volume. Additionally, the temperature at 10,000 meters is much colder due to the decrease in air pressure and density.

2. How does air pressure affect the human body at 10,000 meters?

At 10,000 meters, the lower air pressure means there is less oxygen available per breath. This can lead to altitude sickness, which can cause symptoms such as headaches, dizziness, and shortness of breath. It is important for individuals to acclimate slowly when traveling to high altitudes to avoid these negative effects on the body.

3. Why does air pressure decrease at higher altitudes?

Air pressure decreases with increasing altitude due to the weight of the air above. The lower layers of the atmosphere are under more pressure from the weight of the air above, but as you move higher, there is less air above pushing down, resulting in lower air pressure.

4. How does temperature change with increasing altitude?

The temperature decreases with increasing altitude due to the decrease in air pressure and density. This is because air molecules are able to spread out more at higher altitudes, making it more difficult for them to collide and create heat. Additionally, the sun's rays are less intense at higher altitudes, contributing to the colder temperatures.

5. How does air pressure at 10,000 meters affect weather patterns?

The lower air pressure at 10,000 meters can affect weather patterns as it can prevent air from rising and forming clouds, resulting in clear skies. It can also contribute to the formation of high-pressure systems, which are associated with fair weather. Additionally, the decrease in air pressure at higher altitudes can cause changes in wind patterns, which can influence weather conditions on the ground.

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