Why does air density decrease as we go higher in altitude?

In summary: In the stratosphere, where temperature increases more rapidly, pressure also increases more rapidly than density.
  • #1
sgstudent
739
3
As we go higher up a mountain, the air pressure decreases. But why would that cause the air density to decrease? Since pressure is hpg, so if h decreases pressure decreases but what causes the air density to decrease as well?

Thanks for the help :)
 
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  • #2
Gases are compressible. More pressure means they are compressed into a smaller volume. Liquids not so much. Water has about the same density in a column.
 
  • #3


A.T. said:
Gases are compressible. More pressure means they are compressed into a smaller volume. Liquids not so much. Water has about the same density in a column.

Oh so at the surface of the earth, because the pressure is greater so it is more compressed while higher up the pressure is less so the compression is smaller?

But then again now with only one formula, P=hpg now that h and p decrease so the pressure will decrease disproportionately?
 
  • #4
It's a direct consequence of PV = nRT.
 
  • #5


SteamKing said:
It's a direct consequence of PV = nRT.

How would you apply that formula here?

Thanks
 
  • #6
sgstudent said:
How would you apply that formula here?

Thanks

If you define N as number of particles (as opposed to number of moles), the ideal gas law is PV = NkT where k is the Boltzmann constant, a fundamental physical constant. Divide both sides by V and you get

P = nkT

Where n = N/V is the number of particles per unit volume. Multiply n by m, the mass per particle, and you get the mass per unit volume (aka density) rho. Hence n = rho/m and the ideal gas law becomes

P = (rho/m)kT

For air, there is more than one type of particle so m is a weighted average of the masses of the different molecules.
 
  • #7


cepheid said:
If you define N as number of particles (as opposed to number of moles), the ideal gas law is PV = NkT where k is the Boltzmann constant, a fundamental physical constant. Divide both sides by V and you get

P = nkT

Where n = N/V is the number of particles per unit volume. Multiply n by m, the mass per particle, and you get the mass per unit volume (aka density) rho. Hence n = rho/m and the ideal gas law becomes

P = (rho/m)kT

For air, there is more than one type of particle so m is a weighted average of the masses of the different molecules.

Oh so from this equation how will we show that the density and pressure changes with altitude?
 
  • #8
sgstudent said:
Oh so from this equation how will we show that the density and pressure changes with altitude?

This equation shows that P is proportional to rho so that if P decreases at a constant T, then rho must as well. However, even if T is not constant, as long as it decreases more slowly than P does, then the reduction in pressure leads to a reduction in density. This is true in the troposphere, where temperature decreases linearly with altitude, but pressure decreases as a power law.
 

1. How does altitude affect air density?

As altitude increases, air density decreases. This is because as altitude increases, there is less air above pushing down on the air below, causing it to spread out and become less dense.

2. Why is air density important?

Air density is important because it affects the performance of aircrafts, as well as the behavior of weather systems. It also impacts human health, as lower air density at higher altitudes can lead to altitude sickness.

3. How does air density affect the lift of an aircraft?

Air density plays a crucial role in the lift force that allows an aircraft to fly. As air density decreases with altitude, an aircraft needs to increase its speed to maintain the same amount of lift. This is why airplanes need longer runways at higher altitudes.

4. Does temperature affect air density?

Yes, temperature does affect air density. As temperature increases, air molecules gain more energy and become more spread out, resulting in lower air density. This is why hot air balloons rise and cold air sinks.

5. How is air density measured?

Air density is typically measured in units of mass per volume, such as kilograms per cubic meter or grams per liter. It can be measured using instruments such as a barometer, which measures air pressure, or a density meter, which measures the mass of a known volume of air.

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