How pressure changes with altitude

In summary, the conversation discusses how to find the variation of pressure with altitude in a horizontal slab of air using the fact that the pressure from below must balance the pressure from above and the weight of the slab. The suggested method involves drawing a picture of the slab and writing out its mass and weight in terms of density and thickness. The final answer is found to be dP/dz = -g\rho, where g is the gravitational constant and \rho is the density of the slab.
  • #1
jason177
27
0

Homework Statement



Consider a horizontal slab of air whose thickness (height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for dP/dz, the variation of pressure with altitude, in terms of the density of air.


Homework Equations





The Attempt at a Solution


I have no idea, neither the professor nor the textbook have gone over anything like this.
 
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  • #2
I recommend first drawing a picture of a slab of air with thickness dz. Then finding a way to write out its mass and hence weight in terms of dz and density.
 
  • #3
see ,the change in pressure from bottom to top of the slab (dP) is equal to the pressure due to the weight of the slab.If you can figure this out then by writing out the equation, dP/dz can be easily solved and the answer comes out to be density of slab times g.
 
  • #4
alright, so I got dP/dz = -g[tex]\rho[/tex] does that sound about right?
 
  • #5
Yes.
 

1. How does air pressure change with increasing altitude?

As altitude increases, the air pressure decreases. This is because there is less air above to exert pressure on the air below. Therefore, the higher the altitude, the lower the air pressure.

2. What is the relationship between altitude and air pressure?

The relationship between altitude and air pressure is an inverse relationship. As altitude increases, air pressure decreases and vice versa. This means that as one variable increases, the other decreases.

3. How does temperature affect air pressure with altitude?

Temperature also plays a role in the change of air pressure with altitude. As temperature decreases, air molecules move slower and are closer together, resulting in a decrease in air pressure. Conversely, as temperature increases, air molecules move faster and are farther apart, resulting in an increase in air pressure.

4. Why does air pressure decrease with altitude?

Air pressure decreases with altitude because the weight of the air above decreases as altitude increases. The higher the altitude, the less air above to exert pressure on the air below, resulting in a decrease in air pressure.

5. How does altitude affect the boiling point of water?

As altitude increases, the boiling point of water decreases. This is because at higher altitudes, the air pressure is lower, which means the pressure exerted by the atmosphere on the water's surface is also lower. This results in a lower boiling point for water, as it requires less energy to overcome the lower pressure and reach the boiling point.

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