How Does Pressure Change with Altitude?

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    Altitude Pressure
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Homework Help Overview

The discussion revolves around understanding how pressure changes with altitude, specifically in the context of a horizontal slab of air. The original poster is tasked with deriving an expression for the rate of change of pressure with respect to altitude, given the density of air.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between pressure, weight, and density of the air slab. There are suggestions to visualize the problem and to express the mass and weight of the slab in terms of its thickness and density.

Discussion Status

Some participants have provided guidance on how to approach the problem, including drawing diagrams and relating pressure changes to the weight of the air slab. There is an ongoing exploration of the mathematical relationships involved, with some participants expressing tentative conclusions about the derived expression.

Contextual Notes

The original poster indicates a lack of prior exposure to similar problems, which may affect their confidence in approaching the solution. There is also a focus on deriving the expression without prior examples from the professor or textbook.

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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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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.
 
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.
 
alright, so I got dP/dz = -g\rho does that sound about right?
 
Yes.
 

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