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Why, at lower altitudes, does the atm change more rapidly? 
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#1
Feb2512, 01:06 AM

P: 783

The lower the altitude, the more rapidly the atmospheric pressure changes with respect to altitude.
Why does this happen? I know that the pressure itself is supposed to decrease since the weight of the air column increases as altitude drops, but shouldn't this be a linear relation? Does it have anything to do with the air density and the convection of air? Thanks! BiP 


#2
Feb2512, 03:19 AM

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#3
Feb2512, 07:18 AM

P: 464

[itex]p = p_0 \cdot \left( {1  \frac{{\kappa  1}}{\kappa } \cdot \frac{{M \cdot g}}{{R \cdot T_0 }} \cdot h} \right)^{\frac{\kappa }{{\kappa  1}}}[/itex] 


#4
Feb2512, 07:32 AM

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Why, at lower altitudes, does the atm change more rapidly?
It shows why the dependence is not linear without delving into too many confusing details. Much better from the pedagogical point of view.



#5
Feb2512, 08:53 AM

P: 15,319

A rather simplistic but intuitive way to see why it should not be linear is this:
Examine the graph in your OP and imagine it as a straight line. It would intersect the Xaxis (altitude). It would mean that the edge of space the line between atmosphere and vacuum  would be sharp. You could be at 120,000 feet and be in atmo, and then at 121,000 feet and be in hard vacuum. Does that make sense? 


#6
Feb2512, 11:37 AM

P: 464




#7
Feb2512, 12:32 PM

P: 15,319

I think most people intuitively know that there is no hard boundary at very the edge of the atmo  that it gets tenuous the farther out you go. I'm pointing out that, knowing this, one can immediately deduce that the graph must be curved. 


#8
Feb2512, 12:39 PM

P: 783

Thank you everyone for your replies. I understand it now.
BiP 


#9
Feb2512, 01:54 PM

P: 464




#10
Feb2512, 09:23 PM

P: 15,319

Most us can intuitively grasp that this is not the way the atmo tapers off. Once the OP realizes that he already knew the pressure gradient was curved, he would realize that it's probably curved all the way to the ground. It's the difference between being told something, and selfdiscovery. 


#11
Feb2612, 08:04 AM

P: 346

Solving differential equation with ideal gas law and P=ρgh you would see that it follows an exponential pattern which coincides with your graph.
I think an intuitive explanation would be, with decreasing altitude, more weight of the air above is exerted to the air below. 


#12
Feb2712, 01:48 AM

P: 464




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