# What property of air makes it compressible?

TL;DR Summary
What would you change about air to make it have the same density at sea level but the atmosphere would only be a few miles high instead of a several hundred miles high?
What would you change about air to make it have the same density at sea level but the atmosphere would only be a few miles high instead of a several hundred miles high?

I am a high school physics teacher.

As I ponder this possibility, my first thought is I could increase the strength of the gravitational field. That would cause the height of the atmosphere to decrease. But what I am really trying to get at is: is there something that could make air a little more like a liquid, where the top layer has more of a boundary between "air" and "no air", similar to the way water works? I don't need a hard boundary between "air" and "no air" like there is between "water" and "no water" but what property of air could we change so that the distance between a high altitude weather balloon (33 miles highest ever) and a satellite that doesn't degrade in its orbit due to air friction (well above LEO) is a matter of miles instead of hundreds of miles.

Thanks,

BHD

Mentor
Well, from the ideal gas law, the density of air is $$\rho=\frac{pM}{RT}$$ where M is the molecular weight, R is the universal gas constant, and T is the temperature. From the "barotropic equation," we have that $$\frac{dp}{dz}=-\rho g$$ So, $$\frac{dp}{dz}=-\frac{pMg}{RT}$$or$$\frac{d\ln{p}}{dz}=-\frac{Mg}{RT}$$So, to make the pressure and density drop off more rapidly with altitude, you would either increase g or decrease T. But eventually you would get to the point where the air would liquify.

Homework Helper
Thought about that too, but for the question 'what would you change about air' (as in: properties of air itself) I drew a blank:
air is made up of molecules with a low dipole moment -- hence gaseous under terrrestrial atmospheric conditions. It wouldn't be air otherwise (but hat might be a circular argument ).

And uh, hello Badhairday: ##\quad## ##\quad## !

Staff Emeritus
Do you mean realistic change or fantasy properties?

Change the melting point so that it is solid at ambient temperatures.

Hi,

So, I did think of increasing the gravity field on my own, but I didn't think of lowering the temperature. That would certainly work, because with less energy they won't push as hard against each other. Which brings me to my next realization- if I could magically increase the mass of each atom of air, that would have the same net effect. The atmosphere would weigh more and thus it would squeeze down harder on itself.

But here is where I get a little outside of what I understand. What if I could magically increase the stickiness of the air? If the atoms pulled harder on each other, that would definitely lower the roof of the atmosphere. But what property, exactly, would that be? Surface tension? Viscosity? What do those two things have in common- the intermolecular forces. So, what would I be doing at that point? Increasing the strength of the Van Der Walls force? I'm a little rusty on my chemical bonds, but I know that it isn't ionic or covalent bonding that makes the atmosphere (or any fluid) stick together but also remain a fluid...

Still Considering,

BHD

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