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How much does air weigh?

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Posted by: Mars Rocket

I was half-watching, half-listening to a recent episode of "Air Giants" (really a re-packaged showing of "Superstructures of the World") on the Boeing 747-400 recently, and heard this exchange:

quote:

Narrator: "Even something as light as air takes on a certain 'weight' when it encounters the Jumbo."

Scottish voice: "I suppose the scale can't be underestimated, you know. When you think about the fact that, when it's pressurized, the cabin is so enormous that the air inside of it weighs more than a ton."


Huh?! That made me look up. The guy wasn't speaking metaphorically, he didn't say the air "weighs a ton".

I think this can't be right, that the guy made some kind of mistake. At this site: http://www.boeing.com/commercial/74...f/pf_facts.html I found that the interior volume is 31,285 cubic feet (876 m3).

If the air weighed one ton (2,000 pounds), this would mean it weighed 0.06 pounds (~1 oz) per cubic foot. This still seems high to me, but not completely unreasonable. But what do I know about air?

So maybe he's right after all. How much does air weigh?



Posted by: Damian

Depends on temperature and altitude. I'll bet the hot air balloonist here (rcrew? sorry, forgot who) will be able to tell you, as I found these formulas for calculating the weight on air on a ballooing site.



Posted by: Mars Rocket

Figure the air is pressurized to 1 atmosphere and kept at about 72 degrees F.



Posted by: Philosofy

pV=nrT. P is pressure in atmospheres, V is volume in liter, n is # of moles, r is the universal gas constant (0.0821 liter*atm/mole K) and T is temperature in Kelvin.

So, our volume is 876 m3, or 876,000 liters
The average molecular weight of air is about 28 g/mole (I think, this is all from memory). 2,000 lbs is 907,185 grams, so that's about 32,399 moles.
Temperature is 68F inside the cabin, which is 293 K

Plugging it all in, and finding the pressure, gives us 0.91 atm, which is low for a pressurized cabin. I think there is more than a ton of air in the plane, but its a good approximation. Especially since I don't remember the molecular weight of air.



Posted by: bevinst

A Standard atmosphere density is around 1.2Kg/M^3, which puts the weight of the air inside pretty close to a ton at 15psi. One needs to adjust this for cabin pressure.

-Tommy



Posted by: Damian

quote:
Originally posted by Mars Rocket
Figure the air is pressurized to 1 atmosphere and kept at about 72 degrees F.

Look at the chart I linked to. 1.198oz per cubic foot at 70 degrees Farenheit at sea level. If you want 72, do the math yourself. :)



Posted by: vman41

So what uses more fuel, carrying around a ton of air or keeping the cabin warm enough for human habitation?



Posted by: Francesco

Cabin pressure on a commercial jetliner is usually kept just below the FAA maximum limit of the equivalent of that at 8,000 FASL. This equals 10.9 PSI, and the pP of oxygen is equal to 74% of that at sea level.



Posted by: Combat Medic

quote:
Originally posted by vman41
So what uses more fuel, carrying around a ton of air or keeping the cabin warm enough for human habitation?

Both just use blead air from the engines.

-Mike



Posted by: Dale Sorel

quote:
Originally posted by Philosofy
pV=nrT


Ah, the Ideal Gas Law.

Those were the days :p



Posted by: Otto

quote:
Originally posted by Philosofy
pV=nrT. P is pressure in atmospheres, V is volume in liter, n is # of moles, r is the universal gas constant (0.0821 liter*atm/mole K) and T is temperature in Kelvin.

So, our volume is 876 m3, or 876,000 liters
The average molecular weight of air is about 28 g/mole (I think, this is all from memory). 2,000 lbs is 907,185 grams, so that's about 32,399 moles.
Temperature is 68F inside the cabin, which is 293 K

Plugging it all in, and finding the pressure, gives us 0.91 atm, which is low for a pressurized cabin. I think there is more than a ton of air in the plane, but its a good approximation. Especially since I don't remember the molecular weight of air.



.91 atm doesn't seem all that low. I know that usually it's kept to the pressure you'd encounter at 10,000 feet or so, but beyond that, I'm uncertain.

Edit: Google tells me it's about 10.92 psi in a plane, an equivalent of 8,000 feet. Compared with 14.7 psi on the ground (varies, of course), that's pretty low.



Posted by: kpictjl

How much does 2000lbs of pure O^2 weight?



Posted by: Francesco

quote:
Originally posted by Otto
.91 atm doesn't seem all that low. I know that usually it's kept to the pressure you'd encounter at 10,000 feet or so, but beyond that, I'm uncertain.

Edit: Google tells me it's about 10.92 psi in a plane, an equivalent of 8,000 feet. Compared with 14.7 psi on the ground (varies, of course), that's pretty low.



Federal Aviation Regulation (FAR) 25 puts the minimum air pressure, or maximum equivalent altidude, at 2440m ASL, or 8,000 feet.



Posted by: Otto

quote:
Originally posted by kpictjl
How much does 2000lbs of pure O^2 weight?


Err.. 2000 lbs of anything weighs 2000 lbs. :p



Posted by: Francesco

quote:
Originally posted by kpictjl
How much does 2000lbs of pure O^2 weight?


2000 pounds



Posted by: GoodSpike

quote:
Originally posted by Mars Rocket
Figure the air is pressurized to 1 atmosphere and kept at about 72 degrees F.


I think it's a relative thing, so you'd need to know the outside information too. I think it's correct to say that on the ground, and unpressurized, the air in the cabin would be weightless. It's only when you pressurize the cabin relative to the outside air that it gains weight.



Posted by: nataylor

quote:
Originally posted by GoodSpike
I think it's a relative thing, so you'd need to know the outside information too. I think it's correct to say that on the ground, and unpressurized, the air in the cabin would be weightless. It's only when you pressurize the cabin relative to the outside air that it gains weight.
Huh? Physics would disagree with you. :) A certain volume of air, no matter its pressure or temperature, will weigh the same anywhere on Earth.



Posted by: Metaluna

Typical whiny coach passengers...now they want AIR in the cabin too! Sheesh! Cut the air and shave another 1" off the seat width while your at it.

:D



Posted by: Smiles

quote:
Originally posted by Mars Rocket
I think this can't be right, that the guy made some kind of mistake. At this site: http://www.boeing.com/commercial/74...f/pf_facts.html I found that the interior volume is 31,285 cubic feet (876 m3).

You know, I read this, and the Interior section additionally states that each passenger has about 6 Henways of air volume. That would make it just about a ton of air.



Posted by: Mars Rocket

quote:
Originally posted by Metaluna
Typical whiny coach passengers...now they want AIR in the cabin too! Sheesh! Cut the air and shave another 1" off the seat width while your at it.
:D



Like we used to say at the computer store I worked at while in college:

"This would be a great job if it weren't for all the customers."



Posted by: Marc

quote:
Originally posted by satguymtl
This equals 10.9 PSI, and the pP of oxygen is equal to 74% of that at sea level.


I found out the hard way that there's less oxygen in the cabin of an inflight airplane once when I was flying back from North Carolina and I started feeling ill. As I tried to go down the aisle to get to the lavatory, I passed out. The combination of too strong blood pressure medication plus less oxygen in the air didn't agree with me.

After we had landed (in the terminal), the pilot came up and talked with me to see how I was feeling. He told me that if I hadn't recovered on the plane, he was ready to head down for an emergency landing in Nashville.

--Marc



Posted by: cbordman

maybe this has something to do with why Mike Tyson never shuts up during the weigh in?



Posted by: Ereth

At 10,000 feet you run the risk of Hypoxia, so they keep it a couple thousand feet lower for safety reasons. The airline does not want to keep it pressurized to sea level because (a) it would make planes more expensive and (b) it would cost more to operate and (c) explosive decompression, if it did happen, would be far worse.

Military aircraft aren't pressurised to sea level either.



Posted by: btwyx

quote:
Originally posted by Mars Rocket
How much does air weigh?

An actuate answer has alreay been given, but I remember from my school daze that air is about 1/1000th as heavy as water. That makes it around 1kg/m^3. It was a useful thing to know for approximation.



Posted by: btwyx

quote:
Originally posted by Otto
Err.. 2000 lbs of anything weighs 2000 lbs. :p

It depends if you're using lbs as a unit of mass or a unit of force. As far as I know the US pound is defined as a unit of Mass (in terms of kg), so in orbit 2000lbs (mass) is weightless (weighs zero lbs). At 1 standard gravity 2000lbs (mass) weights 2000lbs (force).



Posted by: bluenoise

quote:
Originally posted by nataylor
Huh? Physics would disagree with you. :) A certain volume of air, no matter its pressure or temperature, will weigh the same anywhere on Earth.


I don't think this is correct. If the volume and temperature are held constant, increased pressure means increased weight.

bluenoise



Posted by: GoodSpike

quote:
Originally posted by nataylor
Huh? Physics would disagree with you. :) A certain volume of air, no matter its pressure or temperature, will weigh the same anywhere on Earth.


So if you took all the air inside a 747 at sea level, with the doors open, and compressed it into one square foot, that would weigh the same as a square foot of uncompressed air?

Or better, how about a balloon filled with Helium. At sea level it would have a significant negative weight. At some point, however, as it rises in elevation and reaches air that is less dense, that same balloon filled with the same amount of helium, would be weightless (neither negative or positive weight).



Posted by: Otto

quote:
Originally posted by btwyx
It depends if you're using lbs as a unit of mass or a unit of force. As far as I know the US pound is defined as a unit of Mass (in terms of kg), so in orbit 2000lbs (mass) is weightless (weighs zero lbs). At 1 standard gravity 2000lbs (mass) weights 2000lbs (force).

Pounds isn't a measure of mass, it's just usually used that way. Pounds, in physics books, is always a force, albeit it's commonly used as the force due to gravity at 1g.

quote:
Originally posted by Ereth
At 10,000 feet you run the risk of Hypoxia, so they keep it a couple thousand feet lower for safety reasons. The airline does not want to keep it pressurized to sea level because (a) it would make planes more expensive and (b) it would cost more to operate and (c) explosive decompression, if it did happen, would be far worse.

Me and friends went skydiving at 14,400 feet once. No door on the plane. Friend of mine fell asleep on the trip up, despite the wind being the loudest thing I've heard in quite a long while. Yeah, that high it gets a bit difficult to breathe. Well, to stay awake anyway.



Posted by: Otto

quote:
Originally posted by nataylor
Huh? Physics would disagree with you. :) A certain volume of air, no matter its pressure or temperature, will weigh the same anywhere on Earth.

No dude. Ask any scuba diver. Compressed air weighs a frickin' ton. More air in less volume = more weight. Weight is mass times gravity, remember. :p



Posted by: jsmeeker

quote:
Originally posted by Otto
Me and friends went skydiving at 14,400 feet once. No door on the plane. Friend of mine fell asleep on the trip up, despite the wind being the loudest thing I've heard in quite a long while. Yeah, that high it gets a bit difficult to breathe. Well, to stay awake anyway.



I maybe mistaken, but I believe oxygen needs to be available to passengers at that altitude. I'm trying to dig up the answer from the Part 91 rules. You *would* run into issues if you stayed at 14,000 feet long enough. At 12,500 feet, the pilot would ahve to be on O2 for any amount of time over 30 minutes. At 14,000, I think he needs to be on it at all times.



Posted by: aciurczak

quote:
Originally posted by bluenoise
I don't think this is correct. If the volume and temperature are held constant, increased pressure means increased weight.

bluenoise



Bluenoise - you are right on. The discrepancy is that gases don't behave like liquids/solids, in that volume doesn't equate to amount.

A liter of water is pretty much the same no matter what pressure is exerted on it, as is a liter of stone.

But a liter of gas can be compressed to a small fraction of its original size, or expanded to many times larger. This compression/expansion relates to the pressure exerted on the gas.


So the same amount of air weighs the same anywhere on earth. It is not as correct to say a certain volume of air weighs the same anywhere on earth.



Posted by: nataylor

quote:
Originally posted by GoodSpike
So if you took all the air inside a 747 at sea level, with the doors open, and compressed it into one square foot, that would weigh the same as a square foot of uncompressed air?

I'm sorry, I mistyped. I meant the same amount of air, e.g. 4.23 billion air molecules. So all the air in a 747 weights the same ,whether it occupies the space in a 747 or one square foot.

quote:
Or better, how about a balloon filled with Helium. At sea level it would have a significant negative weight. At some point, however, as it rises in elevation and reaches air that is less dense, that same balloon filled with the same amount of helium, would be weightless (neither negative or positive weight).
You're confusing weight with buoyancy. Just because a helium balloon floats up doen't mean it has negative weight. I guarantee you that balloon weights something. Put that balloon in a vacuum on a scale and you'll see it weighs something.

Now, given equal volumes of air and helium, the helium will rise because helium is lighter than air. It's not weightless, though, just lighter.



Posted by: trojanrabbit

quote:
Originally posted by kpictjl
How much does 2000lbs of pure O^2 weight?

A ton.



Posted by: nataylor

quote:
Originally posted by Otto
No dude. Ask any scuba diver. Compressed air weighs a frickin' ton. More air in less volume = more weight. Weight is mass times gravity, remember. :p
*slaps forehead* Yup, I mistyped. I meant quantity, not volume.



Posted by: jsmeeker

quote:
Originally posted by jsmeeker
I maybe mistaken, but I believe oxygen needs to be available to passengers at that altitude. I'm trying to dig up the answer from the Part 91 rules. You *would* run into issues if you stayed at 14,000 feet long enough. At 12,500 feet, the pilot would ahve to be on O2 for any amount of time over 30 minutes. At 14,000, I think he needs to be on it at all times.



I was mistaken. 15,000 feet is the point where supplemental O2 must be available to PAX.
Below is the FAR (I omitted section B which deals with pressurized aircraft)

91.211 Supplemental oxygen.

(a) General. No person may operate a civil aircraft of U.S. registry --

(1) At cabin pressure altitudes above 12,500 feet (MSL) up to and including 14,000 feet (MSL) unless the required minimum flight crew is provided with and uses supplemental oxygen for that part of the flight at those altitudes that is of more than 30 minutes duration;

(2) At cabin pressure altitudes above 14,000 feet (MSL) unless the required minimum flight crew is provided with and uses supplemental oxygen during the entire flight time at those altitudes; and

(3) At cabin pressure altitudes above 15,000 feet (MSL) unless each occupant of the aircraft is provided with supplemental oxygen.



Posted by: StanSimmons

quote:
Originally posted by Smiles
You know, I read this, and the Interior section additionally states that each passenger has about 6 Henways of air volume. That would make it just about a ton of air.


OK, I'll bite....

What's a Henway? :D ;)



Posted by: GoodSpike

quote:
Originally posted by nataylor
I'm sorry, I mistyped. I meant the same amount of air, e.g. 4.23 billion air molecules. So all the air in a 747 weights the same ,whether it occupies the space in a 747 or one square foot.

You're confusing weight with buoyancy. Just because a helium balloon floats up doen't mean it has negative weight. I guarantee you that balloon weights something. Put that balloon in a vacuum on a scale and you'll see it weighs something.

Now, given equal volumes of air and helium, the helium will rise because helium is lighter than air. It's not weightless, though, just lighter.



But the question originally what does the air weigh inside a 747, presumably at altitude with a pressurized cabin. The volume of air inside a 747 is not going to change with pressurization, so we're talking about the amount of air.

As to the balloon example, I was trying to show why the answer was relative to the outside air (my original point).

You're right in a vacuum it would weigh something, and that actually does go to the issue of what the air weighs inside a 747 in flight. At sea level, the balloon would have negative weight (relative to the air around it--it would be buoyant). The air inside the 747 at sea level, with the doors open, would not have weight relative to the outside air. Put the balloon in a vacuum, and it would fall to the ground. Fly the 747 to 35,000 feet (after closing the door of course!) and it will weigh more pressurized than unpressurized. The weight (positive or negative) is relative to the air around the object.

Another example. An oil tanker is filled with oil. Steel ship filled with a liquid. But the ship floats, because the oil is significantly lighter than water.



Posted by: jsmeeker

quote:
Originally posted by GoodSpike

Another example. An oil tanker is filled with oil. Steel ship filled with a liquid. But the ship floats, because the oil is significantly lighter than water.



The ship floats because it displaces more water than what it weighs.



Posted by: GoodSpike

quote:
Originally posted by jsmeeker
The ship floats because it displaces more water than what it weighs.


The ship floats because the water it displaces weighs more than what the ship weighs. If the oil did not weigh less than the water, you would not be able to transport as much oil on a ship.



Posted by: nataylor

quote:
Originally posted by GoodSpike
The air inside the 747 at sea level, with the doors open, would not have weight relative to the outside air.
Sure it would have weight. Lets say you can make some kind of magical, weightless container the same size as the interior of a 747 and fill it with air at the same pressure as the air outside the container. Trying to lift that would be the same as trying to lift a 2000lb hunk of lead.



Posted by: Otto

quote:
Originally posted by jsmeeker
I maybe mistaken, but I believe oxygen needs to be available to passengers at that altitude. I'm trying to dig up the answer from the Part 91 rules. You *would* run into issues if you stayed at 14,000 feet long enough. At 12,500 feet, the pilot would ahve to be on O2 for any amount of time over 30 minutes. At 14,000, I think he needs to be on it at all times.

We went up fast. The total plane ride was 15-20 minutes. We were up there less than a minute until we jumped out. So I don't think it was a big issue. And this wasn't in the US, so FAA rules didn't apply (although Australia's are probably about the same).



Posted by: GoodSpike

quote:
Originally posted by nataylor
Sure it would have weight. Lets say you can make some kind of magical, weightless container the same size as the interior of a 747 and fill it with air at the same pressure as the air outside the container. Trying to lift that would be the same as trying to lift a 2000lb hunk of lead.


No weight relative to the air! Of course it has weight. It has mass. But relative to the outside air it has no weight because they weigh the same.



Posted by: Otto

quote:
Originally posted by nataylor
Sure it would have weight. Lets say you can make some kind of magical, weightless container the same size as the interior of a 747 and fill it with air at the same pressure as the air outside the container. Trying to lift that would be the same as trying to lift a 2000lb hunk of lead.


No, it'd be neutrally buoyant. If you filled it with 2000lb of helium, then it certainly wouldn't be hard to lift, the hard part would be keeping it down. ;)

It would have inertia, granted, and moving it wouldn't be effortless, but it wouldn't weigh 2000lbs on a scale. If you pressurized it greater than the outside air, then yes, it would seemingly weigh more and more as you went to greater pressure, because it's now denser than the surrounding air.

It the same reasons boats float and balloons fly. Buoyancy.



Posted by: nataylor

quote:
Originally posted by GoodSpike
No weight relative to the air! Of course it has weight. It has mass. But relative to the outside air it has no weight because they weigh the same.
Ok, I understand what you're saying. But the question was "what does the air inside a 747 weigh." And your answer, that it's relative, is not true. It weighs what weighs. It would take the same amount of energy to get a 747 filled with air off the ground as it would to get a 747 in which the interior of the plane was a vacuum with a 2000lb hunk of lead in it off the ground.



Posted by: GoodSpike

quote:
Originally posted by nataylor
Ok, I understand what you're saying. But the question was "what does the air inside a 747 weigh." And your answer, that it's relative, is not true. It weighs what weighs. It would take the same amount of energy to get a 747 filled with air off the ground as it would to get a 747 in which the interior of the plane was a vacuum with a 2000lb hunk of lead in it off the ground.


But they were talking about a pressurized cabin, so I assumed they're taking about in flight weight, at altitude, not take off weight. I don't believe they pressurize the cabins to sea level pressures (or whatever altitude it takes off from). So the term pressurized cabin to me signifies at flight altitude. And I think the point was that a 747 when pressurized at flight altitude would weigh over a ton more than an unpressurized 747 at flight altitude.



Posted by: btwyx

quote:
Originally posted by Otto
Pounds isn't a measure of mass, it's just usually used that way. Pounds, in physics books, is always a force, albeit it's commonly used as the force due to gravity at 1g.

The pound certainly seems to be defined as a unit of mass by government agencies, such as: <http://physics.nist.gov/Pubs/SP811/appenB8.html>. They define exactly in terms of a kg (which is of course a unit of mass). They have an entirly separate unit for pounds-force (lbf).

Where I grew up pounds had been done away with for anything except shopping so all my physics texts used SI units. The common usage is definatly as a mass, but measured by weight, and any decent text book should really make clear its using pounds-force and not leave it ambiguous.




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