Heavy Air

[ChemEngrMBA]

Most common answers to the question which follows the answers:

1.  "Nothing"
2.  "10,000 pounds"

Now the question:

What is the mass of one cubic mile of air at sea level?

Assume STP, of course, and a perfect cube.  In other words, imagine a strong steel box 1 mile by 1 mile by 1 mile. 
If it were evacuated, sealed, and weighed at sea level, and then unsealed and air allowed to fill it, what is the increase over the tare weight?
The answer will astound you.

[Oceander]

Most common answers to the question which follows the answers:

1.  "Nothing"
2.  "10,000 pounds"

Now the question:

What is the mass of one cubic mile of air at sea level?

Assume STP, of course, and a perfect cube.  In other words, imagine a strong steel box 1 mile by 1 mile by 1 mile. 
If it were evacuated, sealed, and weighed at sea level, and then unsealed and air allowed to fill it, what is the increase over the tare weight?
The answer will astound you.

Mass, or weight?  The two are not the same.  An object has the same mass on the Earth and the Moon (and anywhere else in the Universe for that matter), but that same object weighs only about 1/6th as much on the Moon as it does on the Earth.

Weight is the gravitational force acting on a given body—which differs depending on the gravitational pull of the opposing body (e.g. a person's weight on Earth vs on the Moon) — while mass is an intrinsic property of that body that never changes. In other words, an object's weight depends on its environment, while its mass does not.

[jmyrlefuller]

One cubic mile at sea level. I will assume that that by this, you mean "one cubic mile of air at mean sea level pressure," since if you were to set a one-cubic-mile cube at sea level, the top would be a mile high and have a significantly lower pressure than the bottom (about 15% lower, to be more precise), thus affecting the amount (and thus the mass) in the cube. So since you say "assume STP," that's what we'll do.

Mean sea level pressure = 101,325 Pa (kg/(m*s²))
Standard temperature = 0°C = 273.15 K

Pressure = density * specific gas constant * temperature

We will also assume typical, Earth-atmosphere, dry air, with the specific gas constant of 287.04 m²/(K*s²).

101325 kg/(m*s²) = density * 287.04 m²/(K*s²) * 273.15 K

Solving for density, we get 1.2923 kg/m³.

Now, using the U.S. definition of mile (5280 feet of 12 inches, each of 0.0254 meters; i.e., 1609.3 m), and cubing it, we get a cubic mile of 4.1682 billion m³. Multiply that by our density, and we get 5.3865 billion kg.

Five billion kilograms? Really? Yeah. Well, shave off that 7% or so for altitude differences, but yeah. A volume as big as a cubic mile can hold a lot of gas. Imagine for a moment that same area filled with water (density = 1000 kg/m³). That same cubic mile (encountered frequently in the oceans) has over 4 trillion kg of mass-- 800 times heavier.

So, unless this is a trick question, my final answer is about 5 billion kg. (No, I'm not converting to pounds. Pounds is a unit of weight and is relative. The customary system has no direct unit for mass.)

[ChemEngrMBA]

Mass, or weight?  The two are not the same.  An object has the same mass on the Earth and the Moon (and anywhere else in the Universe for that matter), but that same object weighs only about 1/6th as much on the Moon as it does on the Earth.

YOU mentioned the moon, not I.  YOU conflated mass and weight, not I.
I specifically said "sea level."  There IS no sea on the moon, which in any case, I never mentioned.  Only you did.

[ChemEngrMBA]

STP would refer to standard conditions at sea level ONLY, as you should know.
What the atmospheric pressure is at sea level varies widely, but it is ALWAYS - ALWAYS less one mile up.
You cannot concoct a scenario on earth where air pressure is constant from sea level to one mile high.

The correct answer is about 5.2 million tons.  You overstated the answer with your unwarranted assumption of "one cubic mile of air"
at 14.7 PSI everywhere, top to bottom.  Impossible.

One cubic mile at sea level. I will assume that that by this, you mean "one cubic mile of air at mean sea level pressure," since if you were to set a one-cubic-mile cube at sea level, the top would be a mile high and have a significantly lower pressure than the bottom (about 15% lower, to be more precise), thus affecting the amount (and thus the mass) in the cube. So since you say "assume STP," that's what we'll do.

//

We will also assume typical, Earth-atmosphere, dry air, with the specific gas constant of 287.04 m²/(K*s²).

//
Five billion kilograms? Really? Yeah. Well, shave off that 7% or so for altitude differences, but yeah. A volume as big as a cubic mile can hold a lot of gas.

[jmyrlefuller]

5.2 billion kg is equal to 5.2 million tons. 1 ton = 1000 kg.

[Oceander]

Mass, or weight?  The two are not the same.  An object has the same mass on the Earth and the Moon (and anywhere else in the Universe for that matter), but that same object weighs only about 1/6th as much on the Moon as it does on the Earth.

YOU mentioned the moon, not I.  YOU conflated mass and weight, not I.
I specifically said "sea level."  There IS no sea on the moon, which in any case, I never mentioned.  Only you did.

With all due respect, you have some major reading comprehension problems.  I'd focus on getting that fixed first before you continue looking around for motes in others' eyes.

[ChemEngrMBA]

5.2 billion kg is equal to 5.2 million tons. 1 ton = 1000 kg.

A ton is 2000 pounds.
A metric ton is 2,200 pounds.

[ChemEngrMBA]

Oceander, you are the first person I have ever encountered who failed to understand the ineluctable relationship between altitude and pressure.
The bottom of the theoretical box is at sea level, where the pressure is 760 Torr.  It must decrease as altitude increases, inside or outside.

[Lando Lincoln]

Oceander, you are the first person I have ever encountered who failed to understand the ineluctable relationship between altitude and pressure.
The bottom of the theoretical box is at sea level, where the pressure is 760 Torr.  It must decrease as altitude increases, inside or outside.

I'm just askin'... is that necessary?  Sheese, let's elect a new President!

[Oceander]

Oceander, you are the first person I have ever encountered who failed to understand the ineluctable relationship between altitude and pressure.
The bottom of the theoretical box is at sea level, where the pressure is 760 Torr.  It must decrease as altitude increases, inside or outside.

Why I'm responding I don't know - I suppose it's my own ego - but I'll just say this:  what you know about what I do or do not know would, if converted into mass, be less than the rest mass of an electron.

[ChemEngrMBA]

"Ego" is such a small word to describe your Infinite Wonderfulness which exceeds that of Obama the preening narcissist.

How amazing that you did not so much as attempt to answer the question and show your calculations and reasoning therefor, Oceander, Your Infinite Wonderfulness.

Bowing deeply, as Obama bowed down before the "king" of Saudi Arabia, I now take my humble leave, with your permission.....

[ChemEngrMBA]

Most common answers to the question which follows the answers:

1.  "Nothing"
2.  "10,000 pounds"

Now the question:

What is the mass of one cubic mile of air at sea level?

Assume STP, of course, and a perfect cube.  In other words, imagine a strong steel box 1 mile by 1 mile by 1 mile. 
If it were evacuated, sealed, and weighed at sea level, and then unsealed and air allowed to fill it, what is the increase over the tare weight?
The answer will astound you. [5.2 million tons]

On the subject of a cubic mile, it is a profound truth that every human alive today on earth could hypothetically fit inside one cubic mile.  5,280 cubed = 127 billion cubic feet, almost 20 cubic feet per human alive today.....

[Elderberry]

On the subject of a cubic mile, it is a profound truth that every human alive today on earth could hypothetically fit inside one cubic mile.  5,280 cubed = 127 billion cubic feet, almost 20 cubic feet per human alive today.....

No way Jose'. At the most, one may be able to cram in 10 million in one level, but that's it. Unless you put in multiple floors. So your truth is not so profound. If you are fitting humans into your cube, they have to remain "Fit" and not crushed.

[ChemEngrMBA]

No way Jose'. At the most, one may be able to cram in 10 million in one level, but that's it. Unless you put in multiple floors. So your truth is not so profound. If you are fitting humans into your cube, they have to remain "Fit" and not crushed.

"Hypothetically" is a word you seem to have missed, really.
Let me put it differently.  The volume of all humans alive today is less than one cubic mile.
So your criticism is invalid.

[Cyber Liberty]

 

[Elderberry]

"Hypothetically" is a word you seem to have missed, really.
Let me put it differently.  The volume of all humans alive today is less than one cubic mile.
So your criticism is invalid.

You still fail.

"Hypothetically" Definition: by imagining a possibility rather than reality; as a hypothesis.

Not a possibility or a hypothesis.

[Cyber Liberty]

You still fail.

"Hypothetically" Definition: by imagining a possibility rather than reality; as a hypothesis.

Not a possibility or a hypothesis.

They will fit if you use a  car crusher like the ones in scrap yards.

[Elderberry]

They will fit if you use a  car crusher like the ones in scrap yards.

Think auger or pump. Otherwise they'll ooze out as you put more in.

[Cyber Liberty]

Think auger or pump. Otherwise they'll ooze out as you put more in.

It'll take a combination.  Bones are really bulky.

[Elderberry]

Bones? No problem.

[ChemEngrMBA]

You still fail.

"Hypothetically" Definition: by imagining a possibility rather than reality; as a hypothesis.

Not a possibility or a hypothesis.

How stupid of me to try to claim that the volume of all living humans is less than one cubic mile. 
How utterly stupid of me.
Tell all those reading, then, what IS the approximate volume of all living humans, under assumptions of your choice, of course?

[GtHawk]

I have many times heard the phrase mental masturbation but never thought I would see a prime example...............................until this thread.

[240B]

The sea of tranquility is on the moon.

[ChemEngrMBA]

For the progressive, (SIC)  there is very little to love about the United States. Washington, Jefferson, Madison? A bunch of rotten slaveholders, hypocrites, and cowards even when their hearts were in the right places. The Declaration of Independence? A manifesto for the propertied classes. The Constitution? An artifact of sexism and white supremacy.

1.  "Progressive" is a one-word oxymoron.   Promoting socialism, class and race warfare, and badmouthing America is sick, demented, destructive.  Leave if you hate America so very much.
2.  Badmouthing America and continuing to live here is hypocrisy and cowardice.

http://DemocratInsanity.blogspot.com

[Sanguine]

@DeerSlayer - I'm the mod for this thread.  Is there a point to it?

[ChemEngrMBA]

@DeerSlayer - I'm the mod for this thread.  Is there a point to it?

How surprising that you have to ask.  It begins with the challenge - what is the mass of a cubic mile of air. This is to see if anyone here has the education background to answer the relatively simple question.  Nobody did. 

The second point is how profoundly surprising the answer is - it amazes even commercial pilots, and I have challenged many of them with this question.  Five million tons of air in one cubic mile.
And you had to ask why I posed such a question?

[bigheadfred]

Soooo....

Is this one of those "sucking all the oxygen from the room" moments?

[Wingnut]

Soooo....

Is this one of those "sucking all the oxygen from the room" moments?

Fred Just Breathe, breathe in the air
Run, rabbit run
Dig that hole, forget the sun
And when at last the work is done
Don't sit down, it's time to dig another one
For long you live and high you fly
But only if you ride the tide
And balanced on the biggest wave
You race towards an early grave

[Sanguine]

How surprising that you have to ask.  It begins with the challenge - what is the mass of a cubic mile of air. This is to see if anyone here has the education background to answer the relatively simple question.  Nobody did. 

The second point is how profoundly surprising the answer is - it amazes even commercial pilots, and I have challenged many of them with this question.  Five million tons of air in one cubic mile.
And you had to ask why I posed such a question?

Yeah, I though so.   

[Bigun]

@DeerSlayer

Just so you know, there are plenty of people here with the ability to answer the question but, it seems, no one thought it worth the effort.

[corbe]

   I'm a bit confused, apparently this seems to require a bit of mathematics and I'm stoned so yall are all a bunch of racist.

[DB]

How surprising that you have to ask.  It begins with the challenge - what is the mass of a cubic mile of air. This is to see if anyone here has the education background to answer the relatively simple question.  Nobody did. 

The second point is how profoundly surprising the answer is - it amazes even commercial pilots, and I have challenged many of them with this question.  Five million tons of air in one cubic mile.
And you had to ask why I posed such a question?

Air pressure at sea level is 14.70 psi @ 15C. Air pressure at an elevation of 5,280 feet (one mile) is 12.10 psi @ 15C. The difference is 2.6 psi. There are 4,014,489,600 square inches in a square mile. Therefore a cubic mile of air starting at sea level weighs 2.6 x 4,014,489,600 = 10,437,672,960 lbs or 5,218,836.48 US tons.

[corbe]

    I still don't understand @DB (thanks for trying) so here's some Marianne Williamson with her song

Elvis Costello & The Attractions - (What's So Funny 'Bout) Peace, Love And Understanding


Error 404 (Not Found)!!1

[Elderberry]

Don't forget to factor in the humidity of the air. The more humid the air is the less dense it is. After all where are you going to find a cubic mile of dry air to fill the box?

[ChemEngrMBA]

Don't forget to factor in the humidity of the air. The more humid the air is the less dense it is. After all where are you going to find a cubic mile of dry air to fill the box?

@DB showed how simple it really was to do.  His answer was 5,218,836.48 tons.
This is nine significant figures, using STP (standard temperature and pressure, viz. zero degrees celsius and 760 Torr, or 14.7 PSI at sea level). The whole point was to demonstrate how ENORMOUS is the weight of air.  Many people guess "nothing.  Air is weightless," they say. 
If that were the case, aircraft could not fly.  Nobody ever guesses a weight as huge as five million tons.

The humidity of air is highly dependent on the temperature.   At twenty-five degrees Celsius, the difference in density between dry air and saturated air is on the order of 1 or 2 percent.  It's lost in the long line of numbers of tons.

https://www.engineeringtoolbox.com/density-air-d_680.html

There is no need to "find" dry air.  It's all a mind exercise.  No such box will ever exist, much less a scale with which to weigh it.

[ChemEngrMBA]

Soooo....

Is this one of those "sucking all the oxygen from the room" moments?

Only if you don't enjoy using the brain God gave you, and expects you to use.

[Bigun]

@DB showed how simple it really was to do.  His answer was 5,218,836.48 tons.
This is nine significant figures, using average figures. The whole point was to demonstrate how ENORMOUS is the weight of air.  Many people guess "nothing.  Air is weightless," they say. 
If that were the case, aircraft could not fly.  Nobody ever guesses a weight as huge as five million tons.

The humidity of air is highly dependent on the temperature.   At twenty-five degrees Celsius, the difference in density between dry air and saturated air is on the order of 1 or 2 percent.  It's lost in the long line of numbers of tons.

https://www.engineeringtoolbox.com/density-air-d_680.html

There is no need to "find" dry air.  It's all a mind exercise.  No such box will ever exist, much less a scale with which to weigh it.

I suppose I would have gotten the wrong answer because I would simply have determined the number of cubic feet in a cubic mile and divided by 379 which results in a number very much larger than 5 million.

1 pound mole of any gas equals 379 scf.

[ChemEngrMBA]

I suppose I would have gotten the wrong answer because I would simply have determined the number of cubic feet in a cubic mile and divided by 379 which results in a number very much larger than 5 million.

1 pound mole of any gas equals 379 scf.

I have never seen the figure 379 scf before you presented it.  The reason your method would overstate the weight is that it implicitly assumes standard pressure, which is only the case very close to sea level.    Of course it diminishes considerably at elevation.

Pilots learn an interesting aspect of elevation, by the way. It is called the "lapse rate" and is ~3 degrees F per thousand feet.  On a flying vacation with my family, it was 100 degrees over the deserts of Arizona and Utah, but I few at 10,000 feet where it was a cool 70 degrees.  I dropped  down into the Grand Canyon which is huge enough to do figure eights in.  My radio speaker went quiet beneath the rim as radio waves travel line of sight.

[Bigun]

I have never seen the figure 379 scf before you presented it.  The reason your method would overstate the weight is that it implicitly assumes standard pressure, which is only the case very close to sea level.    Of course it diminishes considerably at elevation.

Pilots learn an interesting aspect of elevation, by the way. It is called the "lapse rate" and is ~3 degrees F per thousand feet.  On a flying vacation with my family, it was 100 degrees over the deserts of Arizona and Utah, but I few at 10,000 feet where it was a cool 70 degrees.  I dropped  down into the Grand Canyon which is huge enough to do figure eights in.  My radio speaker went quiet beneath the rim as radio waves travel line of sight.

I think I have discovered our problem @DeerSlayer.  Your question was "what is the mass..."  and I took that to mean weight when you were talking about the density.  But then why was your answer given in pounds?   

[Elderberry]

Slugs, not pounds, are used for mass in the US Customary Measurement System. Anyhow for the results to be mass, one would need to divide the weight by 32.1740.

[Bigun]

1 cubic foot of air at standard temperature and pressure assuming average composition weighs approximately 0.0807 lbs.

[Elderberry]

But he asked for mass not weight.

[Bigun]

But he asked for mass not weight.

Yes.  They are not unrelated

[corbe]

    TTIUWP:



                    Explain the mass of a woman on air?

[Elderberry]

  I agree. Related most definitely.

[Sanguine]

Y'all keep that up and I'm bringing out the men in kilts.

[Bigun]

As is the norm for me, I wish to hell I had read through the entire thread before I  chimed in.

[corbe]

    @Bigun it also took me almost 7 years to get through it.
     I still think there's a conspiracy. 

[Bigun]

    @Bigun it also took me almost 7 years to get through it.
     I still think there's a conspiracy.

I blame it on late Sunday evening boredom @corbe.