NF Model of How much Air and Water Exist on the Earth

[Guest lundboy]

http://blog.phiffer.org/post/27344630

 

Just a blog post, but someone had to do the math.... Everything below is just a cut and paste from he website above, the commentary is not Lundboys!

 

 

Left: All the water in the world (1.4087 billion cubic kilometres of it) including sea water, ice, lakes, rivers, ground water, clouds, etc. Right: All the air in the atmosphere (5140 trillion tonnes of it) gathered into a ball at sea-level density. Shown on the same scale as the Earth. Update: this image has received a lot of attention and several people have emailed me asking whether I created it. Both the text and image were found on an internet message board, so I’m not sure who made it or whether it’s accurate. A commenter at Boing Boing credits this to Adam Nieman and the Science Photo Library. I’ve replaced the image with a watermarked version after getting permission from the rights holder.

 

Andrew Nowicki writes:

 

The mass of the oceans is approximately 1.35 × 10^18 tonnes, or about 1/4400 of the total mass of the Earth (ranges reported: 1.347 × 10^21 to 1.4 × 10^21 kg.)

source

 

The average mass of the atmosphere is about 5 quadrillion metric tons or 1/1,200,000 the mass of Earth. According to the National Center for Atmospheric Research, “The total mean mass of the atmosphere is 5.1480 × 10^18 kg with an annual range due to water vapor of 1.2 or 1.5 × 10^15 kg depending on whether surface pressure or water vapor data are used; somewhat smaller than the previous estimate. The mean mass of water vapor is estimated as 1.27 × 10^16 kg and the dry air mass as 5.13 × 10^18 kg.â€

source

 

Andrew’s numbers are a good starting point, but I’m not sure they refute the image’s depiction or its caption. I’m currently traveling so I can’t do the math right now, but I will make an attempt to verify this once I have a chance. If anyone else wants to take a shot, I’d be happy to post your results.

 

Update #2 Pat Stanton writes:

 

My son sent me a link to the image of spheres representing all the water and air on Earth. He was skeptical and suspected it was an example of “tree-hugger shock media.â€

 

I decided to do the math, starting with the data provided by Andrew Nowicki. The math appears to verify the posted image. Although I applaud my son’s skepticism, tree-hugger shock media sometimes brings us an important and informative message.

 

General approach:

 

1. Measure the spheres representing Earth, water and air in the image. Obtain the diameter in pixels of each sphere. Also, identify relevant physical constants.
   
   
2. Starting with data independently provided by Andrew Nowicki, calculate the diameters of spheres that would contain Earth’s water and air.
   
   
3. Normalize the results from Step 2 into pixels and compare with measurements from Step 1.
   
   

Detailed results:

 

1. Image Measurements

 

The image was imported into Adobe Photoshop Elements, enhanced to better reveal spherical outlines, and measured using the Info tool. Measurements from several trials were averaged.

 

Earth diameter = 185 pixels Water diameter = 22 pixels Air diameter = 30 pixels

 

Relevant physical constants and relationships:

 

Spherical volume = (1/6) x Pi x diameter^3 Earth diameter = 12,732 km Mean molar mass of air = 28.94 g / mol Atmospheric pressure (sea level) = 101,325 Pa Temperature (sea level) = 20 C = 293 K Universal gas law constant = R = 8.3145 m^3 Pa / (mol K)

 

2. Water Calculations

 

Ocean mass = 1.35 x 10^18 tonnes (Andrew Nowicki) = 1.35 x 10^21 kg

 

Ocean volume = 1.35 x 10^21 L = 1.35 x 10^24 cm^3 = 1.35 x 10^9 km^3

 

Solving for diameter, Sphere diameter = 1.371 x 10^3 km

 

Normalizing to pixels, Sphere diameter = 1.371 x 10^3 km x (185 pixels / 12,732 km) = 20 pixels

 

This value compare favorably with the measured diameter of 22 pixels. Note that the preceding calculations are based on ocean mass, while the image also included ice, water vapor, fresh water, etc.

 

3. Air Calculations

 

Air mass = 5.1480 x 10^18 kg (Andrew Nowicki) = 5.1480 x 10^21 g

 

Air molecules = 5.1480 x 10^21 g / (28.94 g / mol) = 1.777 x 10^20 mol

 

Using the Ideal Gas Law, PV = nRT (101,325 Pa) x (Air volume) = (1.777 x 10^20 mol) x (8.3145 m^3 Pa / (mol K)) x 293 K

 

Air volume = 4.273 x 10^18 m^3 = 4.273 x 10^9 km^3

 

Solving for diameter, Sphere diameter = 2.013 x 10^3 km

 

Normalizing to pixels, Sphere diameter = 2.013 x 10^3 km x (185 pixels / 12,732 km) = 29 pixels

 

This value compare very favorably with the measured diameter of 30 pixels.

 

Conclusion: The posted image is correct.

 

Well done, thanks Pat!

 

Update #3 A representative from a company called Photo Researchers has contacted me and we had a phone conversation about my unauthorized use of the image. He works for the actual rights holder, represented by Science Photo Library, and said he’d contact him to get his take on the situation.

 

The Boing Boing linkage changes the scale of things a bit and I think SPL would be savvy to find an official response that doesn’t involve a take down notice. I’ll post more on this when I hear back, but for now here are the official sources in the US and UK.

 

I’m interested in how this experience relates to the theme I’ve been posting about. How does education happen in a networked context, as opposed to a textbook or television program (where SPL would normally license an image of this sort)? How can the two support each other? More on that later.

Edited March 16, 2008 by lundboy

[Tarzan's Jane]

I think the formulas caused a major shut down in my brain. So what does it all mean?

[Guest lundboy]

don't have to figure out the formulas, the picture shows the results of the formulas.

little tiny blue ball equals all the water on earth compared to the size of the earth, the pink one is all the air compared to the size of the earth.

[Deano]

That would make fishing easier, although the boat launches would be a zoo. LOL

[ccmtcanada]

So, I have a better chance at catching fish in water than I do hunting birds, since there is less water than air? Cool.

[keram]

I like this kind of science One question: Why they include everything, let's say 1 km below see level in his comparison (6,355.750 km earth radius) ?

[Deano]

If you like comparisons, here's a few more.

 

The Size Of Our World

[Tarzan's Jane]

little tiny blue ball equals all the water on earth compared to the size of the earth, the pink one is all the air compared to the size of the earth.

 

Well that can't be good...

[SlowPoke]

Well that can't be good...

We're still way better off than people on Mars

[shane]

Well that can't be good...

 

 

Hasn't this proportion of air/water/land always been this way?

[Guest lundboy]

Hasn't this proportion of air/water/land always been this way?

 

As far as we know. I don't think the picture is trying to say "Thing's are getting bad and We're in Deep Doo Doo", it's just trying to illustrate the ratios.

[Casey123]

I have a head ache!

[keram]

Well that can't be good...

Do not worry twilight. In reality it is 100 + (even more ) times better then it looks like. The picture ( very nice anyway) was to set your mind in the "right direction",

[Tarzan's Jane]

Do not worry twilight. In reality it is 100 + (even more ) times better then it looks like. The picture ( very nice anyway) was to set your mind in the "right direction",

 

Whew...I was truly contemplating doing my part and taking a shower only once a week and a deep breath once every thirty seconds....