[bonanova]

Al Gore is stranded on a cubic iceberg that measures 100 miles on a side.

To pass the time until his rescue, he recites from memory all his speeches on Global Warming.

The hot air he produces melts the iceberg.

What is the resulting rise in sea level world wide?

You may assume:

1. Water expands 10% when it freezes.
2. The earth has a 4000 mile radius.
3. Three quarters of the earth's surface is covered by connected oceans.

[Guest]

Not sure if i did the math right but...

I get about 5.97 miles

How's that for global warming, maybe Al Gore should shut his mouth.

[Guest]

Depends whether the is stranded on an Antarctic or an Arctic iceberg.

Here's why:

When the iceberg melts, the volume changes but the weight remains the same (conservation of mass). Meaning that the melted water occupies the same volume as the displcaed water (by iceberg). So the sea level will not change.

This is true only if the sea water and the iceberg have the the same water. The arctic ice pack is made of the same sea water so melting of iceberg on the arctic will have no effect on the sea level. However, in Antarctic, the icebergs are made of fresh water.

Fresh water has less density than sea water (saline). Although the fresh water iceberg weighs the same as the weight of displaced sea water, because of the difference in density, the volume displaced is slightly greater which would be a function of difference in densities.

The above cases apply when the ice is floating. However, if the ice is supported at the bottom, then the water level will rise. Since icebergs are floating pieces of ice, the increase or the status quo of melting ice only depends only on the location.

So, in case he Al Gore melted an antarctic iceberg, the sea level would rise as below:

Density of water = 1

Density of sea water = 1.025

Volume = Mass x Density

Then for a given mass(same weight), the difference in volume = 2.4% (approx)

So incremental volume is (100)³ x 2.4% = 24000 cubic miles

Surface area of earth = 4.pi.r²

Increase in sea level = increased volume/ (3/4th of earth surface area)

This comes to nearly 19 cm! Quick, somebody stop him!

Edited July 15, 2009 by DeeGee

[Guest]

My answer was totally off, I guess i'm too tired to be doing this right now.

[bushindo]

Depends whether the is stranded on an Antarctic or an Arctic iceberg.

Here's why:

When the iceberg melts, the volume changes but the weight remains the same (conservation of mass). Meaning that the melted water occupies the same volume as the displcaed water (by iceberg). So the sea level will not change.

This is true only if the sea water and the iceberg have the the same water. The arctic ice pack is made of the same sea water so melting of iceberg on the arctic will have no effect on the sea level. However, in Antarctic, the icebergs are made of fresh water.

Fresh water has less density than sea water (saline). Although the fresh water iceberg weighs the same as the weight of displaced sea water, because of the difference in density, the volume displaced is slightly greater which would be a function of difference in densities.

The above cases apply when the ice is floating. However, if the ice is supported at the bottom, then the water level will rise. Since icebergs are floating pieces of ice, the increase or the status quo of melting ice only depends only on the location.

So, in case he Al Gore melted an antarctic iceberg, the sea level would rise as below:

Density of water = 1

Density of sea water = 1.025

Volume = Mass x Density

Then for a given mass(same weight), the difference in volume = 2.4% (approx)

So incremental volume is (100)³ x 2.4% = 24000 cubic miles

Surface area of earth = 4.pi.r²

Increase in sea level = increased volume/ (3/4th of earth surface area)

This comes to nearly 19 cm! Quick, somebody stop him!

I would like to point out that all iceburg, whether they are from artic and antartic ocean, are composed primarily of fresh water. When water freezes, the complex crystal structure of ice generally does not provide any space for the salt to become incorporated into the crystal structure.

In general, the difference in density between salt water and freshwater is ignored in these sort of puzzles, since the iceberg concerned are pretty small. However, the ice cube given is so large (100 miles on a side) that density makes a difference. By the way, the average ocean depth is 2-3 miles. So Al Gore is standing about 98 miles above sea level. I hope he has a space suit on.

[Guest]

You can only see 10% of an ice burg (90% under water) and if water expands 10% when frozen, when it melts it will not displace any more. Like if you have a glass full of soda and ice. When the ice melts the glass doesn't overflow. Hence, the water level will not rise at all.

Edited July 15, 2009 by kennyb43

[Guest]

Depends whether the is stranded on an Antarctic or an Arctic iceberg.

Here's why:

When the iceberg melts, the volume changes but the weight remains the same (conservation of mass). Meaning that the melted water occupies the same volume as the displcaed water (by iceberg). So the sea level will not change.

This is true only if the sea water and the iceberg have the the same water. The arctic ice pack is made of the same sea water so melting of iceberg on the arctic will have no effect on the sea level. However, in Antarctic, the icebergs are made of fresh water.

Fresh water has less density than sea water (saline). Although the fresh water iceberg weighs the same as the weight of displaced sea water, because of the difference in density, the volume displaced is slightly greater which would be a function of difference in densities.

The above cases apply when the ice is floating. However, if the ice is supported at the bottom, then the water level will rise. Since icebergs are floating pieces of ice, the increase or the status quo of melting ice only depends only on the location.

So, in case he Al Gore melted an antarctic iceberg, the sea level would rise as below:

Density of water = 1

Density of sea water = 1.025

Volume = Mass x Density

Then for a given mass(same weight), the difference in volume = 2.4% (approx)

So incremental volume is (100)³ x 2.4% = 24000 cubic miles

Surface area of earth = 4.pi.r²

Increase in sea level = increased volume/ (3/4th of earth surface area)

This comes to nearly 19 cm! Quick, somebody stop him!

What about the 10% expansion in volume mentioned in the assumption part of the original question?, with that in place calcs don't add up in my head

[Guest]

the cube root of [the cubic volume of water (100³ * 90%) divided by the surface area of ocean-covered earth (4*pi*r² * 75%)] gives a rise of approximately .18 miles or 958 ft.

[Guest]

Assuming the density of melted water from the iceberg and the density of seawater are the same, the rise in sea level will be zero. The volume of seawater displaced by the iceberg will be equal to the volume of melted iceberg.

[Guest]

quote name='dumb_luck' date='15 July 2009 - 07:51 AM' timestamp='1247662303' post='188102']

the cube root of [the cubic volume of water (100³ * 90%) divided by the surface area of ocean-covered earth (4*pi*r² * 75%)] gives a rise of approximately .18 miles or 958 ft.

[Guest]

Kennyb43 got it right.

The iceberg is already floating, thus already displacing all the water it can.

Edited July 15, 2009 by seeksit

[Guest]

I think you would have also needed to include as an assumption that the surface area of the water covering the earth's surface will not increase as the ocean level rises.

Edited July 15, 2009 by ~Z~

[Guest]

That's what I got too, Rattiar.

Reminds me of that futurama episode "Crimes of the Hot," where they dump giant ice cubes into the ocean to slow warming. lol.

quote name='dumb_luck' date='15 July 2009 - 07:51 AM' timestamp='1247662303' post='188102']

the cube root of [the cubic volume of water (100³ * 90%) divided by the surface area of ocean-covered earth (4*pi*r² * 75%)] gives a rise of approximately .18 miles or 958 ft.

I think your final math is a bit off, but yeah.

Cubic volume of ice = 1,000,000 cu. mi.; Volume of water = 1,000,000/1.1 = 909091 cu. mi.

Surface of Earth = 4*4000*4000*pi = 201,061,952 sq. mi.; Portion covered in water = 201,061,952*.75 = 150,796,464 sq. mi.

Volume divided by area = 909091 cu. mi. / 150,796,464 sq. mi = .00603 mi. = 31.8 ft. rise in ocean level

[

Edited July 15, 2009 by Aldahir

[Guest]

Next you should find out what happens if that ice is covering land instead of water.

[Guest]

Next you should find out what happens if that ice is covering land instead of water.

That would be an interesting problem. How would you solve that one?

[Guest]

Assuming:

1) The volume of water currently being displaced by the iceberg is 0 (e.g. He's stranded 1 mile up on a 1000x1000 mile iceberg over LAND)

2) The surface area of water remains at 75% of the earth (e.g. all land masses are like giant walls)

3) All of the water, when melted, contributes to the volume of water on the earth, and only to the volume of water on the earth.

Water expands 10% when frozen... therefore the volume of water when melted (assuming no loss to evaporation )

= 100³/1.1 mi³.

= 10⁷/11 mi³.

The surface area of the water

= 3/4*4*pi*(4*10³)² mi².

= 3*pi*16*10⁶ mi².

= 48*pi*10⁶ mi².

divide volume by area to get height

= 10⁷/11 mi³ * 1/48*pi*10⁶ mi².

= 10/(528pi) mi

= 10/528pi mi * 5280ft/1 mi

= 100/pi feet

~ 31.830988618379067153776752674503 feet

[Guest]

This is a trick question. The answer is sea level will not rise, it will fall. After Gore melts the iceberg he will become even more incensed by the "climate change" that he will blather on endlessly as he sinks into the water. The heating of the water from his out gassing will cause the oceans to evaporate, expanding the atmosphere outward until most of the water sublimates out into space, thus reducing sea levels..

[Guest]

Assuming the density of melted water from the iceberg and the density of seawater are the same, and the ocean depth is greater than the submerged depth of the iceberg, the rise in sea level will be zero. The volume of seawater displaced by the iceberg will be equal to the volume of melted iceberg.

[Guest]

Assuming:

1) The volume of water currently being displaced by the iceberg is 0 (e.g. He's stranded 1 mile up on a 1000x1000 mile iceberg over LAND)

2) The surface area of water remains at 75% of the earth (e.g. all land masses are like giant walls)

3) All of the water, when melted, contributes to the volume of water on the earth, and only to the volume of water on the earth.

Water expands 10% when frozen... therefore the volume of water when melted (assuming no loss to evaporation )

= 100³/1.1 mi³.

= 10⁷/11 mi³.

The surface area of the water

= 3/4*4*pi*(4*10³)² mi².

= 3*pi*16*10⁶ mi².

= 48*pi*10⁶ mi².

divide volume by area to get height

= 10⁷/11 mi³ * 1/48*pi*10⁶ mi².

= 10/(528pi) mi

= 10/528pi mi * 5280ft/1 mi

= 100/pi feet

~ 31.830988618379067153776752674503 feet

Good thought, but two things you did not account for; the expansion of the sea into land and the increase in the radius of the earth as water level increases. I think you need to use a quadratic equation to solve the overall increase in sea level.

Edited July 15, 2009 by jule5

[Guest]

Thoreathole is right. you guys are thinking too much.

[Guest]

this solution has already been given, but the level does not change. 90% of an iceberg is underwater, leaving 10% out of the water, which is the same 10% of volume gained by the water freezing. Thus if it melts, the sea level will not change.

[Guest]

The deepest part of the ocean is just under 7 miles deep (just round to 7 miles) which means that even if an entire 100 x 100 mile iceberg could fit to that depth it would still stick up over 93 miles out of the water....

My question is "How did Al Gore get up there?!"

[Guest]

All joking aside, the puzzle stated that the iceberg was a cube 100 miles on a side. There is no way 90% of this could be under water. The deepest places in the oceans are only about 7 miles deep. This would put the top of the iceberg at around 93 miles above sea level. Since the earths atmosphere only extends about 75 miles above the surface Gore is gonna have a hard time melting the ice with his breath as he won't have any. Whether the author intended it or not, it would seem evident that this berg is planted firmly on terra firma. It would still displace sea water but the amount would depend on where it was located. All in all a very poorly worded puzzle. Hopefully meant more as a joke than anything.

Edited July 15, 2009 by Jacca

[Guest]

And I still think my first answer was the most correct one.

[Guest]

All joking aside, the puzzle stated that the iceberg was a cube 100 miles on a side. There is no way 90% of this could be under water. The deepest places in the oceans are only about 7 miles deep. This would put the top of the iceberg at around 93 miles above sea level. Since the earths atmosphere only extends about 75 miles above the surface Gore is gonna have a hard time melting the ice with his breath as he won't have any. Whether the author intended it or not, it would seem evident that this berg is planted firmly on terra firma. It would still displace sea water but the amount would depend on where it was located. All in all a very poorly worded puzzle. Hopefully meant more as a joke than anything.

and if it the side was horizontal - sheet ice? would it make a difference?

[Guest]

I got 0.006029 mi which is approximately 10 meters! This is how I got it. (91% of (100)^3) / (3/4 of 4*PI*4000^2)