Archimedes Princple - Sigh.

[The Law]

I always struggle with this concept.

 

What is the effect of sea level when icebergs melt in the ocean?

 

A) Sea levels rise because of the increase in liquid from melted ice

Sea levels lower because of the lower salinity of the freshwater added to the sea

C) Sea levels remain the same because a floating iceberg displaces its weight in water

D) Sea level rises because the local temperature of the water is lowered

 

 

 

See, I knew to eliminate B and D immediately. Now, I knew C 's second half was true. A floating object displaces its weight in fluid, but I also knew that the density of water changes as it changes state and that a solid water has a lower density, so assumed that the water levels would rise slightly. Turns out that this difference is very small, and the AAMC book says it is negligible.

 

I just wanted to get someone's advice, was there anything else that I missed while trying to get this question? It's rated as difficult by AAMC, but is there anything wrong with my thinking?

[The Ace of Spades]

A kilogram of ice weighs the same as a kilogram of water. Therefore, the water level remains the same as the ice melts, and the answer C is correct.

 

Try it out: fill up a glass with ice and top it off with water. When the ice melts, the water level will remain the same!

 

Edit: Thinking about density doesn't affect the amount of water displaced, only the buoyancy of the object.

[UTPEOPLE]

I always struggle with this concept.

 

 

 

A) Sea levels rise because of the increase in liquid from melted ice

Sea levels lower because of the lower salinity of the freshwater added to the sea

C) Sea levels remain the same because a floating iceberg displaces its weight in water

D) Sea level rises because the local temperature of the water is lowered

 

 

 

See, I knew to eliminate B and D immediately. Now, I knew C 's second half was true. A floating object displaces its weight in fluid, but I also knew that the density of water changes as it changes state and that a solid water has a lower density, so assumed that the water levels would rise slightly. Turns out that this difference is very small, and the AAMC book says it is negligible.

 

I just wanted to get someone's advice, was there anything else that I missed while trying to get this question? It's rated as difficult by AAMC, but is there anything wrong with my thinking?

 

 

You are correct in thinking that a floating object would displace a volume of the fluid equal to the objects mass (so that the bouyancy negates the force of gravity). Thus, the iceberg displaces a certain volume of water equal to its mass when in solid form. HERE IS THE KEY. You are just melting the ice, so the MASS OF THE ICEBERG does not change. Even if the density changes from solid to liquid, the overall mass of the iceberg remains the same.

 

Thus, if you started off with displacing a volume of water equal to the mass of the iceberg, and then your iceberg became an amount of water that conserved its original mass, then it would become apparent that the volume of water that the iceberg transformed into is exactly equal to the volume of water initially displaced. THus, if you magically removed the iceberg and left a hole in the water, the water from the melted iceberg would EXACTLY fill in that hole (but with minor deviations due to the fact that freshwater has a slightly lower density than seawater, so the sea level might rise a really small amount, but unless this was told to you by the passage, you assume that the density of all liquid water is the same).

 

100 (original sea level?) - X (volume of water displaced) + X (amount of water generated from the melting iceberg) =100

[The Law]

Thanks Ace. I just screwed up in assuming that the density of water and ice was different, I guess for now I will assume they are the same.

[The Law]

You are correct in thinking that a floating object would displace a volume of the fluid equal to the objects mass (so that the bouyancy negates the force of gravity). Thus, the iceberg displaces a certain volume of water equal to its mass when in solid form. HERE IS THE KEY. You are just melting the ice, so the MASS OF THE ICEBERG does not change. Even if the density changes from solid to liquid, the overall mass of the iceberg remains the same.

 

Ah! That makes sense, even more clarification. Another mistake was to equate density with weight. It's the overall mass that's going to determine weight. The density of water changes because of volume, not mass.

[UTPEOPLE]

Thanks Ace. I just screwed up in assuming that the density of water and ice was different, I guess for now I will assume they are the same.

 

LAW!!! THEY ARE DIFFERENT! thats why ice floats on water!!!!

 

teeheee... feel free to throw all your MCAT questions out there... This is great practice for when I teach during the summer... do my explanations for stuff make sense?

[Leon]

See, I knew to eliminate B and D immediately. Now, I knew C 's second half was true. A floating object displaces its weight in fluid, but I also knew that the density of water changes as it changes state and that a solid water has a lower density, so assumed that the water levels would rise slightly. Turns out that this difference is very small, and the AAMC book says it is negligible.

 

Lol at "solid water" haha.

 

If I remember right from 3 years ago, the iceberg will displace in volume, its weight. Since the weight doesn't change, neither should be volume.

 

But, since ice is less dense than water, and if the rise in density from ice to water is significant at all:

 

Density = Mass/Volume , so the density rises (slightly) as you go from ice to water. Since density and volume are in an inverse relationship, you'd expect the volume to *decrease.*

 

So if 1kg of ice had a certain volume, that volume would drop slightly if you melt it.

 

 

_______________________________________________________

 

I think something's wrong here but can't pinpoint it.

[Leon]

Thus, the iceberg displaces a certain volume of water equal to its mass when in solid form. HERE IS THE KEY. You are just melting the ice, so the MASS OF THE ICEBERG does not change. Even if the density changes from solid to liquid, the overall mass of the iceberg remains the same.

 

Since mass is constant, if the density changes (as you go from ice to water) would not the volume also be forced to change inversely, to keep mass constant?

 

If BOTH mass and volume are constant, density is forced to be constant. But density can't be constant since ice has a slightly lower density than water. Sorry, I guess I'm confusing everyone.

[UTPEOPLE]

Lol at "solid water" haha.

 

If I remember right from 3 years ago, the iceberg will displace in volume, its weight. Since the weight doesn't change, neither should be volume.

 

But, since ice is less dense than water, and if the rise in density from ice to water is significant at all:

 

Density = Mass/Volume , so the density rises (slightly) as you go from ice to water. Since density and volume are in an inverse relationship, you'd expect the volume to *decrease.*

So if 1kg of ice had a certain volume, that volume would drop slightly if you melt it.

 

 

_______________________________________________________

 

I think something's wrong here but can't pinpoint it.

 

but the water level wont change, because initially, the iceberg initially pokes above the water. thus, the iceberg initially displaces an amount of water equal to its mass, BUT NOT ITS VOLUME (volume of displaced water is less than volume of iceberg). After melting, the decrease in iceberg volume will mean that the iceberg-water will exactly be level with the original water level

[astrogirl]

It may also help to think about the process in reverse. Imagine that you have an ocean. Now imagine that a little cube of the ocean near the surface freezes (not gonna happen, but we're imagining here). Since ice is less dense than water, the chunk that freezes is going to have to expand and stick up above the water level a bit, but the water level stays the same. So the water level is the same whether the ice is frozen or melted. I don't know if that helps, but that's just another way of approaching it, and sometimes it helps me to turn problems upside down like that in order to solve them.

[Leon]

but the water level wont change, because initially, the iceberg initially pokes above the water. thus, the iceberg initially displaces an amount of water equal to its mass, BUT NOT ITS VOLUME (volume of displaced water is less than volume of iceberg). After melting, the decrease in iceberg volume will mean that the iceberg-water will exactly be level with the original water level

 

Ah.

 

If I'm understanding correctly, the drop in volume that occurs from ice to water is compensated for by the portion of the iceberg that is usually above the water, resulting in an overall neutral effect on the level of the sea itself.

 

Yes, that would make perfect sense.

Thanks! Physics major, UTPEOPLE?

[UTPEOPLE]

Ah.

 

If I'm understanding correctly, the drop in volume that occurs from ice to water is compensated for by the portion of the iceberg that is usually above the water, resulting in an overall neutral effect on the level of the sea itself.

 

Yes, that would make perfect sense.

Thanks! Physics major, UTPEOPLE?

 

Correct! and Nope, not physics major... bio major!... but I love physics (except optics... grrr... optics) ... although I decided not to teach for MCAT physics this summer... But nice to know that my explanations can be understood