# If the polar ice caps were to melt....

by warfreak131
Tags: caps, melt, polar
 P: 5,462 Consider a beaker of salt water, density p1 add a quantity of pure water, density p0 This results in a quantity of salt water, density p2 Since density is a function of salinity p1 > p2 > p0 Whether this effect is significant depends upon the relative quantities of original saline and meltwater. go well
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 Quote by SW VandeCarr You didn't address my point that even if fresh water is released, it will be dispersed in the much larger volume of salt water so that its true effect in raising sea levels is negligible, even for large Antarctic icebergs.
I agree it is a small effect.

To put it into perspective consider the sea level, $z$ in relation to the volume of the basin, $V$ and the area, $A$ of the basin $V=Az$.

$$V_{new}=V_{old}+\Delta V$$

$$Az_{new}=Az_{old}+\Delta V$$

Change in sea level is denoted $\Delta z$

$$\Delta z=z_{new}-z_{old}=\Delta V/A$$

$$\Delta z=(V_{freshwater}-V_{displaced seawater})/A$$

If for example $V_{freshwater}=1.05V_{displacedseawater}$, then
$$\Delta z=0.05V_{displaced seawater}/A$$

and $V_{displaced seawater}=\frac{\rho_{ice}}{\rho_{seawater}}V_{ice}\approx0.9V_{ice}$

$$\Delta z=0.045V_{ice}/A$$

So for example with these numbers a 1000 km3 volume of ice melting in a 100 million km2 expanse of ocean basin will contribute about .45mm of sea level rise. Not much but I would not call this negligible.
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 Quote by Studiot Consider a beaker of salt water, density p1 add a quantity of pure water, density p0 This results in a quantity of salt water, density p2 Since density is a function of salinity p1 > p2 > p0 Whether this effect is significant depends upon the relative quantities of original saline and meltwater. go well
Right. But we are considering volume.

Is the volume of stratified p1 + p0 any different from well mixed p2?
 P: 5,462 As you rightly pointed out, the mass does not change just because the ice melts. The volume is always governed by the equation volume = mass/density. Since the mass remains constant, the volume changes with density.
P: 749
 Quote by Studiot As you rightly pointed out, the mass does not change just because the ice melts. The volume is always governed by the equation volume = mass/density. Since the mass remains constant, the volume changes with density.
The volume of what though? I don't think you've thought this one through.
 Sci Advisor PF Gold P: 1,783 This reminds me of a physics problem I had many many years ago. In the following case you are to determine whether the water level will rise, fall or stay the same after the ice melts: A block of ice is floating in a beaker of water. Within the block of ice is frozen: 1.) Nothing, the ice is solid. (level stays the same) 2.) A ball bearing which will sink to the bottom when the ice melts. 3.) A ball of foam which will float when the ice melts. 4.) A sphere of air at ambient air density. 5.) A spherical void which is a vacuum.
P: 5,462
 I don't think you've thought this one through.
??????????????????????

If you float some pure ice in a beaker of pure water and let the ice melt, the level will not change after melting as Jambaugh has said.

However this statment is predicated upon the composition of the liquid being the same before and after melting.

If we live in magicland and the action of melting transforms all the mass of material to paraffin the level will be different.

A little less obviously, if the action of melting transforms the resultant liquid to a different composition the level will be different.

What I don't (readily) have is the information as to how much ice there is realative to the ocean mass so I can't make a judgement as to how significant the effect is.
As a geologist, you should be able to do this.
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 Quote by Studiot ?????????????????????? If you float some pure ice in a beaker of pure water and let the ice melt, the level will not change after melting as Jambaugh has said. However this statment is predicated upon the composition of the liquid being the same before and after melting. If we live in magicland and the action of melting transforms all the mass of material to paraffin the level will be different. A little less obviously, if the action of melting transforms the resultant liquid to a different composition the level will be different. What I don't (readily) have is the information as to how much ice there is realative to the ocean mass so I can't make a judgement as to how significant the effect is. As a geologist, you should be able to do this.
Which bit of any of this really is relevant? It seems to me like you're taking a stab at me but you're not quite sure where you're putting the knife.
 P: 5,462 [QUOTE]It seems to me like you're taking a stab at me but you're not quite sure where you're putting the knife. QUOTE] Perhaps if you were to address my point instead of posting insulting comments. I have treated all your posts seriously but would argue, most strongly, my right to assert that Two equal masses of liquids of different composition and therefore density occupy different volumes. Therefore any attempt to assess the change in world ocean volume due to melting icecaps must take into account, or show to be negligeable, the change in composition due to the dilution of saline water by meltwater.
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 Quote by Studiot Therefore any attempt to assess the change in world ocean volume due to melting icecaps must take into account, or show to be negligeable, the change in composition due to the dilution of saline water by meltwater.
If you add salt to water the volume doesn't change significantly. This is because salt is soluble in water.

At the risk of repeating myself, all I am saying is that when ice melts it turns into fresh water. The addition of this fresh water to the sea does more to increase the sea level than would the insertion of the ice into the sea. The maths is all there and I have made it very easy to follow for anybody interested in taking apart the logic.

What I think you are saying is that I have made an erroneous assumption in saying that the addition of the fresh water will increase the volume of the sea by exactly the volume of the fresh water. Instead the fresh water will take in some salt from the sea, and therefore it will become more dense. Up to here I would agree, but the next point I think is where we disagree.

You seem to argue that because the density of this water increases the volume must decrease to accommodate this increase in density. However, that is wrong because the increase in mass (by the influx of salt) is what causes the density to increase, the volume stays pretty much the same. I argue that the transfer of salt from one water body to the other makes no difference to the volume of the water, and therefore that this point is moot, and all my previous arguments stand unaffected.

This is my reading of your argument, I hope that I have made it clear enough for you to tell me where exactly I am wrong.
P: 5,462
 This is my reading of your argument, I hope that I have made it clear enough for you to tell me where exactly I am wrong.
1) I have never stated that the volumes are additive. To do so would be to promote a falsehood.

2) I have stated (repeatedly) that the density of salt water is greater than that of fresh water.

3) That if you mix some salt water with some fresh water the resultant liquid will have a density intermediate between the two.

4) The the volume of the mixture will be equal to the mass of the mixture divided by its density.

Which of these statements do you disagree with?
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 Quote by Studiot 1) I have never stated that the volumes are additive. To do so would be to promote a falsehood.
So if you have a 1 litre of salt water, and 1 litre of fresh water, put them together and shake them up, how much water do you have?

The answer may not be exactly 2 litres, but in my calculations I have assumed that it will be. Please can you clarify for me that this is your objection. If not what is your objection?

(If yes: How important is this effect? Anyone)
P: 5,462
 So if you have a 1 litre of salt water, and 1 litre of fresh water, put them together and shake them up, how much water do you have?
I assert that my comment (4) is the only way to answer this, using experimental salinity-density curves which are published in geoscience texts. Temperature will also need to be accounted for.

I also said that I do not know if the variation is significant only proper calculation will show this.
However I do know that there has been discussion in this thread about the effects of the difference in density btween salt and fresh water. I also know that there is no maximum density at 4oC in seawater as with fresh. The density/temperature cureve follows that of a normal substance, increasing steadily to the freezing point.

go well
 Sci Advisor PF Gold P: 1,783 OK Now, let's just do the math. Put 1.025Kg of ice afloat in (V-1) cubic meters of sea-water with surface density 1.025 kg/m^3. The sea water then contains V-1 cubic meters of water = (V-1) kg and 0.025(V-1) kg of dissolved salt. The ice displaces 1.025 kg = 1 m^3 of sea-water. So the containing volume below surface is (V-1)+1 = V cubic meters. Now melt the ice. You have V+0.025 Kg of water containing 0.025*V kg of salt. The below-surface volume will have increased from V to V+0.025. This assumes no significant change in volume of a fixed mass of water due to the amount of salt added. Remember that surface salinity is a bit less than at depth. There may be a slight affects due to changes in compressibility of water at depth but remember that water is supporting the same weight above it whether its ice or brackish water unless you significantly change the density at depth. That would cause slight additional increase in volume. Change in salt concentration may also change the compressibility of water and I'm not sure how. But I think all this is negligible relative to the 2.44% addition of the ice's mass to the below surface volume upon melting. That in turn is a small percentage of the total ice volume for floating ice. Finally remember that this does not apply to water resting upon land e.g. the Southern ice-cap. Since the only water it displaces is the amount needed to fill the volume of ice which is below the sea-level.
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 Quote by jambaugh OK Now, let's just do the math. Put 1.025Kg of ice afloat in (V-1) cubic meters of sea-water with surface density 1.025 kg/m^3. The sea water then contains V-1 cubic meters of water = (V-1) kg and 0.025(V-1) kg of dissolved salt. The ice displaces 1.025 kg = 1 m^3 of sea-water. So the containing volume below surface is (V-1)+1 = V cubic meters. Now melt the ice. You have V+0.025 Kg of water containing 0.025*V kg of salt. The below-surface volume will have increased from V to V+0.025. This assumes no significant change in volume of a fixed mass of water due to the amount of salt added. Remember that surface salinity is a bit less than at depth. There may be a slight affects due to changes in compressibility of water at depth but remember that water is supporting the same weight above it whether its ice or brackish water unless you significantly change the density at depth. That would cause slight additional increase in volume. Change in salt concentration may also change the compressibility of water and I'm not sure how. But I think all this is negligible relative to the 2.44% addition of the ice's mass to the below surface volume upon melting. That in turn is a small percentage of the total ice volume for floating ice. Finally remember that this does not apply to water resting upon land e.g. the Southern ice-cap. Since the only water it displaces is the amount needed to fill the volume of ice which is below the sea-level.
I think we agree then. I already did "the math" on page 1. Now we're discussing how valid that little assumption of 'no significant change in volume of a fixed mass of water due to the amount of salt added.'
P: 5,462
 The ice displaces 1.025 kg = 1 m^3 of sea-water