Level of ice dropped in water after it melts

[djsourabh]

1. If we drop an ice cube in a glass of water ,check the level of water & let it melt, what happens to the water level afterwards? Does it rise, remains the same or lowers?

Homework Equations

The Attempt at a Solution

 

[rude man]

What do you think? Figure it out based on Archimedes' principle.

 

[djsourabh]

well I think it should lower.

 

[adjacent]

well I think it should lower.

Why?Use common sense and think.If you put something with a volume in water,would the total volume increase or decrease?

 

[Tanya Sharma]

Why?Use common sense and think.If you put something with a volume in water,would the total volume increase or decrease?

Are you trying to say volume of ice and molten ice is same ? I think common sense can lead you to wrong answer in this case .Better use principles of physics.

 

[adjacent]

Are you trying to say volume of ice and molten ice is same ?

Volume of ice and water doesn't matter.Ice melts and it will increase the total water volume.If it is to decrease,Ice would melt to liquid of volumes -x.

 

[Tanya Sharma]

Volume of ice and water doesn't matter.Ice melts and it will increase the total water volume.If it is to decrease,Ice would melt to liquid of volumes -x.

So according to you,after ice melts total water level should rise .Is that what you are trying to say?

 

[adjacent]

So according to you,after ice melts total water level should rise .Is that what you are trying to say?

Yes.And I said that in that post #6

 

[Tanya Sharma]

Yes.

In that case you need to study Archimedes principle .Your answer as well as your reasoning is completely wrong .

 

[adjacent]

In that case you need to study Archimedes principle .Your answer as well as your reasoning is completely wrong .

What?I don't see any reason why my answer is wrong.Please explain.

 

[Tanya Sharma]

What?I don't see any reason why my answer is wrong.Please explain.

We should allow OP to come up with the answer .

Hint has already been given by rude man in post#2 and by me in post#9 .

 

[adjacent]

In that case,OP has given the answer that it should lower.

 

[Doc Al]

What?I don't see any reason why my answer is wrong.Please explain.

You are to compare the water level immediately after the ice cube is placed in the glass with the water level after the ice cube melts.

 

[djsourabh]

You are to compare the water level immediately [I]"after [/I]the ice cube is placed in the glass with the water level after the ice cube melts."

Yes this is what my question is. Answer:-The level should lower. Anomalous behaviour of water...

 

[ehild]

It would happen if you forced the ice under the water level. But it floats, not the whole volume is immersed.ehild

 

[djsourabh]

It would happen if you forced the ice under the water level. But it floats, not the whole volume is immersed.ehild

Please Elaborate. I don't think this would be easy question...We may have to consider the temperature of water before adding & after melting the ice cube...If its at 4 degree Celsius...ohh man this gets interesting...

 

[rude man]

Please Elaborate. I don't think this would be easy question...We may have to consider the temperature of water before adding & after melting the ice cube...If its at 4 degree Celsius...ohh man this gets interesting...

You do not need to consider the water temperature. Assume that doesn't matter.

Hint: since you know that ice floats in water you also don't need to know the density of either the ice or the water, nor anything else.

As I said before: your first step is to invoke Archimedes' principle: what is the volume of displaced water when the ice is first immersed? Relate to the mass of the ice.

 

[SammyS]

Please Elaborate. I don't think this would be easy question...We may have to consider the temperature of water before adding & after melting the ice cube...If its at 4 degree Celsius...ohh man this gets interesting...

While it is true that water displays anomalous expansion between 0°C and approximately 4°C, that's a very small effect compared to the amount of expansion that water undergoes as it transitions from liquid to solid.

I assume that if the question you are trying to answer

"If we drop an ice cube in a glass of water ,check the level of water & let it melt, what happens to the water level afterwards? Does it rise, remains the same or lowers?"​

comes from a textbook, or was asked by a teacher, then the small amount that the liquid water expands or contracts as it cools while that the ice melts, is ignore-able.

Ice near 0°C is about 9% less dense that liquid water near 0°C

Liquid water at 4°C has a density of about 999.8395kg/m³.

Liquid water at 0°C has a density of about 999.9720kg/m³.

That's a decrease in density of about 0.013% in cooling from 4° to 0°C .

That's likely negligible compared to the 9% difference for the phase change.

The following graph is on Wikipedia .

 

[ehild]

The problem does not say what time after the ice melts should you check the water level.
The glass of water is not isolated from its surroundings. It has the same temperature as the room before you drop the ice. Check the level of water immediately you drop the ice, before the temperature changes.
The ice melts and the water cools down. Because of the temperature difference, heat is transferred from the surroundings. After some time, the water becomes in thermal equilibrium with the surrounding again. Check the water level at that time. Is it lower of higher that it was just after dropping the ice in?
It also could happen that the initial temperature of the water was very near to 0 °C so the ice melted very slowly and the temperature did not change during the process.

ehild

 

[Simon Bridge]

The problem does not say what time after the ice melts should you check the water level.

That's why the context matters. The context should be provided by OP.

Lets cut djsourabh some slack huh?
I suspect this is a secondary-level class in the principle of Archimedes.

@djsourabh: is that correct?

Asked at college level, there would, indeed, have to be some discussion about assumptions made and the significance of various possible initial and final conditions (compared with the methods used for measurement) - but for a high-school level question this would be overthinking things somewhat.

Lynchpin: A floating object displaces it's own mass in water.

It may work out to be instructive to invent a bunch of dimensions (i.e. how big is the glass and how high is the water to begin with? How big is an ice cube? Don't know? Make them up!) and use your textbook figures for the densities of water and ice. The fact that ice is water means that these figures are not needed if you understands the principle. The discussion shows you do not - no problem, you don't have to because, if I'm right, you are still learning the principle - therefore the longer approach is recommended.

Aside: I last encountered this problem at a teachers conference - only, instead of a glass of water, it was a Gin and Tonic. Kept people busy for weeks. I was the only one did the experiment. To get good statistics the experiment had to be repeated many times. Trouble is, the conclusion was illegible.

 

[rude man]

The water before immersion could be an arbitrarily large volume at a temperature arbitarily close to the freezing point, so there need not be any significant water temperature difference before & after the ice melted to begin with.

 

[Simon Bridge]

Yes - or anything you like. Although "a glass of water" does not normally call to mind something like an ocean.
We also need to consider that the "arbitrarily large..." etc way of describing things may not be familiar to a high school student.

This is the stage we really need feedback from the student.