Water and Ice Density Question

[Josh138]

Hi everyone,

I just had a quick question in the phase change (chapter 7) of the 2nd book of the TBR Chem book series. My question is on example 7.21 on page 94:

If an ice cube floats in a glass of water in such a way that the surface of the water is flush with the brim, and the ice cube sticks out above the level of the water, what will occur as the ice cube melts?
A) The water level will drop below the top of the glass
B) The water will overflow the top of the glass
C) The water will remain flush with the top of the glass.
D) The water will rise above the top of the glass, but will not overflow it.

Answer: C. Explanation given by the book: The mass of the water displaced by the floating ice cube is equal to the mass of the water generated by melting the ice cube. When the ice cube melts, the water that is formed has exactly the same mass and density as the water displaced. This means that it also has the same volume, so it fills the volume occupied by the submerged portion of the ice cube. The net result is that the level of the water remains constant at the top of the glass.


I thought the answer was A, because isn't ice less dense than water? Therefore taking up a larger volume of space? Thus if the ice melts into its liquid form (less dense), shouldn't it take up less space and therefore the water level would drop?

Could anyone clarify this for me? Thanks in advance!


EDIT: Yes I made a typo, the correct answer is C

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[milski]

Either you or TBR has a typo - the correct answer is C and that seems to match with their explanation.

It is correct that ice is less dense, it would not float otherwise. That means that its liquid form is more dense and when it melts its volume will decrease. Keep in mind that some of the ice is above water, so its initial volume is whatever it occupies under water + whatever is above the water.

 

[sakabato93]

Hi everyone,

I just had a quick question in the phase change (chapter 7) of the 2nd book of the TBR Chem book series. My question is on example 7.21 on page 94:

If an ice cube floats in a glass of water in such a way that the surface of the water is flush with the brim, and the ice cube sticks out above the level of the water, what will occur as the ice cube melts?
A) The water level will drop below the top of the glass
B) The water will overflow the top of the glass
C) The water will remain flush with the top of the glass.
D) The water will rise above the top of the glass, but will not overflow it.

Answer: C. Explanation given by the book: The mass of the water displaced by the floating ice cube is equal to the mass of the water generated by melting the ice cube. When the ice cube melts, the water that is formed has exactly the same mass and density as the water displaced. This means that it also has the same volume, so it fills the volume occupied by the submerged portion of the ice cube. The net result is that the level of the water remains constant at the top of the glass.


I thought the answer was A, because isn't ice less dense than water? Therefore taking up a larger volume of space? Thus if the ice melts into its liquid form (less dense), shouldn't it take up less space and therefore the water level would drop?

Could anyone clarify this for me? Thanks in advance!


EDIT: Yes I made a typo, the correct answer is C

When you place the ice cube into the glass, the water moves up in displacement, correct? This is in accordance with Archimedes' Principle which states that the MASS of water displaced equals the MASS of the object inserted into the water. In this case, the volume of water in the glass will not change as the ice melts, because it corresponds to the mass of the ice cube, not the density. If you were to drop an object that was more dense than water and it were to melt, then the resulting volume would also be equal to the volume after initial water displacement.

http://www.planetseed.com/posted_faq/50440

 

[mehc012]

When you place the ice cube into the glass, the water moves up in displacement, correct? This is in accordance with Archimedes' Principle which states that the MASS of water displaced equals the MASS of the object inserted into the water. In this case, the volume of water in the glass will not change as the ice melts, because it corresponds to the mass of the ice cube, not the density. If you were to drop an object that was more dense than water and it were to melt, then the resulting volume would also be equal to the volume after initial water displacement.

http://www.planetseed.com/posted_faq/50440

Wait a second...if you were to place a solid object with a greater density than that of water into the glass, then the volume of water displaced would be equivalent to the VOLUME of the object, not the mass. In fact, the mass of the water displaced would by definition be less than the mass of the object.

When the object melted, it would then take up more volume, and the glass would overflow. The case of ice works only because mass ice = mass water displaced AND density water = density melted ice. In other words, it only works because it is floating initially.


To throw out a counter example, if you were to tether a block of ice below the surface of the water, then when it melted, the water level would lower, because mass_ice < mass_{waterdisplaced}, so when the ice melted, it would become less water than the amount it was displacing initially.