Question about Melting and its effect on volume.

[hferdjal]

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One of the answers to my kaplan questions say that when you transfer heat to a ice-water bath, the ice begins to melt. And since ice has a smaller density than water, its melting decreases the volume of the bath. Thus, the height of the bath increases, and volume increases.

My question is this. What does ice's smaller density have to do with a decrease in the volume OF THE BATH? Doesn't the ice's melting into liquid INCREASE the volume?

And more so, I don't exactly understand why the height of the bath increases either!

Would anyone be so kind to clear my misconceptions? 🙂

 

[axp107]

I remember this question.. I thought the height stays the same if you melt an icecube in a cup of water.

 

[baby methuselah]

ht stays same

 

[thecoolest47]

density = mass/volume

rearranging this formula, mass=density*volume

given that the ice, and the water that it is melted into will have the same mass, increasing the density of a substance (as is done when ice melts to water) will decrease the volume of that substance.

Hopefully I was clear!

Cheers

 

[hferdjal]

I remember this question.. I thought the height stays the same if you melt an icecube in a cup of water.

Yea, come to think of it, that's correct. And yup, this is related to Kaplan FL 8. I'd post it, but not sure if that's okay with kaplan. I'm hoping it's irrelevant since it's the principle I'm confused on, and that's "How does the height of a bath increase when ice is melting?"

 

[hferdjal]

density = mass/volume

rearranging this formula, mass=density*volume

given that the ice, and the water that it is melted into will have the same mass, increasing the density of a substance (as is done when ice melts to water) will decrease the volume of that substance.

Hopefully I was clear!

Cheers

Yea that explains why the volume decreases, thanks. But as a follow-up, why does the overall height of the bath increase then?

 

[xlr8]

The overall height remains the same. I was very bothered by this at first since it isnt very intuitive, so I worked the entire problem out the long way.

Sparing the details, for an object that floats in a liquid, the portion of the liquid that is submerged and above the liquid sums to a volume of (I worked out the volumes submerged and not submerged separately and added them):
Ps/Pl * Vs (Ps = density of solid, Pl = density of liquid, Vs = volume of solid)

This is also equal to the portion of the solid submerged using the ratio of densities trick. So from this you can say that for any object that floats in a liquid, when it melts it will occupy the portion that was submerged, resulting in no height change.