Case 1:

You take x litres of water and cool it to solid ice(say 0 degree) and measure the volume of ice as V1 liters. Now you let this ice melt at room temperature for some time T1 and measure the volume of water after melting as V2 litres. Will it reduce or increase or be the same ?

Case 2:

You take V1 litres of solid ice (say 0 degrees) floating in water. When it melts, what happens to the volume of the system (water + ice in a container) ? Does it increase or decrease or remains the same ?

Case 3:

Repeat case 2, except that you tie the ice cube to the bottom of the container. Now, does the water level increase or decrease or remains the same ?

Some doubts:

  • In case 2, when ice is floating, the water level remains the same, floating ice displaces water equivalent to its weight. Mass of the system is unchanged, so water level remains the same.

  • In a contradiction, if the system (water + ice) is isolated, they come to the equilibrium position between ice and water. Ice contracts till 4 degree Celsius and expands after that, water contracts as temperature drops. This confuses me as to decide upon what will happen to the volume of the system.

  • In first case, the volume is reducing till 4 degree celsius and increasing after that. At what temperature will the volume of water be the same as volume of ice ?


closed as off-topic by John Rennie, Rob Jeffries, ACuriousMind, Brandon Enright, Qmechanic Oct 25 '14 at 19:19

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  • $\begingroup$ Case 1 Volume of water decreases Case 2 Volume decreases, but the level of water remains the same. Case 3 Water level decreases. This is because teh water is more dense than ice. when the ice melts into water, it occupies lesser volume than it was occupying, this decrease in volume causes water level to decrease. $\endgroup$ – user49111 Oct 25 '14 at 7:00
  • $\begingroup$ It seems we answered at the same time. =) $\endgroup$ – QuantumBrick Oct 25 '14 at 7:02
  • $\begingroup$ Which part of the question requires rewording ? $\endgroup$ – Boopathi Rajaa Oct 26 '14 at 5:54

Ice floats. That's the reason life is possible in winter, when the lakes freeze: the water remains liquid under the ice, which floats (and forms) on the surface. This means $\rho_{ice} < \rho_{water}$, that is, ice is less dense than water ($\rho$ stands for density). If you take a certain mass $m$ of water and freeze it, then

$$\rho_{ice} = \frac{m}{V_{ice}} < \frac{m}{V_{water}} = \rho_{water} .$$

This implies that $V_{water} < W_{ice}$, that is, if you freeze a certain cube of water, then the icecube will be bigger than the original water cube. So, if you have a glass of water and ice and the ice melts, the volume will actually decrease. The level of the water must, on the other hand, remain the same, because the volume dislocated by the ice is a direct response to buoyancy. This is not true when the ice is tied at the botton of the glass: now, after the ice melting, the level will decrease.

What you meant in doubt 2 was "the volume of $water$ starts to increase as it freezes under 4 degrees celsius". Yes, that's true. That's why ice's density is larger than water's.

EDIT: Their volumes will actually be the same at some temperature, but to find that you would need to know the law of increase in volume due to temperature of water. I believe you can approximate the law for liquid water (over 4ºC) by

$$V = \left(\frac{nR}{p} \right) T ,$$

but for solid water and water under 4ºC I've no idea.


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