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A beaker is exactly full of liquid water at its freezing point and has an ice cube floating in it, also at its freezing point. As the cube melts, what happens to the water level in these three cases: (a) the cube is solid ice; (b) the cube contains some grains of sand; and (c) the cube contains some bubbles?

A beaker is exactly full of liquid water at its freezing point and has an ice cube floating in it, also at its freezing point. As the cube melts, what happens to the water level in these three cases: (a) the cube is solid ice; (b) the cube contains some grains of sand; and (c) the cube contains some bubbles?

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
According to Archimedes’ principle, the weight of the ice is equal to the weight of the volume of the water displaced by it. When the ice cube melts, it fills the volume of the water displaced by it.
(a) When the solid ice melts, the volume of the liquid that is melted from ice is equal to the volume of the water displaced by it. Thus, it simply fills the volume of the water displaced by it. This means that the level of the water will not change.
(b) When the ice cube that contains some grains of sand floats in the water, the total weight of the ice cube and sand grains is equal to the weight of the water displaced by it. As the ice melts, the sand grains were settled down the water. The water that is melted from cube has to fill the displaced volume of the water. Due to the presence of the sand grain at the bottom of the water, there is extra volume occupied by them also. Therefore, the level of the water will rise.
(c) When the ice cube that contains air floats in the water, the total weight of the ice cube and the air is equal to the weight of the displaced the water. As the cube melts, the corresponding air is expelled out from the water. This means that the water that is melted from ice has to fill the volume of the water displaced by the ice cube containing air. As the air is expelled out, the melting ice is filling only the volume displace by it and not by air. In order to fill the volume displaced by air, the level of the water should decrease. Thus, there will be a fall in the level of the water.

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