Melting Ice

Classical Mechanics Level 2

You have a beaker of water with ice floating on top. The beaker has markings to indicate the amount of liquid in it. The current level of the water (with ice) is at a mark of 100 ml 100 \, \text {ml} on the beaker.

You are in a room at a temperature of 2 0 ∘ C 20^\circ C . What will the level of the water be after all of the ice has melted? (to the nearest ml)

Details and assumptions

  • The density of water is 1 gram per cubic centimeter

  • The density of ice is 0.9167 grams per cubic centimeter

105ml 50ml 100ml 96ml

Joe Aulicino by Joe Aulicino , 21, USA

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1 solution

Pratyush Pandey
Feb 21, 2017

The melted ice continues occupying the volume it was initially occupying. The crux of this problem is that floating ice, after melting completely, occupies same amount of volume that the submerged part of ice was initially occupying. This can be proved easily by densities given. Bonus - If this is true, why do melting ice caps by global warming is said to cause rise in sea levels?

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Because the Antarctic ice caps are not floating in water but rather resting on land

Joe Aulicino - 4 years, 3 months ago

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This is perfect. I am glad my explanation did not confuse the basics as to where majority of melting ice caps really reside.

Pratyush Pandey - 4 years, 3 months ago

Joe has given right answer but I have a different one. Because sea water is salty and has higher density so when ice melt with density lower than sea water, it causes the rise in level. Reply me if I am wrong.

Kaushik Chandra - 4 years, 3 months ago

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Perfect again. To elaborate, the common misconception that floating ice won’t increase sea level when it melts occurs because the difference in density between fresh water and salt water is not taken into consideration. Archimedes’ Principle states that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces. However, freshwater is not as dense as saltwater(1.028 g/cc), freshwater actually has greater volume than an equivalent weight of saltwater. Thus, when freshwater ice melts in the ocean, it contributes a greater volume of melt water than it originally displaced.

Pratyush Pandey - 4 years, 3 months ago

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