# Will level of liquid increase if ice melts in it?

1. May 3, 2012

### jd12345

How will the level of liqid change if ice melts in it?
If its water then there is no change - i know this will happen but i don't understand it( intuitively )

Moving on to other liquids - like oil and mercury - what will happen to their levels?

I actually did find the result for water by writing equations but i do not understand it intuitively - same for others. Thank you

2. May 3, 2012

Assuming the cross-section is constant, the level of water can be said to be directly proportional to the volume of water + volume of water displaced due to the solid object. Now, the solid object here is ice, which is lighter than water, and hence, the volume displaced by it is equal to the weight of the ice cube (since the other portion is then out of water.) Now, when the ice melts, the weight does not change, and hence, the level does not change since the density of ice is less than water. The important facts here are:
1. Ice is lighter than water hence, the displacement is equal to the weight
2. Ice melts into water and not some other liquid whose density is different and hence, the displacement of weight is equal to the displacement of volume after melting.

3. May 4, 2012

### jd12345

Thanx a lot
But could you do the same thing for another liquid like oil
Ice floating in oil? What would happen when ice melts - would help me a lot - thank you

4. May 4, 2012

### haruspex

Any object floating in a liquid displaces a volume of the liquid corresponding to the mass of the object.
If it changes state but still floats then there will be no change to the level of liquid.
Water ice floating on oil, then melting, would sink, water being heavier than (most if not all) oil. It would therefore be displacing less volume than before and the level would drop.
In fact, it's not quite straightforward with ice floating in water. The melting ice will cool the water, causing it to shrink slightly if warmer than 4C, or expand slightly if cooler.

5. May 4, 2012

Thank you!