Question

A block of 100g of ice at 0˚C is added to some water at 40˚C contained in a vessel of negligible water equivalent. What should be the least amount of water for entire block to melt? If the amount of water (at 40˚C) is twice the required amount to just melt the block, what is the final temperature of the mixture?

Answer 1

We know thermal expansion, that is, when we heat any material, it expands and its expansion depends on its thermal coefficient of expansion. 

But water behaves anomalously. When water(ice) is heated upto 0°C it expands with the heat supplied. But if we continue heating, it starts getting compressed. This compression continues upto 4°C. After that it starts expanding again. This behavior of water from 0°C to 4°C is called as the anomalous behaviour of water.

From this we understand that volume of same amount of water at 4°C will be less than that at 0°C.

Now if we add ice at 0°C to water at 4°C, the ice will melt absorbing heat from water. As water losses heat, it's temperature will decrease.  Now the temperature of whole system will be between 0°C to 4°C but not 4°C. Thus temperature of the system has definitely decreased and according to anomalous behaviour its volume will increase with decrease in temperature upto 0°C

Thus the volume of water will increase