# Temperature change in ice water interface

1. Mar 1, 2016

### Elena14

A metal block at 500 K is kept on a large ice slab at 273 K.The metal block completely sinks inside the ice slab. I was told that the water in contact with ice would not change its temperature while the block sinks down and hence the "only" heat transfer from the metal block to ice slab will occur to provide for the latent heat of fusion. Why would not the water in contact with ice change its temperature?
I understand that the block would start to sink as soon as the ice at 273 K converts to water at 273 K. But is it correct to say that the water in contact cannot change its temperature until it is in contact with ice?

Last edited: Mar 1, 2016
2. Mar 1, 2016

### BvU

In the ice cube, I should hope ?
The ice keeps the water at 273 K. At that temperature ice and water are in phase equilibrium: add heat $\Rightarrow$ ice melts; remove heat $\Rightarrow$ water freezes.
Don't understand the question. In contact with the metal ? Change the temperature from what to what ?

3. Mar 1, 2016

### Elena14

By changing the temperature I mean the effect the hot metal block will have on water.
How will the ice keep the water at 273 K

4. Mar 1, 2016

By melting !

5. Mar 1, 2016

### Elena14

Why will it melt? What will provide it latent heat of fusion to do that?

6. Mar 1, 2016

### BvU

If the water warms up above 273 K the heat is taken away by the ice: it melts.

7. Mar 1, 2016

### BvU

The metal melts a very thin layer of water (*). The weight of the metal pushes the water to the sides where it can escape upwards, thus allowing the metal block to sink into the ice.

(*) That thin layer of water is in contact with the metal topside and with the ice on the bottom side. So there is a temperature difference that drives downward heat transfer.

8. Mar 1, 2016

### Elena14

The metal block would convert the ice at 273 K to water at 273 K and make its way to the bottom. And since the water so converted is at 273 K and the ice is also at 273 K there will be no heat flow. When the metal block reaches bottom, it has no more heat left and it is also at 273 K, and hence the heat transfer would stop. But while the metal block is inside the ice cube, it will be in contact with water it had just converted as well as ice at the same time but it will provide the latent heat of fusion to ice to convert it to water at 273 and not provide more heat to water. Correct me if I am wrong?

9. Mar 1, 2016

### jbriggs444

To re-state and amplify what BvU has said...
The layer of water between metal and ice has non-zero thickness. There is a temperature gradient within the water and a corresponding heat flow.

Consider an even thinner layer surrounding the current water/ice interface. This region moves over time. There is a mass flow of 273 K ice into this interface layer. There is a mass flow of 273 K water out of this interface layer. There can be no temperature gradient in the ice -- it is already at 273 K. It cannot become warmer without melting. Accordingly, there is no heat flow within the ice at the boundary of this interface layer. There is a temperature gradient within the water and a corresponding heat flow within the water into this interface layer.

The rate of of heat flow into the water/ice interface region will correspond to the mass flow rate times the latent heat of fusion per unit mass.