# Why won't water freeze if you put ice in it, despite ice being frozen?

Just now I got some room temperature water and added some ice to cool it, and it just came to me, like the scientist I wish I was ... why doesn't frozen (freezing point) ice added to higher temperature liquid compound force the water molecules to solidify?

Why won't water freeze if you put ice in it?

It will, even at room temperature. You just need a big enough, cold enough ice cube.

Don't believe it? Add a few drops of water to an ice cube in an ice cube tray (which is the same as adding an ice cube to a few drop of water). Wait a few seconds, turn the tray upside down. No water will fall, presumably because it has frozen. Repeat, but immediately turn the tray upside down. You'll get a wet floor. You can conclude that, given enough time, the water will be frozen by the ice. To the whys and hows:

From the second law of thermodynamics we know that:

An isolated system, if not already in its state of thermodynamic equilibrium, spontaneously evolves towards it.

And

Heat cannot spontaneously flow from a colder location to a hotter location.

So if you put ice and water together in a cup, heat will flow from the water to the ice until they reach thermal equilibrium, which will be a temperature between the water's initial temperature and the ice's initial temperature. If the temperature of the ice was low enough or if there was enough ice for the water to keep giving away heat, then the water will freeze. That's considering our cup is an isolated system.

Why don't you usually see that happening? Well, regular ice cubes are probably around −5 °C, and there usually is more water than ice in a cup, so before the water has a chance to reach 0 °C all the ice has already melted. Besides that, the ice is receiving heat from the room, unless you're in a place where's below 0 °C. In that case, the water WILL eventually freeze, but mostly because of the environment.

Water, like most substances, requires more energy gain or loss to undergo a state change (from solid to liquid, liquid to gas) than to be warmed or cooled by a degree of temperature without changing state. Liquid water requires about 4.2 Joules per milliliter per degree Celsius to raise or lower its temperature. However, the Latent Heat of Fusion (Lf) of water (the energy that must be added to ice to melt it or removed from water to solidify it at the freezing point) is 334 Joules per milliliter.

Therefore, for ice to freeze the surrounding water, the ice must be cold enough that it can afford to gain enough energy to invoke this state change, without melting itself. Now, solid ice has a lower volumetric heat capacity; it only takes about 1.9 J/(mL * K) to change its temperature. So, for an ice cube, let's say 10mL in volume, to freeze 1mL of the surrounding water (at 0°C) without melting itself, the ice must be able to absorb 334J of energy without melting. That means the ice must be -16.7°C, or about 2°F.

That's well within the range of your average freezer (which in the US is normally kept around 0°F to ensure everything stays good and frozen), but that back-of-the-envelope calculation assumes the energy is gained evenly throughout the entire ice cube. This doesn't happen; it's common knowledge that ice melts from the outside in, and that's because it's a relatively poor conductor of heat compared to substances like metals, which sometimes seem to instantly liquefy when they reach their melting point. For the ice to be able to cool that kind of water volume without melting, therefore, it must be much colder; cold enough that the ice can afford to gain enough heat just in a few millimeters of its outer surface layer to freeze the water.

Regardless of this, if you have a fridge with in-door ice and water, and you fill a cup with the ice and then pour the water over it, the ice will clump; the combination of two cubes in close proximity, a small volume of already-cold liquid water in a thin layer between them, and the ice being colder than freezing, results in the ice freezing the water, joining the two cubes. This happens throughout the ice. If you go with crushed ice, which has smaller pieces but more surface area and a larger volume of frozen water to total water, the effect is even more pronounced. But, eventually, the overall thermal energy of the room adds more energy into the glass of water than the ice can absorb without melting. So, it melts.

• The latent heat of vaporization (now normally referred to as the enthalpy of vaporization) and the latent heat of fusion (enthalpy of fusion) are different. The former is boiling, the latter is melting. For water, the enthalpy of vaporization (boiling) is 40.7 kJ/mol (2300 J/mL) whereas the enthalpy of fusion (melting) is 6.01 kJ/mol (334 J/mL) - but aside from the "typo", good points.
– R.M.
Feb 25 '16 at 20:37
• @R.M. Thanks for the comment. The edited answer fixes the "typo". Feb 3 '20 at 19:36

At room temperature, water is a liquid. So the ice will gradually turn into liquid.

You may ask your question in a different way: if you add water to ice, why doesn't the ice turn into liquid? It does, at room temperature.

If you add water to ice, at freezing temperature (Antarctica), the water turns to ice.

I think it is mostly due to the surrounding air temperature.

• Well, yes and no. Ice will freeze cold water in a glass sitting on a table, as the colder ice and warmer water exchange energy to reach a rough equilibrium. But, the overall equilibrium of the larger system, at room temperature, eventually adds more energy than the ice can absorb without melting, so it does. Jun 13 '13 at 19:31
• The question did not specify what the ambient temperature is (it said room temperature water, not system at room temperature). It might be best to first look at the question for an insulated system (no heat transfer), and then perhaps say what happens if you allow heat transfer. Feb 3 '20 at 19:48

Now if we have a look on values of sp heats of ice and water.

L(ice)=334 kJoule per kg

C(water)=4200 Joule per kg per degree Celsius

C(ice)=2100 Joule per kg per degree celsius

If we want 1 kg of water at 1 degree celsius to first reach zero degree Celsius and then be converted to ice the amount of heat released will be greater than 4200 joules

On the other hand, If we want 1 kg of ice at minus one degree celsius to first reach zero degree Celsius and then be converted to water the amount of heat required will be around 2100 joules

Therefore in general if we want water to be converted to ice the ratio of ice to water should be more than 2 isto 1. (Assuming temp of both are at same distance from 0degree celsius)