A popular physics trivia question asks what the temperature of ice water is. The answer is, unsurprisingly, 0 °C, 32 °F, 273 K, but the surprising bit about it is that this is inevitably so; even if you put the vessel with ice water on a stove and heat it, the temperature of the water will - so the story goes - remain at that level as long as there is still ice left in it. Supposedly, this is because any heat added to the vessel will lead to the melting of more ice, which is a phase transition that requires energy, and this energy is extracted from the water and reduces its temperature. The temperature of the water can, supposedly, only begin to rise once all ice is gone.
It doesn’t sound implausible in theory, but I wonder if it really holds in practice. I wouldn’t find it far-fetched, for instance, to think that some kind of thin film of cold water forms around the ice that insulates it from the surrounding water and allows that ice not to melt even though the water is warmer than 0 °C. I am also rather confident that I’ve had drinks that were not chilly cold even though there were still some sad remnants of ice cubes floating in them. So, thermodynamically speaking, is there truth to that trivia that water with ice in it will inevitably have this constant temperature?
I have never heard this trivia question and I don’t agree with the answer. First, it does not define “ice water.” One cube? More ice than water? Second, if you plop ice into a glass of water it does not cause the water in the glass to drop to the freezing point. It will eventually come to equilibrium at the weighted average temperature of the ice and the water before you added the ice, which happens after the ice melts. Which is why it melts. Second, if you heat it, the water is not changing temperature uniformly. The water nearest the heat source will heat, circulate, and melt the ice.
Can you cite a source for this specious “fact”?
In theory, at the micro level, if you have ice at the freezing point and add just enough heat to make it melt, the water will be at the freezing point, because all the added energy went into making the ice melt, not raising the temperature. This is somewhat theoretical because it’s hard to add heat to the ice without adding it also to the water created by melting the ice. And this is not the same as a glass of ice water.
As water heats, it rises, right? The ice water on a stove will be heated at the bottom, and that hot water will create mini current through the container, possibly convection currents. The warm water will brush against the ice, transfer some of its heat to the ice, melting the ice and cooling itself, and sink back to the bottom of the pan.
As a different counterfactual, suppose this principle were true. If it were, then ocean water would all be 0 Celsius (or -2 Celsius, the ocean’s freezing point), since there are ice bergs floating in it. But of course it’s not, because temperature doesn’t tranfer instantaneously between different areas of liquid.
Of course there is truth to it, but for a really accurate fixed temperature you need a triple-point cell and there is a whole procedure to make sure everything is in equilibrium, that there is no air or impurities in the system, and so on.
Thermodynamics deals with steady state or equilibriums (I don’t know why the word dynamics is in there). So for the ice water case, if you use thermodynamics: you are looking at a well stirred vessel or the liquid after infinite time.
You are looking to a branch of science/engineering called Heat Transfer. This is where thermal gradients / mixing like these are studied. Ask someone familiar with CFD and they can make a 3-D model of the system you are describing.
Also look at the Leidenfrost phenomenon. A droplet of water on a hot metal pan does not immediately evaporate but instead skitters around on a layer of steam which reduces the speed at which the water is heated to evaporation, air being a poorer heat conductor than metal.
You can as others point out also see the effect of dropping an ice cube in a room temperature glass of water. It takes quite a while to melt. My theory is this:
As mentioned in previous post, the ice will surround itself with a layer of cold water. The ice ha to draw - by conduction - heat from the water in order to melt; but after a bit of melting. the surface layer coat of water is fairly cold so transfers less heat than if it were the same temperature as the rest of the glass. Obviously, convection currents will slowly transfer this heat to the rest of the water and supply warmer water to the coating of the ice cube. The question is how fast heat transfers between the ice surface and the surrounding water.
The one-day course I took once on modelling ths sort of thermodynamics said the best way to estimate heat transfer speed is to start with the assumption it is proportional to the difference in temperature. (And then do real-world experiments or observations to validate that hypothesis) Whether the water is heated from down below simply increases the convection currents.
Also be aware that water is unusual in that at 4°C it stops contracting with lowering temperature and starts expanding. This is why ice floats, it is slightly less dense than water at approximately(!) the same temp. So left to its own devices, with minimal external heat being added, a collection of ice and water will find an equilibrium where ice is 0°C or less but the water underneath the ice is about 4°C or slightly less - which we see happening in every pond every winter up north here.
The original thermodynamic question as stated seems to be for steady state. If we observe this mix in anything except a walk-in refrigerator at 0°C then it is not in a steady state; it is absorbing (or giving off) heat to the surrounding environment.
Also, oceans have salt (believe it or not) and so a much lower freezing point. I read some report about the Titanic once that said the water temperature in the ice-water ocean when the ship went down was about -1.5°C.
It is actually a bit of work to get a beaker of water to 32 F. You need a lot of crushed ice like slush and constant stirring. We used ice baths for thermocouple reference and they had a small impeller in the bath.
The “temperature” of a bucket of ice and water is the average temperature of all the stuff in the bucket. Not the temperature of any, much less every, subset of the stuff in the bucket.
Lots of confusion comes from talking about the temperature of a macroscopic something that consists of lots of subcomponents each at a different temperature.
Yeah, the missing bit of the OP’s trivia question is “in thermal equilibrium”. So you are heating the water so slowly that the entire system maintains a uniform temperature at all times.
The concept is Latent Heat of Fusion (wikipedia calls it “Enthalpy of Fusion”, but I learned it as “Latent Heat”) (Also fusion means “melting” – not the cool fusion). Basically as you add energy to a normal solid substance (while keeping it in equilibrium), the temperature of the substance increases until it starts to melt, then while it’s melting the temperature doesn’t increase and the energy goes into melting until all of the melting is done, and only then does the temperature start to increase again.
Exactly. An underutilized property of sous vide circulators is their ability to transform a cooler into a rapid chiller device. You can cool a bottle of champagne or a couple of six packs of beer in just a few minutes by dropping them in an ice water bath with a sous vide device in use.
Actually no, not between 0°C and 4°C. As md-2000 wrote: “Also be aware that water is unusual in that at 4°C it stops contracting with lowering temperature and starts expanding.” Thus between 4°C and freezing water behaves just the other way around: it rises when it gets colder and sinks when it warms up.
If you have more volume of crushed ice than liquid water in a cup, and you stir it up pretty well, it’s going to approach the freezing point of water. Depending on how precise you need it, it is probably going to be close enough for most purposes. This is how I used to calibrate bi-therms.
Any other situation is going to have the water at a larger temperature gradient, in fact, as noted above, the bottom of a container that has ice in it is going to actually be warmer, approaching 4C.
The water that touches the bottom of the pan will necessarily heat beyond that point, though: prior to that point, it’ll stay close to the bottom of the pan where the heat is. So while this is a nifty note, it doesn’t affect the dynamic.
Nobody said anything about the whole setup being heated from below, I think you are not right in your assumtions. I think we are speaking about water and ice. Mixing is required, heating is more than superfluous: it changes the whole thermodynamics. There is no equilibrium while heating.
You are right. My mind must have ignored it, it makes no sense. I stand by my post: if you heat it, you will get a gradient. It’s unavoidable. And convection for water between 4°C and 0°C works counter intuitively.
Well, not quite. The last time someone carefully measured the freezing/melting point of pure water was in 1995. And they concluded it was 0.000089(10) °C. I am not aware of any studies since then.
I stand by my post: if you heat it, you will get a gradient. It’s unavoidable. And convection for water between 4°C and 0°C works counter intuitively.