Que se passerait-il si je versais une quantité X d’eau bouillante dans un récipient constitué d’une quantité équivalente X de glace ?

[u/Educational_Car_2588]

À quantités équivalentes, que se produit-il lorsqu'on verse de l'eau bouillante dans un récipient entièrement constitué de glace? Lequel des deux cède en premier, et quel est l'état final du système?

Je ne suis point un scientifique, un chercheur ou tout autre synonyme de ces fabuleux corps de métier. Toutefois, si vous voulez aller plus loin, voici une difficulté plus élevé à mon sens:
La structure du contenant est décisive.

[u/TXOgre09]

Boiling water is at 100C by definition.

Ice can be any temperature at or below 0C. The problem is underdefined until you state the starting ice temperature. Let’s assume the ice is barely frozen, 0C.

If we ignore any heat gain or loss from the environment, and only consider the boiling water and the ice container, and we assume the ice and water are somehow contained (ie the water doesn’t melt a hole in the ice and drain out, the problem becomes pretty straightforward.

The ice gains whatever heat the water loses, and they reach a final combined temperature.

Let’s assume “same amount of each” means equal mass. Let’s say 1kg of each.

First we have to melt all the ice before it can start warming up beyond 0C. The amount of heat needed to melt it is called the latent heat of fusion. Water needs 334 kJ/kg to melt from ice to water. Then we need to look at how much heat is gained it lost as temperature changes, this is called specific heat. For water it is 4.2 kJ/kg*C. It take 4.2 kJ to heat a kg of water 1C.

So the 1 kg of boiling water will cool 79.5C from 100C to 20.5C as it gives up the 334kJ needed to melt the 1kg of ice at 0C. Now we have 1kg water at 0C and 1kg water at 20.5C, so it will average out to 10C once everything is equal.

In reality, the boiling water would give up a significant amount of heat to the environment while all that’s happening. And the whole process would happen on a smooth continuum, you’d have different temperature gradients of warm water, frozen ice, cold water, melting ice all at once. But the final equilibrium point is about right.

The thinner or flatter the ice the faster it will melt. The more surface area exposed to air the more the boiling water will cool to the air.

[u/CrateDane → u/TXOgre09]

Boiling water is at 100C by definition.

Depends on the pressure. But it's the reasonable place to start for a question like this.

If you performed the same experiment at the top of a mountain, the boiling water would not be as hot, and thus might not even have enough energy to melt all the ice. If you did it in a higher pressure environment, the boiling water would be hotter and you'd thus end up with a warmer puddle at the end.

[u/TXOgre09 → u/CrateDane]

Good point.

But I’d argue that “boiling” water means at atmospheric pressure and not higher pressure. The whole question changes wildly if we start going to the bottom of the ocean or on top of Everest or out in space or to other planets. Freezing sublimation points start changing with extremem pressures as well. It’s reasonable to assume the setting is somewhere people commonly live on Earth.

About half the world population lives where water boils at 100C, 85% live where it boils at 98C or greater, and 99% live where it boils at 90C or greater. The melting lowered the water temp 80C, so for practically anywhere on Earth you still end up with a cool puddle of water at the end, plus or minus a few C.

[u/Starlit-Dog → u/TXOgre09]

yeah, the starting ice temperature makes a huge difference in the outcome.

[u/TXOgre09 → u/Starlit-Dog]

Yes. It could quickly and easily make it to where the whole thing ends up a 0C mix of ice and water.

The ice would have to be super cold to start if you want to freeze all the boiling water and end up with just a block of ice. But it’s possible.

[u/GoGoGreenGiant → u/TXOgre09]

Finally someone actually answered the question.

Thank you

[u/Dixiehusker]

This depends a little on how cold the ice is. Ice can be below 0° c, but boiling water can't be above 100° c (except for occasional variances in the environment around it or any impurities in it). If I assume from your question that the ice is at 0° c, then both are right at the borders of phase changes. The ice will start to melt, which will take energy because it's changing its phase, and because of that it will drastically cool down the boiling water, which while it is boiling has not actually changed phases yet (except for any steam that has escaped and therefore is not applicable to this scenario) and will immediately begin cooling down and will immediately stop boiling. After all is said and done, you're going to get a a puddle of lukewarm water.

The boiling water will stop boiling first. If your question is when will the ice container fail and start to leak, that depends entirely on the dimensions of the ice container, but at some point you will have a puddle of water and no more ice.

[u/ShortysTRM → u/Dixiehusker]

Also, wouldn't ice violently fracture when you expose it to boiling water? I would think that would be the first thing to likely cause a leak, which alone would be a failure of the ice vessel.

[u/Dixiehusker → u/ShortysTRM]

It certainly could. I wouldn't call it violent because it's not likely to shatter into pieces, but this too depends a little on the dimensions. My money is on fractures running through the ice, but not enough to shatter it. Leaks are a different thing altogether. The crack will be very thin and water running through it could actually freeze inside of it and re-seal it. Similar to how ice in a cup sometimes freezes together instead of staying individual cubes.

[u/duane11583]

google translate of the french:

What would happen if I poured a quantity X of boiling water into a container made of an equivalent quantity X of ice?

Physics

Given equivalent quantities, what happens when boiling water is poured into a container made entirely of ice? Which of the two gives way first, and what is the final state of the system?

I am by no means a scientist, a researcher, or anything else synonymous with those amazing professions. However, if you want to take it a step further, here is a challenge that I consider more difficult:

The structure of the container is the deciding factor.

[u/duane11583 → u/duane11583]

first one woukd need a larger container to hold ghe combined items.

but that said the ice will melt some.

i donot know the thermodynamics math but i am sure somebody can calculate this.

i would think intuitively the heat energy (0deg c) plus (100deg c) would average out between the two temperatures at about 50deg c.

but that assumes the heat energy held in the ice transformed to boiling is an.inesr conversion.

but probably less because the vessel holding the ice or the hot water also holds heat energy or in the case of the ice container would need to absorb the heat.or the hot container holding the boiling water will dissipate heat both to the ice and the surrounding environment

so it might not get that hot (50deg c)

[u/TXOgre09 → u/duane11583]

The ice needs lots of heat to melt before it starts warming. You have lots of heat at phase transitions. The heat needed to melt the ice is the same as needed to heat or cool it 80C. So you end up around 10C.

[u/duane11583 → u/TXOgre09]

ok so the heat transfer function is non linear. with it heavily weighted at the liquid/solid phase change event

i did not know that thermodynamics property. is that also true with other melting things? ie metal or is that non linearity unique to water/ice?

[u/TXOgre09 → u/duane11583]

Any phase change for any material is a stall point. Melting and boiling require a continuous input of heat with no temperature change until fully melted or vaporized. Condensing and freezing require a continuous removal of heat until fully transformed.

Water is unique because it exists in all 3 phases at atmospheric pressure and fairly normal temperatures. But all materials have the same dynamic (well, some things combust before they melt or take wild conditions to reach certain phases). But melting steel has the same stall as melting ice.

Start with a block of steel and assume uniform temperature distribution. Add heat steadily and it will increase in temperature until it reaches the melting point. Then it will start melting without getting any hotter until you have a fully melted puddle. Then the hot puddle of molten steel will start increasing in temperature beyond the melt point.

[u/Korazair]

The container would melt. The amount of energy to turn ice in to water is approximately equivalent to the energy of 80c water. So the same amount of 100c water would have significantly more energy than the amount of heat needed to melt the ice. So if the entire system was contained within another container you would have a bucket of completely liquid water at a little over 10c.

[u/Munchskull]

Let's assume that you have an adiabatic container (no heat moves across the walls) and that based on the mass you would have equal parts ice and boiling water. Boiling water being a 100°C an ice being 0° would combined to have an equilibrium temperature that is the average of the two plus whatever is used for the latent heat of fusion in order to melt the ice. I don't have the tools to do the math on me because the specific heat of water changes with its temperature however you're going to have something that's closer to zero degrees and 100°. If I had to guess it would be somewhere around 40 to 30°.

[u/Fredissimo666]

L'eau bouillante a une température de 100 celcius (en conditions normales). La glace peut avoir n'importe quelle température inférieure à 0 celcius. Le mélange aura une température égale à la moyenne des deux. C' est donc de l'eau si la glace a une température supérieure à -100 celcius, et de la glace autrement.

Edit : everybody correcting me is totally right!

[u/MoyerD → u/Fredissimo666]

No, because you also have the latent heat of fusion of water in addition to the sensible heat, so you can't just average them

[u/trf84 → u/Fredissimo666]

Not quite. The ice will also consume some of the heat energy in the water as it melts, since it takes energy to change phase even if you don't change temperature. The reverse is true if the ice is cold enough to freeze the water. If the balance is just right, you could also get an equilibrium of solid and liquid phases. What would actually happen here depends on a bunch of things including the initial temperature of the ice, solutes in the water, whether or not the system is closed, etc.

For more detail: https://en.wikipedia.org/wiki/Enthalpy_of_fusion

[u/Primeval_Revenant → u/Fredissimo666]

You’re missing the energy inherently required for a phase change, so more energy will be expended with the addition of changing the ice to water than would simply be required to equalize temperature.

[u/yet_another_heath → u/Fredissimo666]

It’s not that simple. It takes about 333 J to melt one gram of ice at 0°C to get liquid which will also be at 0°C. Liquid water has a specific heat of about 4.184 J/g°C, which means to cool one gram of 100°C water to 0° you need to remove 418 J.

So if you combine 1g of ice at 0°C and 1g of water at 100°C, first the ice absorbs 333J to melt , cooling the hot water to about 20° which also mixes with the 0° melt water leaving the combined average at 10° (ignoring any interaction with the surrounding environment)