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| Freezing Speed of Hot Versus Cold Water |
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| IanB:
--- Quote from: Nominal Animal on February 21, 2022, 12:06:53 am ---At the core of the real Mpemba effect is that heat capacity is not constant in non-equilibrium states. --- End quote --- What do you mean by "equilibrium state"? Thermal equilibrium? Mechanical equilibrium? Chemical equilibrium? Furthermore, heat capacity is not constant. You do not have to qualify this. Specific heat capacity is a function of many variables, notably temperature. However, setting all this aside, if you start out with 1 kg of water at 100°C and 1 kg of water at 25°C, and place them in identical containers in identical cold surroundings (for example still air at 5°C), then the water that starts our cooler will remain cooler for as long as you wait. The hotter water will never overtake it. |
| Nominal Animal:
--- Quote from: T3sl4co1l on February 21, 2022, 02:40:55 am ---Holy shit, you mean "structured water" actually exists?! --- End quote --- Not really, no, because the structures themselves do not last, and it is more to do with individual water molecules' degrees of freedom (specifically, the one corresponding to the lengths of the hydrogen-oxygen bond) than molecular structures per se. The forces that form the molecular structures are much weaker than the molecular bonds between the oxygen and hydrogen atoms, best approximately described as Van der Waals forces. (The molecular structures "observed" in simulations is typically a result of using too few water molecules, and periodic boundary conditions. Essentially, the simulated volume is too small, and un-physical structures can pop up because of artificial effects due to the boundary conditions.) Even though weak, the traditional example of showing how such weak forces can become observable in the macro scale, is to bring a magnet (or something with a static charge) close to running water running from a faucet: the stream bends, because each individual water molecule is polar. To simplify A LOT, the core feature with water seems to be (based on simulations matching the experiments) that the hydrogen-oxygen bond length varies slower than the angular vibrational degrees of freedom. Because the potential energy function is not symmetric, it takes "significant" amount of time for the energies in the different degrees of freedom to find the internal equilibrium state corresponding to Boltzmann distribution. Simply put, when water molecules with different velocities and internal kinetic energies interact, the vibrational degrees of freedom are coupled better than the degrees of freedom related to the bond lengths, and it takes appreciable time for the internal kinetic energy distribution across the degrees of freedom to relax to the expected distribution. When water molecules with very different energies (at very different temperatures) interact, the interactions tend to enforce that disparity rather than smooth it out. Atoms and molecules do not actually collide like marbles; the outermost interacting electrons interact instead. The end result can be treated like collisions, usually. But, when you have polar molecules or complex molecules like proteins, these interesting effects can become measurable at the macro scale. --- Quote from: T3sl4co1l on February 21, 2022, 02:40:55 am ---Mind blown. --- End quote --- Anyone having done any numerical simulations dealing with water molecules, has an intuitive grasp of how complex water chemistry really is. So much so that when you first suggest simulating water molecules, every experienced numerical simulation person will be taken aback a bit, and will ask you if you realize how complicated and computationally-heavy task that is, especially compared to e.g. metals like iron or copper. --- Quote from: IanB on February 21, 2022, 03:28:01 am --- --- Quote from: Nominal Animal on February 21, 2022, 12:06:53 am ---At the core of the real Mpemba effect is that heat capacity is not constant in non-equilibrium states. --- End quote --- What do you mean by "equilibrium state"? Thermal equilibrium? Mechanical equilibrium? Chemical equilibrium? --- End quote --- Thermal equilibrium. Given fast enough heating or cooling, the heat capacity of a water molecule at a specific "temperature" (kinetic energy) will depend on its recent "temperature", because the kinetic energy within the molecule is distributed asymmetrically in the internal degrees of freedom, and it takes a relatively long time for the kinetic energy to reach the distribution among the degrees of freedom described by Boltzmann. --- Quote from: IanB on February 21, 2022, 03:28:01 am ---However, setting all this aside, if you start out with 1 kg of water at 100°C and 1 kg of water at 25°C, and place them in identical containers in identical cold surroundings (for example still air at 5°C), then the water that starts our cooler will remain cooler for as long as you wait. The hotter water will never overtake it. --- End quote --- That is what you believe. Yet, it is not exactly true. In still air, yes, because the cooling effect is not fast enough for Mpemba effect to occur. However, if we use a heat bath with sufficient surface area to speed up the heat flow, based on the peer-reviewed articles I've read, it is possible for the originally hot water to become temporarily cooler than the other water sample. This effect occurs, when the energy flow from the originally hotter sample to the surrounding heat bath is faster than from the originally cooler sample at that same temperature. |
| IanB:
--- Quote from: Nominal Animal on February 21, 2022, 05:03:27 am ---Thermal equilibrium. Given fast enough heating or cooling, the heat capacity of a water molecule at a specific "temperature" (kinetic energy) will depend on its recent "temperature", because the kinetic energy within the molecule is distributed asymmetrically in the internal degrees of freedom, and it takes a relatively long time for the kinetic energy to reach the distribution among the degrees of freedom described by Boltzmann. --- End quote --- Sorry, but this is not any kind of recognized or accepted physics or thermodynamics. There is no such thing as "temperature", there is only temperature. And a single water molecule does not have a temperature or a heat capacity. Temperature is a macroscopic phenomenon resulting from averaging on a non-quantum scale. What you can accurately say is that any system where heat is flowing is not in equilibrium, and also any system where the temperature varies from one point to another is not in equilibrium. But these are both macroscopic observations and do not have anything to do with individual molecules. --- Quote ---That is what you believe. Yet, it is not exactly true. In still air, yes, because the cooling effect is not fast enough for Mpemba effect to occur. However, if we use a heat bath with sufficient surface area to speed up the heat flow, based on the peer-reviewed articles I've read, it is possible for the originally hot water to become temporarily cooler than the other water sample. --- End quote --- I sincerely doubt that such peer reviewed articles appear in mainstream physics journals, or if they do, you are misinterpreting what they are saying. --- Quote ---This effect occurs, when the energy flow from the originally hotter sample to the surrounding heat bath is faster than from the originally cooler sample at that same temperature. --- End quote --- The laws of thermodynamics say that the heat flow depends on the temperature difference. If two samples have the same temperature difference with the surroundings, then all other things being equal the heat flow is the same. If the heat flow is different, then the temperature is different. You have to keep in mind that if you try to cool something down fast, it becomes even harder to get the heat out of it. Because you will rapidly cool down the outside surface while the interior remains warmer due to the limits of thermal conductivity. |
| Nominal Animal:
I'm trying to explain things in a way that laymen understand it. Feel free to nitpick. --- Quote from: IanB on February 21, 2022, 08:40:32 am ---I sincerely doubt that such peer reviewed articles appear in mainstream physics journals, or if they do, you are misinterpreting what they are saying. --- End quote --- If you had bothered to read any related articles before spouting your beliefs, you'd have known better. My previous posts in this thread – which you obviously didn't bother to read, just posted your superior beliefs – even had links to related articles. For even more focused support for my arguments, see e.g. Zhang et al., "Hydrogen-bond memory and water-skin supersolidity resolving the Mpemba paradox". Phys. Chem. Chem. Phys., 2014, 16, 22995-23002. Arxiv preprint. Lu, Raz, "Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse". PNAS May 16, 2017 114 (20) 5083-5088. PDF. There is no scientific consensus yet, but the above definitely support my argument here, and are quite mainstream. |
| magic:
--- Quote from: Nominal Animal on February 21, 2022, 12:06:53 am ---To simplify what happens in the real Mpemba effect, is that the liquid at hand is far from an equilibrium state, and because of recently been at much higher temperature, can lose heat energy much faster than the same liquid at the same temperature in an equilibrium state would. Simply put, the recently-hot liquid has smaller heat capacity. (The reality is more interesting, especially when the sample starts getting nearer to an equilibrium state of the heat bath, as localized heating can often be detected due to the latent heat. But close enough for an intuitive understanding, the interesting parts and the actual mechanism, are more like technical details.) If we had some kind of device or meter that could measure the net energy flow between the heat bath (freezer) and the (originally liquid) sample, we'd find that at the same temperature, the energy flow from the recently-hot sample to the heat bath is higher than for the sample that was not originally that hot. --- End quote --- That makes no sense. You are now making claims about the container or surrounding environment having higher thermal conductivity because it "knows" something about the water inside. Reduced heat capacity means that at the same temperature and the same energy flow, dT/dt is faster. Not quite as you explained it. Another explanation you could reasonably attempt is increased thermal conductivity of water, i.e. less internal gradient across its volume. |
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