# Tag Info

9

Yes, of course, the freezing point will decrease by the pressure developed, while part of the water freezes. But do not underestimate the pressures! In such an experiment easily some thousand bares may be developed. (Depends on the rigidity of the vessel and the volume of water) Here is a video showing how freezing water cracks a cast iron sphere: ...

8

Generalities on Conformal Invariance In two dimensions, a lot is known / conjectured about statistical models at criticality. For instance, at $T_c$, the spin configuration that you see will not only be self-similar (what others here have been calling "fractal") but actually fully conformally invariant (in the continum limit); that is, the probability ...

7

I have read that true steam is clear (transparent) water vapor. According to this theory, the white "steam" you see is really a small cloud of condensed water vapor droplets, a fine mist in effect. So what you are seeing is not more steam, but more condensation and more mist. The speed with which the steam/vapor/mist rises and disperses may also change.

7

A simple material will not undergo a liquid to solid transition as the temperature is raised. When you see this it means somthing more complicated than a simple phase transition is going on. In the example of egg white, what you are seeing is denaturation of the protein albumin. The heat causes the protein to lose its tertiary structure then form cross ...

6

Option 3. An equilibrium phase transition is a non-analytic point of the thermodynamic free-energy. For a finite number of particles, the free-energy is always analytic. So you cant get a phase transition. Kardar discusses this point.

6

There are three phenomena that occur before vigorous boiling of water that produce sound. 1) Air dissolved in water on heating forms small air bubbles at the bottom of the container. These air bubbles get released from the bottom of the container on reaching a sufficient size. The process of release produces a sound of frequency ~ 100Hz. 2) On boiling, ...

6

It's certainly possible for ice to sink in water under the right conditions. The diagram this section of Wikipedia's ice page will show you the conditions under which the various types of ice can form. Most of the "exotic" ones such as XII will form only at pressures greater than around 200MPa. These high-pressure forms are all denser than water, so they ...

6

In physics, critical behavior means the behavior in which there are no localized boundaries between phases. More quantitatively, the correlation length diverges (is infinite). For example, at the critical point of water, one sees clouds of vapor at all possible length scales. This is only possible because the relevant laws of physics around this point ...

5

The size of these bubbles is growing nearly by the speed of light. So if the boundaries of two such bubbles are close enough to each other, the exponential expansion of the parent space in between them, even if this expansion exists, is negligible relatively to the shrinking distance between the bubbles due to their growth. That's why the bubbles collide ...

5

It seems pretty clear that if you take a very diluted subset of, say, the horizontal line through $0$, then you'll be able to make a Peierls argument. For example, put $h=+\infty$ (worst possible case, amounting to fixing the corresponding spins to $+1$) at all vertices with coordinates (10^k,0), with $k\geq 1$. Then, when removing a contour surrounding a ...

5

The situation is well represented in the following very pictorial picture but this is a very active field of study. It is interesting to note that a real proof of existence for the critical endpoint (CEP, indicated as a critical point in the figure), both from a theoretical and numerical point of view, does not exist yet. The reason, at least for the ...

5

Yes mean-field theory is wrong for the one-dimensional case (and wrong for the two and three dimensional cases as well, where the transition exists but the mean-field approximation gets the wrong critical temperature and exponents). In fact it's a typical first year exercise to solve the 1D Ising model exactly using transfer matrices, and I suggest you look ...

5

No, the boundary doesn't suddenly "end" or "fade away", as the liquid-gas boundary fades away near the critical point. Instead, the sudden end indicates that many other things may happen in the region of these extremely high pressures and the diagram doesn't want to discuss those because they're outside the limits of interest of the author of the diagram. ...

4

Let me state first that one should not speak about energies but about free energies, as soon as temperature is not absolute zero. Discussion of energies has in this case no sense. Second, a very simple answer to the original question is pointing out that according to its definition the heat, $Q = T \Delta S$, where $S$ is entropy, $\Delta S$ is its ...

4

You should add the salt befor you start heating the water. For the technical details of why this is have a look at Why does salty water heat up quicker than pure water? and Why does adding solutes to pure water lower the the specific heat?. Salt lowers the specific heat of the water so for a given rate of heat input e.g. a given setting on your electric ...

4

See wikipedia. It says that a quantum phase transition is second-order, which means there is no latent heat. There is apparently some controversy about this. From the abstract of this article: "It is frequently argued that only second order phase transitions at T = 0 deserve to be called quantum phase transitions, while first order quantum phase ...

3

While this isn't necessarily going to answer your request, I think it might be interesting none the less: Phases of N=2 Theories in Two Dimensions In a String Theory context: The Basic Idea is to study a GLSM in 2D which exhibits the interesting property to lead to Calabi-Yau compactification in one phase and Orbifold compactification in the other. The ...

3

Depending on the mass region of $\Phi$, either A or B can be taken as source and the corresponding response (vev). If $B\neq 0$ when $A=0$, it means that the system can spontaneously have a nontrivial vev even without any source. That indicates a phase transition. In the case both $A\neq 0$ and $B\neq 0$, it doesn't mean any phase transition. If we treat ...

3

The correlation length is something that you can see from the spins (looking at the lattice). You can determine it from a sequence of snapshots of an Ising model simulation. Visually, as the critical point is reached, you will see that the typical size of clusters having the same magnetization (up or down) becomes larger and larger, and this size is none ...

3

The basic classification of phase transitions is into first and second order transitions. The former is characterized by having a nonzero latent heat, e.g. the liquid-vapor transition of $H_2 O$. Often one can adjust a thermodynamic parameter to construct a line of first order transitions and this line terminates at a critical point where there is a second ...

3

I believe the term is "critical velocity". For liquid He-4, the dispersion relation can be found here: Elementary excitations of superfluid 4He The critical velocity is usually the lowest slope which intersects with the dispersion relation, since then at that speed one can create excitations that will damp the motion. Notice that for He-4 in particular, ...

3

In a sense you are right. The heat capacity only becomes discontinuous for a system of infinite extent. For all others it is continuous. But that's a theoretical concern only. At the theoretical point of discontinuity the slope of the heat capacity is infinite. Pick any finite value for the slope, no matter how large and I can find a finite system where ...

3

Adding salt to water makes it freeze at a lower temperature. This fact is being used in two different ways in the two scenarios you mention. Dissolving sodium chloride in water is slighly endothermic, but this effect is small and to the best of my knowledge isn't important in the drink cooling process. Putting salt on the highway is quite straightforward: ...

3

The inflating universe can for example be described by the FLRW metric $$d\tau = dt^2-a(t)^2(dx^2 + dy^2 + dz^2)$$ The scale factor $a(t)$, which describes the expansion, is obtained from the appropriate Friedman equation which contains only the vacuum energy $\rho_0$ as source of gravity $$\frac{\dot{a}}{a} = \sqrt\frac{8\pi G \rho_0}{3} = H$$ with ...

3

Amazingly someone has written a paper on this very subject (some people have far too much free time) and you can find it here. I wish I could claim this was my encyclopaedic knowledge of Physics at work, but it was just some lucky Googling. Anyhow, the theoretical limit for superheating of water is (astonishingly) about 600K, but in real life you wouldn't ...

3

Your first answer was completely OK. Order parameters can be also used for the description of first order transitions, why not? Think for example of water to ice transition. There is a jump when you look at the plot of density against temperature (see for example: Density of water (wikimedia)) and this is what we understand (loosely speaking of course!) ...

3

The explanation of egg turning solid which is a chemical change has well been explained by John. Interestingly, if we can trust the following article from Physics World, A liquid solution of α-cyclodextrine (αCD), water and 4-methylpyridine (4MP) turns from liquid to solid when heated to 45-75 degrees C. The interesting part to note here is the reversible ...

2

Consider a spherical drop of water, initial temp 40C, radius 3mm, mass 0.1g To get it down to 0C, you need to remove 4.18 (J/gK) * 0.1 g * 40 K = 17 J then, to freeze it solid, you need to remove latent heat of fusion 333 (J/g) * 0.1 g = 33 J for a total of 50 J. The heat conductivity equation is $H=\frac{\Delta Q}{\Delta t} = k A\frac{\Delta T}{x}$ ...

2

That depends mostly on the time the liquid is exposed to the other gases and the container you are keeping it in. A quantitative answer is hard to give though.In a clean glass dewar a little bit of evaporated nitrogen will hover over the liquid phase and will slow down the condensation of other gases into the liquid phase. In a open container with more ...

2

At a first order phase transition, both phases extend a little (superheated or supercooled metastable phases), so that one can assume them to be continuous across the coexistence curve, and we have two competing differentiable functions, of which the thermodynamically more stable phase ''wins''.

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