How many states does a substance have?

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by her. Pozny, if we now calculate the total work done by external forces and reaction forces for any virtual displacement, then it turns out to be equal to zero. But regarding reaction forces, we already know that they do not do any complete work. Therefore, for any virtual displacement, the total work done by external forces must also be equal to zero.

So, the equilibrium conditions of a mechanical system can be formulated in the form of the so-called principle of virtual (possible) displacements:

For the equilibrium of a mechanical system with ideal connections, it is necessary and sufficient that the sum of the work of all external forces acting on the system for any virtual displacements of the system is equal to zero.

Thanks to this principle, formulated by Johann Bernouli in 1717, to find equilibrium conditions there is no need to consider a large number of reaction forces. It is enough to select convenient virtual displacements, calculate the corresponding total work of only external forces and equate it to zero.

Let us illustrate the application of this principle with a simple example: we will find the elastic force of a spring from which a load of mass $m$ is suspended. Let’s choose the load itself as the system. Two external forces are applied to it - the elastic force of the spring $T$ and the gravitational force of the load $mg$. Let’s imagine that we have shifted the load in equilibrium by a small amount $\Delta x$ down. Then the work done by the gravitational force will be equal to

$$\Delta A_1 = mg\Delta x,$$

and the work done by the elastic force of the spring is

$$\Delta A_2 = -T\Delta x.$$

According to the principle of virtual movements, the sum of the work of both should be equal to zero:

$$\Delta A_1 + \Delta A_2 = mg\Delta x - T\Delta x = 0,$$

where do we get it from

$$T = mg.$$

This problem, of course, could be solved in the usual way - using the conditions of equilibrium of bodies. Moreover, in this case, both methods are the same in terms of complexity. However, in a number of cases, the method of virtual displacements leads to a faster and simpler solution, and sometimes even allows one to solve problems that, in principle, cannot be solved on the basis of general equilibrium conditions.

Note also that the method of virtual displacements can be successfully used in solving not only mechanical problems, but also problems of electronics and molecular physics.

A. A. Varlamov

How many states does a substance have?

In this note we want to talk a little about the different states of matter - the most famous, somewhat less known and very little known.

Any body is a huge number of molecules moving and interacting with each other. Every perfection is natural, that when the interaction of molecules with each other is weak, the molecules must form a gas; otherwise, when the interaction is strong, it is a solid body; in the intermediate case - liquid. This is certainly true. Only in physics there is no understandable small or large quantity without comparison with something. In this case, the interaction energy of molecules must be compared with their kinetic energy.

From the molecular-kinetic theory it is known that the average kinetic energyxaotic energyxaotic energy of molecules $\bar{E}$ is directly related to the temperature $T$ of the system: $\bar{E} = \frac{3}{2}kT$. Since we are only interested in qualitative considerations, we can

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we will not take into account the tel $^3/2$. Let us denote the average energy of interaction of molecules with their environment by $U$. Let us introduce the parameter $\varepsilon$, equal to the ratio of the average interaction energy to the average kinetic energy: $\varepsilon=U/kT$. Now we can write down the conditions for the existence of gas, liquid and solid. If $\varepsilon\ll 1$, we have a gas (the molecules move quickly, with almost no interaction with each other). When $\varepsilon\gg 1$, the system is a solid (the molecules are “sandwiched” in their places). The intermediate case, when $\varepsilon\approx 1$, corresponds to a liquid. But within each of these very large classes of condition there is quite a lot of diversity.

Let us first focus on the solid body. From the condition $\varepsilon\gg 1$ it is clear that the state of a solid is determined mainly by the energetic interactions of molecules. As is known, any system presented to itself tends to occupy a position such that its potential energy is minimal (by potential energy here we must remember precisely the energy of interaction of molecules with each other). So, it turns out that the minimum energy corresponds to the state when the molecules are arranged strictly periodically. In other words, stable equilibrium corresponds not just to a solid body, but specifically to a crystal. This is the first, most studied type of solid. The properties of crystals are entirely determined by the type of crystal lattice. There are lattices composed of cups, hexagonal prisms, parallelepids, etc. When crystals are heated (for example, at atmospheric pressure), there is a temperature (attention! a very specific temperature) at which the crystal lattice becomes unstable. Swimming begins (it is clear that the swimming temperature must be determined from condition $\varepsilon\approx 1$, i.e. $kT_{\pi l}\approx U$).

Another type of solid will arise when, upon cooling, liquids lose their mobility before they have time to protrude into the crystal lattice. Now they would “want” to get organized, but they can’t. More precisely, they can, but for this they need a lot of time. We get a solid, but not a crystalline, but an amorphous body. A typical example of such bodies is glass. When heated, glass gradually softens and eventually turns into a liquid, but there is no specific melting point.

Whether cooling a given liquid produces a crystal or an amorphous body strongly depends on the cooling rate. For example, to obtain amorphous metals, the cooling rate must be enormous (molten metal is sprayed onto a surface cooled with liquid nitrogen). But this is not the only condition. For example, no matter how hard it melts, glycerin will not form a crystal (the reason for this is not entirely clear today).

If we are talking about bodies consisting of molecules of simple shape, then, apparently, there are no other possibilities. But fortunately, the world is not that simple. You know very well that there are limited (and not only limited) molecular properties of complex shapes. Substances built from such molecules can be in non-forming states that cannot be classified as either liquid or solid. Here are some examples.

A typical property of a liquid is its isotropy, i.e., the same properties in all directions. However, now it is now possible to use mechanical properties, the speed of propagation of various waves (elastic or electromagnetic), etc. So, about a hundred years ago, liquids that were not isotropic were discovered - the so-called anisotropic liquids. Since then, huge amounts of liquid have been discovered (and artificially created). Their main feature is that in some directions they have