Physics. molecules
Molecules and atoms of a solid body are arranged in a certain order and form crystal lattice. Such solids are called crystalline. The atoms oscillate about the equilibrium position, and the attraction between them is very strong. Therefore, solid bodies under normal conditions retain volume and have their own shape.
Thermal equilibrium is the state of a thermodynamic system into which it spontaneously passes after a sufficiently long period of time under conditions of isolation from the environment.
Temperature - physical quantity characterizing the average kinetic energy of particles of a macroscopic system in a state of thermodynamic equilibrium. In an equilibrium state, the temperature has the same value for all macroscopic parts of the system.
Degree Celsius(symbol: °C) is a common unit of temperature used in the International System of Units (SI) along with the kelvin.
Mercury medical thermometer
Mechanical thermometer
The degree Celsius is named after the Swedish scientist Anders Celsius, who in 1742 proposed a new scale for measuring temperature. Zero on the Celsius scale was the melting point of ice, and 100° was the boiling point of water at standard atmospheric pressure. (Initially, Celsius took the melting temperature of ice as 100 °, and the boiling point of water as 0 °. And only later did his contemporary Carl Linnaeus “turn over” this scale). This scale is linear in the range 0-100° and also continues linearly in the region below 0° and above 100°. Linearity is a major issue with accurate temperature measurements. Suffice it to mention that a classic thermometer filled with water cannot be marked for temperatures below 4 degrees Celsius, because in this range the water begins to expand again.
The original definition of the degree Celsius depended on the definition of standard atmospheric pressure, because both the boiling point of water and the melting point of ice depend on pressure. This is not very convenient for standardizing the unit of measurement. Therefore, after the adoption of the kelvin K as the basic unit of temperature, the definition of the degree Celsius was revised.
According to modern definition, a degree Celsius is equal to one kelvin K, and the zero of the Celsius scale is set so that the temperature of the triple point of water is 0.01 °C. As a result, the Celsius and Kelvin scales are shifted by 273.15:
26)Ideal gas - mathematical model gas, in which it is assumed that the potential energy of interaction of molecules can be neglected in comparison with their kinetic energy. There are no forces of attraction or repulsion between molecules, the collisions of particles between themselves and with the walls of the vessel are absolutely elastic, and the time of interaction between molecules is negligibly small compared to the average time between collisions.
Where k is the Boltzmann constant (the ratio of the universal gas constant R to the number of Avogadro N A), i- the number of degrees of freedom of molecules (in most problems about ideal gases, where molecules are assumed to be spheres of small radius, the physical analogue of which can be inert gases), and T is the absolute temperature.
The main equation of the MKT relates macroscopic parameters (pressure, volume, temperature) gas system with microscopic (the mass of molecules, the average speed of their movement).
Kinetic energy of a molecule
In a gas, the molecules perform free (isolated from other molecules) movement, only from time to time colliding with each other or with the walls of the vessel. As long as the molecule is in free motion, it has only kinetic energy. During the collision, the molecules also have potential energy. Thus, the total energy of a gas is the sum of the kinetic and potential energies of its molecules. The rarefied the gas, the more molecules at each moment of time are in a state of free movement, having only kinetic energy. Consequently, when the gas is rarefied, the share of potential energy decreases in comparison with kinetic energy.
The average kinetic energy of a molecule in the equilibrium of an ideal gas has one very important feature: in a mixture of different gases, the average kinetic energy of a molecule for different components of the mixture is the same.
For example, air is a mixture of gases. The average energy of an air molecule for all its components under normal conditions, when air can still be considered as an ideal gas, is the same. This property of ideal gases can be proved on the basis of general statistical considerations. An important consequence follows from it: if two different gases (in different vessels) are in thermal equilibrium with each other, then the average kinetic energies of their molecules are the same.
In gases, the distance between molecules and atoms is usually much greater than the size of the molecules themselves, the interaction forces of molecules are not large. As a result, the gas does not have its own shape and constant volume. The gas is easily compressible and can expand indefinitely. Gas molecules move freely (translationally, they can rotate), only occasionally colliding with other molecules and the walls of the vessel in which the gas is located, and they move at very high speeds.
Motion of particles in solids
The structure of solids is fundamentally different from the structure of gases. In them, the intermolecular distances are small and the potential energy of the molecules is comparable to the kinetic one. Atoms (or ions, or whole molecules) cannot be called immobile, they perform random oscillatory motion around their middle positions. The higher the temperature, the greater the energy of oscillations, and hence the average amplitude of oscillations. Thermal vibrations of atoms also explain the heat capacity of solids. Let us consider in more detail the motions of particles in crystalline solids. The entire crystal as a whole is a very complex coupled oscillatory system. The deviations of the atoms from the average positions are small, and therefore we can assume that the atoms are subjected to the action of quasi-elastic forces obeying the linear Hooke's law. Such oscillatory systems are called linear.
There is a developed mathematical theory of systems subject to linear oscillations. It proves a very important theorem, the essence of which is as follows. If the system performs small (linear) interconnected oscillations, then by transforming the coordinates it can be formally reduced to a system of independent oscillators (for which the oscillation equations do not depend on each other). The system of independent oscillators behaves like an ideal gas in the sense that the atoms of the latter can also be considered independent.
It is using the idea of the independence of gas atoms that we arrive at Boltzmann's law. This very important conclusion provides a simple and reliable basis for the whole theory of solids.
Boltzmann's law
The number of oscillators with given parameters (coordinates and velocities) is determined in the same way as the number of gas molecules in a given state, according to the formula:
Oscillator energy.
Boltzmann's law (1) in the theory of a solid body has no restrictions, however, formula (2) for the energy of an oscillator is taken from classical mechanics. In the theoretical consideration of solids, one must rely on quantum mechanics, which is characterized by a discrete change in the energy of the oscillator. The discreteness of the oscillator energy becomes insignificant only at sufficiently high values of its energy. This means that (2) can only be used at sufficiently high temperatures. At high temperatures of a solid, close to the melting point, Boltzmann's law implies the law of uniform distribution of energy over degrees of freedom. If in gases for each degree of freedom, on average, there is an amount of energy equal to (1/2) kT, then the oscillator has one degree of freedom, in addition to kinetic, has potential energy. Therefore, one degree of freedom in solid body when enough high temperature there is an energy equal to kT. Based on this law, it is not difficult to calculate the total internal energy solid body, followed by its heat capacity. A mole of a solid contains NA atoms, and each atom has three degrees of freedom. Therefore, the mole contains 3 NA oscillators. Mole energy of a solid body
and the molar heat capacity of a solid at sufficiently high temperatures
Experience confirms this law.
Liquids occupy an intermediate position between gases and solids. Molecules of a liquid do not diverge over long distances, and the liquid under normal conditions retains its volume. But unlike solids, molecules not only oscillate, but also jump from place to place, that is, they make free movements. When the temperature rises, liquids boil (there is a so-called boiling point) and turn into a gas. When the temperature is lowered, liquids crystallize and become solids. There is a point in the temperature field at which the boundary between gas (saturated vapor) and liquid disappears (critical point). The pattern of thermal motion of molecules in liquids near the solidification temperature is very similar to the behavior of molecules in solids. For example, the heat capacity coefficients are almost the same. Since the heat capacity of a substance during melting changes slightly, it can be concluded that the nature of the movement of particles in a liquid is close to the movement in a solid (at the melting temperature). When heated, the properties of the liquid gradually change, and it becomes more like a gas. In liquids, the average kinetic energy of particles is less than the potential energy of their intermolecular interaction. The energy of intermolecular interaction in liquids and solids differ insignificantly. If we compare the heat of fusion and the heat of evaporation, we will see that when passing from one state of aggregation in another, the heat of fusion is substantially lower than the heat of vaporization. An adequate mathematical description of the structure of a liquid can only be given with the help of statistical physics. For example, if a liquid consists of identical spherical molecules, then its structure can be described by the radial distribution function g(r), which gives the probability of finding any molecule at a distance r from the given one, chosen as a reference point. Experimentally, this function can be found by examining the diffraction of X-rays or neutrons, one can carry out computer modelling this function using Newtonian mechanics.
The kinetic theory of liquid was developed by Ya.I. Frenkel. In this theory, the liquid is considered, as in the case of a solid body, as dynamic system harmonic oscillators. But unlike a solid body, the equilibrium position of molecules in a liquid is temporary. After oscillating around one position, the liquid molecule jumps to a new position located in the neighborhood. Such a jump occurs with the expenditure of energy. The average "settled life" time of a liquid molecule can be calculated as:
\[\left\langle t\right\rangle =t_0e^(\frac(W)(kT))\left(5\right),\]
where $t_0\ $ is the period of oscillations around one equilibrium position. The energy that a molecule must receive in order to move from one position to another is called the activation energy W, and the time the molecule is in the equilibrium position is called the “settled life” time t.
For a water molecule, for example, at room temperature, one molecule makes about 100 vibrations and jumps to a new position. The forces of attraction between the molecules of a liquid are great to maintain volume, but the limited sedentary life of molecules leads to the emergence of such a phenomenon as fluidity. During particle oscillations near the equilibrium position, they continuously collide with each other, therefore, even a small compression of the liquid leads to a sharp "hardening" of particle collisions. This means a sharp increase in the pressure of the liquid on the walls of the vessel in which it is compressed.
Example 1
Task: Determine the specific heat capacity of copper. Assume that the copper temperature is close to the melting point. (Molar mass of copper $\mu =63\cdot 10^(-3)\frac(kg)(mol))$
According to the law of Dulong and Petit mole chemically simple substances at temperatures close to the melting point, has a heat capacity:
Specific heat capacity of copper:
\[C=\frac(c)(\mu )\to C=\frac(3R)(\mu )\left(1.2\right),\] \[C=\frac(3\cdot 8,31) (63\cdot 10^(-3))=0.39\ \cdot 10^3(\frac(J)(kgK))\]
Answer: The specific heat capacity of copper is $0.39\ \cdot 10^3\left(\frac(J)(kgK)\right).$
Task: Explain in a simplified way from the point of view of physics the process of dissolution of salt (NaCl) in water.
The basis of the modern theory of solutions was created by D.I. Mendeleev. He found that during dissolution, two processes proceed simultaneously: physical - uniform distribution particles of the dissolved substance throughout the volume of the solution, and chemical - the interaction of the solvent with the dissolved substance. We are interested in the physical process. Salt molecules do not destroy water molecules. In this case, it would be impossible to evaporate the water. If salt molecules were attached to water molecules, we would get some new substance. And salt molecules cannot penetrate inside water molecules.
An ion-dipole bond occurs between the Na+ and Cl- ions of chlorine and polar water molecules. It turns out to be stronger than the ionic bonds in the salt molecules. As a result of this process, the bond between ions located on the surface of NaCl crystals is weakened, sodium and chlorine ions are detached from the crystal, and water molecules form so-called hydration shells around them. The separated hydrated ions under the influence of thermal motion are uniformly distributed among the solvent molecules.
Molecular physics is easy!
Interaction forces of molecules
All molecules of a substance interact with each other by forces of attraction and repulsion.
Proof of the interaction of molecules: the phenomenon of wetting, resistance to compression and stretching, low compressibility of solids and gases, etc.
The reason for the interaction of molecules is the electromagnetic interactions of charged particles in matter.
How to explain it?
An atom consists of a positively charged nucleus and a negatively charged electron shell. The charge of the nucleus is equal to the total charge of all electrons, therefore, as a whole, the atom is electrically neutral.
A molecule consisting of one or more atoms is also electrically neutral.
Consider the interaction between molecules using the example of two immobile molecules.
Gravitational and electromagnetic forces can exist between bodies in nature.
Since the masses of molecules are extremely small, negligible forces gravitational interaction between molecules can be ignored.
At very large distances, there is no electromagnetic interaction between molecules either.
But, with a decrease in the distance between the molecules, the molecules begin to orient themselves so that their sides facing each other will have charges of different signs (in general, the molecules remain neutral), and attractive forces arise between the molecules.
With an even greater decrease in the distance between the molecules, repulsive forces arise as a result of the interaction of negatively charged electron shells of the atoms of the molecules.
As a result, the molecule is affected by the sum of the forces of attraction and repulsion. At large distances, the attractive force prevails (at a distance of 2-3 molecular diameters, attraction is maximum), at short distances, the repulsive force.
There is such a distance between molecules at which the forces of attraction become equal forces repulsion. This position of the molecules is called the position of stable equilibrium.
Distanced apart and connected electromagnetic forces molecules have potential energy.
In the position of stable equilibrium, the potential energy of molecules is minimal.
In a substance, each molecule interacts simultaneously with many neighboring molecules, which also affects the value of the minimum potential energy of molecules.
In addition, all the molecules of a substance are in continuous motion, i.e. have kinetic energy.
Thus, the structure of a substance and its properties (solid, liquid and gaseous bodies) are determined by the ratio between the minimum potential energy of interaction of molecules and the kinetic energy of the thermal motion of molecules.
The structure and properties of solid, liquid and gaseous bodies
The structure of bodies is explained by the interaction of body particles and the nature of their thermal motion.
Solid
Solids have a constant shape and volume, and are practically incompressible.
The minimum potential energy of interaction of molecules is greater than the kinetic energy of molecules.
Strong interaction of particles.
The thermal motion of molecules in a solid is expressed only by oscillations of particles (atoms, molecules) around the position of stable equilibrium.
Due to the large forces of attraction, molecules practically cannot change their position in a substance, which explains the invariance of the volume and shape of solids.
Most solids have a spatially ordered arrangement of particles that form a regular crystal lattice. Particles of matter (atoms, molecules, ions) are located at the vertices - the nodes of the crystal lattice. The nodes of the crystal lattice coincide with the position of stable equilibrium of the particles.
Such solids are called crystalline.
Liquid
Liquids have a certain volume, but do not have their own shape, they take the shape of the vessel in which they are located.
The minimum potential energy of interaction of molecules is comparable to the kinetic energy of molecules.
Weak particle interaction.
The thermal motion of molecules in a liquid is expressed by oscillations around the position of stable equilibrium within the volume provided to the molecule by its neighbors
Molecules cannot move freely throughout the entire volume of a substance, but transitions of molecules to neighboring places are possible. This explains the fluidity of the liquid, the ability to change its shape.
In liquids, the molecules are quite strongly bound to each other by attractive forces, which explains the invariance of the volume of the liquid.
In a liquid, the distance between molecules is approximately equal to the diameter of the molecule. With a decrease in the distance between molecules (compressing a liquid), the repulsive forces sharply increase, so liquids are incompressible.
In terms of their structure and nature of thermal motion, liquids occupy an intermediate position between solids and gases.
Although the difference between a liquid and a gas is much greater than between a liquid and a solid. For example, during melting or crystallization, the volume of a body changes many times less than during evaporation or condensation.
Gases do not have a constant volume and occupy the entire volume of the vessel in which they are located.
The minimum potential energy of interaction of molecules is less than the kinetic energy of molecules.
Particles of matter practically do not interact.
Gases are characterized by a complete disorder in the arrangement and movement of molecules.
This material not only talks about how particles are located in solids, but also how they move in gases or liquids. The types of crystal lattices in various substances will also be described.
State of aggregation
There are certain standards that indicate the presence of three typical states of aggregation, namely: liquid and gas.
Let us define the components for each state of aggregation.
- Solids are substantially stable in volume and shape. It is extremely problematic to change the latter without additional energy costs.
- A liquid can easily change shape, but retains its volume.
- Gaseous substances do not retain either shape or volume.
The main criterion by which the state of aggregation is determined is the arrangement of molecules and the methods of their movement. In a gaseous substance, the minimum distance between individual molecules is much greater than themselves. In turn, the molecules do not diverge over long distances under their usual conditions and retain their volume. The active particles in solids are located in a strictly defined order, each of them, like a clock's pendulum, moves around a certain point in the crystal lattice. This gives solids particular strength and rigidity.
Therefore, in this case, the most relevant question is how the acting particles are located in solids. In all other cases, atoms (molecules) do not have such an ordered structure.
Fluid Features
Need to pay Special attention to the fact that liquids are a kind of intermediate link between the solid state of the body and its gaseous phase. So, when the temperature drops, the liquid solidifies, and when it rises above the boiling point of a given substance, it passes into a gaseous state. However, the liquid has common features with both solid and gaseous substances. So, in 1860, the outstanding Russian scientist D. I. Mendeleev established the existence of the so-called critical temperature - absolute boiling. This is the value at which the thin boundary between the gas and the solid state disappears.
The next criterion that combines two neighboring states of aggregation is isotropy. In this case, their properties are the same in all directions. Crystals, in turn, are anisotropic. Like gases, liquids do not have a fixed shape and occupy the entire volume of the vessel in which they are located. That is, they have low viscosity and high fluidity. Colliding with each other, microparticles of a liquid or gas make free movements. Previously, it was believed that in the volume occupied by a liquid, there is no ordered movement of molecules. Thus, liquid and gas were opposed to crystals. But as a result of subsequent studies, the similarity between solid and liquid bodies was proved.
In the liquid phase at a temperature close to solidification, thermal motion resembles motion in solids. In this case, the liquid may still have a certain structure. Therefore, giving an answer to such a question, how particles are located in solids in liquids and gases, we can say that in the latter the movement of molecules is chaotic, disordered. but in solids, the molecules in most cases occupy a certain, fixed position.
In this case, the liquid is a kind of intermediate link. Moreover, the closer its temperature to boiling, the more the molecules move as in gases. If the temperature is closer to the transition to the solid phase, then the microparticles begin to move more and more orderly.
Change in the state of substances
Let's take a look at simple example change in the state of the water. Ice is the solid phase of water. Its temperature is below zero. At a temperature equal to zero, the ice begins to melt and turns into water. This is due to the destruction of the crystal lattice: when heated, the particles begin to move. The temperature at which a substance changes its state of aggregation is called the melting point (in our case, for water it is 0). Note that the temperature of the ice will remain at the same level until it completely melts. In this case, the atoms or molecules of the liquid will move in the same way as in solids.
After that, we continue to heat the water. In this case, the particles begin to move more intensively until our substance reaches the next point of change in the state of aggregation - the boiling point. Such a moment occurs when the bonds between the molecules that form it are broken due to the acceleration of movement - then it acquires a free character, and the liquid in question passes into the gaseous phase. The process of transformation of a substance (water) from a liquid phase into a gaseous one is called boiling.
The temperature at which water boils is called the boiling point. In our case, this value is equal to 100 degrees Celsius (temperature is dependent on pressure, normal pressure is one atmosphere). Note: until the existing liquid completely and completely turns into vapor, its temperature remains constant.
The reverse process of the transition of water from a gaseous state (vapor) to a liquid, which is called condensation, is also possible.
Next, you can observe the process of freezing - the process of transition of a liquid (water) into a solid form (the initial state is described above - this is ice). The processes described earlier provide a direct answer to how particles are arranged in solids, liquids and gases. The location and state of the molecules of a substance depends on its state of aggregation.
What is a solid body? How do microparticles behave in it?
A solid body is a state of the material environment, the distinctive feature of which is to maintain a constant shape and permanent thermal motion of microparticles making slight vibrations. Bodies can be in a solid, liquid and gaseous state. There is also a fourth state, which modern scientists tend to classify as aggregate - this is the so-called plasma.
So, in the first case, any substance, as a rule, has a permanent, unchanging shape, and the way the particles are arranged in solids has a key effect on this. At the microscopic level, you can see that the atoms that make up a solid body are connected to each other. chemical bonds and are located at the nodes of the crystal lattice.
But there is an exception - amorphous substances that are in a solid state, but cannot boast of having a crystal lattice. It is starting from this that one can give an answer to how the particles are located in solids. Physics in the first case indicates that atoms or molecules are located at the lattice sites. But in the second case, there is certainly no such order, and such a substance is more like a liquid.
Physics and possible structure of a solid body
In this case, the substance tends to retain its volume and, of course, its shape. That is, in order to change the latter, efforts must be made, and it does not matter whether it is a metal object, a piece of plastic or plasticine. The reason lies in its molecular structure. And to be more precise, in the interaction of the molecules that make up the body. In this case, they are located closest. This arrangement of molecules is repetitive. That is why the forces of mutual attraction between each of these components are very large.
The interaction of microparticles explains the nature of their movement. It is very difficult to correct the shape or volume of such a solid body in one direction or another. Particles of a solid body are unable to move randomly throughout the entire volume of a solid body, but can only oscillate around a certain point in space. Molecules of a solid body vibrate randomly in different directions, but stumble upon similar ones, which return them to their original state. That is why particles in solids are arranged, as a rule, in a strictly defined order.
Particles and their location in a solid
Solids can be of three types: crystalline, amorphous, and composites. Exactly chemical composition affects the arrangement of particles in solids.
Crystalline solids have an ordered structure. Their molecules or atoms form a crystalline spatial lattice of the correct form. Thus, a solid body in a crystalline state has a certain crystal lattice, which, in turn, sets certain physical properties. This is the answer to how particles are arranged in a solid.
Let us give an example: many years ago, in St. Petersburg, a stock of shiny white tin buttons was kept in a warehouse, which, when the temperature dropped, lost their luster and turned gray from white. The buttons crumbled into a gray powder. "Tin Plague" - this is how this "disease" was called, but in fact it was a restructuring of the structure of crystals under the influence of low temperature. Tin, upon transition from a white variety to a gray one, crumbles into powder. Crystals, in turn, are divided into mono- and polycrystals.
Single crystals and polycrystals
Single crystals (common salt) are single homogeneous crystals represented by a continuous crystal lattice in the shape of regular polygons. Polycrystals (sand, sugar, metals, stones) are crystalline bodies, which have grown together from small, randomly arranged crystals. In crystals, such a phenomenon as anisotropy is observed.
Amorphous: a special case
Amorphous bodies (resin, rosin, glass, amber) do not have a clear strict order in the arrangement of particles. This is a non-standard case of the order in which particles are in solids. In this case, the phenomenon of isotropy is observed, the physical properties of amorphous bodies are the same in all directions. At high temperatures they become like viscous liquids, and at low temperatures they look like solids. Under external influence, elastic properties are simultaneously detected, that is, upon impact, they break into miniature particles, like solids, and fluidity: with prolonged temperature exposure, they begin to flow like liquids. They do not have specific melting and crystallization temperatures. When heated, amorphous bodies soften.
Examples of amorphous substances
Take, for example, ordinary sugar and find out the arrangement of particles in solids in various cases using its example. In this case, the same material may occur in crystalline or amorphous form. If the melted sugar hardens slowly, the molecules form even rows - crystals (lump sugar, or granulated sugar). If melted sugar, for example, is poured into cold water, cooling will occur very quickly, and the particles will not have time to form the correct rows - the melt will solidify without forming crystals. This is how sugar candy is obtained (this is non-crystalline sugar).
But after some time, such a substance can recrystallize, the particles gather in regular rows. If the sugar candy lies for several months, it will begin to become covered with a loose layer. This is how crystals appear on the surface. For sugar, the period will be several months, and for stone - millions of years. Carbon is a unique example. Graphite is crystalline carbon, its structure is layered. And diamond is the hardest mineral on earth, capable of cutting glass and sawing stones, it is used for drilling and polishing. In this case, the substance is one - carbon, but the peculiarity lies in the ability to form different crystalline forms. This is another answer to how particles are arranged in a solid.
Results. Conclusion
The structure and arrangement of particles in solids depends on the type of substance in question. If the substance is crystalline, then the arrangement of microparticles will be ordered. Amorphous structures do not have this feature. But composites can belong to both the first and second groups.
In one case, a liquid behaves similarly to a solid (at a low temperature, which is close to the crystallization temperature), but can also behave like a gas (as it rises). Therefore, in this review material, it was considered how the particles are located not only in solids, but also in other basic aggregate states of matter.
Kinetic energy of a molecule
In a gas, the molecules perform free (isolated from other molecules) movement, only from time to time colliding with each other or with the walls of the vessel. As long as the molecule is in free motion, it has only kinetic energy. During the collision, the molecules also have potential energy. Thus, the total energy of a gas is the sum of the kinetic and potential energies of its molecules. The rarefied the gas, the more molecules at each moment of time are in a state of free movement, having only kinetic energy. Consequently, when the gas is rarefied, the share of potential energy decreases in comparison with kinetic energy.
The average kinetic energy of a molecule in the equilibrium of an ideal gas has one very important feature: in a mixture of different gases, the average kinetic energy of a molecule for different components of the mixture is the same.
For example, air is a mixture of gases. The average energy of an air molecule for all its components under normal conditions, when air can still be considered as an ideal gas, is the same. This property of ideal gases can be proved on the basis of general statistical considerations. An important consequence follows from it: if two different gases (in different vessels) are in thermal equilibrium with each other, then the average kinetic energies of their molecules are the same.
In gases, the distance between molecules and atoms is usually much greater than the size of the molecules themselves, the interaction forces of molecules are not large. As a result, the gas does not have its own shape and constant volume. The gas is easily compressible and can expand indefinitely. Gas molecules move freely (translationally, they can rotate), only occasionally colliding with other molecules and the walls of the vessel in which the gas is located, and they move at very high speeds.
Motion of particles in solids
The structure of solids is fundamentally different from the structure of gases. In them, the intermolecular distances are small and the potential energy of the molecules is comparable to the kinetic one. Atoms (or ions, or whole molecules) cannot be called immobile, they perform random oscillatory motion around their middle positions. The higher the temperature, the greater the energy of oscillations, and hence the average amplitude of oscillations. Thermal vibrations of atoms also explain the heat capacity of solids. Let us consider in more detail the motions of particles in crystalline solids. The entire crystal as a whole is a very complex coupled oscillatory system. The deviations of the atoms from the average positions are small, and therefore we can assume that the atoms are subjected to the action of quasi-elastic forces obeying the linear Hooke's law. Such oscillatory systems are called linear.
There is a developed mathematical theory of systems subject to linear oscillations. It proves a very important theorem, the essence of which is as follows. If the system performs small (linear) interconnected oscillations, then by transforming the coordinates it can be formally reduced to a system of independent oscillators (for which the oscillation equations do not depend on each other). The system of independent oscillators behaves like an ideal gas in the sense that the atoms of the latter can also be considered independent.
It is using the idea of the independence of gas atoms that we arrive at Boltzmann's law. This very important conclusion provides a simple and reliable basis for the whole theory of solids.
Boltzmann's law
The number of oscillators with given parameters (coordinates and velocities) is determined in the same way as the number of gas molecules in a given state, according to the formula:
Oscillator energy.
Boltzmann's law (1) in the theory of a solid body has no restrictions, however, formula (2) for the energy of an oscillator is taken from classical mechanics. In the theoretical consideration of solids, one must rely on quantum mechanics, which is characterized by a discrete change in the energy of an oscillator. The discreteness of the oscillator energy becomes insignificant only at sufficiently high values of its energy. This means that (2) can only be used at sufficiently high temperatures. At high temperatures of a solid, close to the melting point, Boltzmann's law implies the law of uniform distribution of energy over degrees of freedom. If in gases for each degree of freedom, on average, there is an amount of energy equal to (1/2) kT, then the oscillator has one degree of freedom, in addition to kinetic, has potential energy. Therefore, one degree of freedom in a solid at a sufficiently high temperature has an energy equal to kT. Based on this law, it is not difficult to calculate the total internal energy of a solid, and after it, its heat capacity. A mole of a solid contains NA atoms, and each atom has three degrees of freedom. Therefore, the mole contains 3 NA oscillators. Mole energy of a solid body
and the molar heat capacity of a solid at sufficiently high temperatures
Experience confirms this law.
Liquids occupy an intermediate position between gases and solids. Molecules of a liquid do not diverge over long distances, and the liquid under normal conditions retains its volume. But unlike solids, molecules not only oscillate, but also jump from place to place, that is, they make free movements. When the temperature rises, liquids boil (there is a so-called boiling point) and turn into a gas. As the temperature drops, liquids crystallize and become solids. There is a point in the temperature field at which the boundary between gas (saturated vapor) and liquid disappears (critical point). The pattern of thermal motion of molecules in liquids near the solidification temperature is very similar to the behavior of molecules in solids. For example, the heat capacity coefficients are almost the same. Since the heat capacity of a substance during melting changes slightly, it can be concluded that the nature of the movement of particles in a liquid is close to the movement in a solid (at the melting temperature). When heated, the properties of the liquid gradually change, and it becomes more like a gas. In liquids, the average kinetic energy of particles is less than the potential energy of their intermolecular interaction. The energy of intermolecular interaction in liquids and solids differ insignificantly. If we compare the heat of fusion and the heat of evaporation, we will see that during the transition from one state of aggregation to another, the heat of fusion is significantly lower than the heat of vaporization. An adequate mathematical description of the structure of a liquid can only be given with the help of statistical physics. For example, if a liquid consists of identical spherical molecules, then its structure can be described by the radial distribution function g(r), which gives the probability of finding any molecule at a distance r from the given one, chosen as a reference point. Experimentally, this function can be found by studying the diffraction of X-rays or neutrons; it is possible to conduct computer simulations of this function using Newtonian mechanics.
The kinetic theory of liquid was developed by Ya.I. Frenkel. In this theory, the liquid is considered, as in the case of a solid body, as a dynamic system of harmonic oscillators. But unlike a solid body, the equilibrium position of molecules in a liquid is temporary. After oscillating around one position, the liquid molecule jumps to a new position located in the neighborhood. Such a jump occurs with the expenditure of energy. The average "settled life" time of a liquid molecule can be calculated as:
\[\left\langle t\right\rangle =t_0e^(\frac(W)(kT))\left(5\right),\]
where $t_0\ $ is the period of oscillations around one equilibrium position. The energy that a molecule must receive in order to move from one position to another is called the activation energy W, and the time the molecule is in the equilibrium position is called the “settled life” time t.
For a water molecule, for example, at room temperature, one molecule makes about 100 vibrations and jumps to a new position. The forces of attraction between the molecules of a liquid are great to maintain volume, but the limited sedentary life of molecules leads to the emergence of such a phenomenon as fluidity. During particle oscillations near the equilibrium position, they continuously collide with each other, therefore, even a small compression of the liquid leads to a sharp "hardening" of particle collisions. This means a sharp increase in the pressure of the liquid on the walls of the vessel in which it is compressed.
Example 1
Task: Determine the specific heat capacity of copper. Assume that the copper temperature is close to the melting point. (Molar mass of copper $\mu =63\cdot 10^(-3)\frac(kg)(mol))$
According to the Dulong and Petit law, a mole of chemically simple substances at temperatures close to the melting point has a heat capacity:
Specific heat capacity of copper:
\[C=\frac(c)(\mu )\to C=\frac(3R)(\mu )\left(1.2\right),\] \[C=\frac(3\cdot 8,31) (63\cdot 10^(-3))=0.39\ \cdot 10^3(\frac(J)(kgK))\]
Answer: The specific heat capacity of copper is $0.39\ \cdot 10^3\left(\frac(J)(kgK)\right).$
Task: Explain in a simplified way from the point of view of physics the process of dissolution of salt (NaCl) in water.
The basis of the modern theory of solutions was created by D.I. Mendeleev. He found that during dissolution, two processes occur simultaneously: physical - the uniform distribution of particles of the dissolved substance throughout the volume of the solution, and chemical - the interaction of the solvent with the dissolved substance. We are interested in the physical process. Salt molecules do not destroy water molecules. In this case, it would be impossible to evaporate the water. If salt molecules were attached to water molecules, we would get some new substance. And salt molecules cannot penetrate inside water molecules.
An ion-dipole bond occurs between the Na+ and Cl- ions of chlorine and polar water molecules. It turns out to be stronger than the ionic bonds in the salt molecules. As a result of this process, the bond between ions located on the surface of NaCl crystals is weakened, sodium and chlorine ions are detached from the crystal, and water molecules form so-called hydration shells around them. The separated hydrated ions under the influence of thermal motion are uniformly distributed among the solvent molecules.
