All molecules of a substance participate in thermal motion, therefore, with a change in the nature of thermal motion, the state of the substance and its properties also change. So, when the temperature rises, water boils, turning into steam. If the temperature is lowered, the water freezes and turns from a liquid into a solid.
DEFINITION
Temperature- scalar physical quantity, which characterizes the degree of heating of the body.
Temperature is a measure of the intensity of the thermal motion of molecules and characterizes the state thermal equilibrium systems of macroscopic bodies: all bodies of the system that are in thermal equilibrium with each other have the same temperature.
Temperature is measured thermometer. Any thermometer uses a change in some macroscopic parameter depending on the change in temperature.
The SI unit of temperature is the degree Kelvin (K). The formula for the transition from the Celsius scale to the Kelvin temperature scale (absolute scale) is:
where is the temperature in Celsius.
The minimum temperature corresponds to zero on an absolute scale. At absolute zero thermal motion molecules stops.
The higher the temperature of the body, the greater the speed of thermal movement of molecules, and, consequently, the greater the energy of the molecules of the body. Thus, temperature serves as a measure of the kinetic energy of the thermal motion of molecules.
Root mean square velocity of molecules
The root-mean-square velocity of molecules is calculated by the formula:
where is the Boltzmann constant, J/K.
Average kinetic energy of motion of one molecule
The average kinetic energy of the movement of one molecule:
The physical meaning of the Boltzmann constant lies in the fact that this constant determines the relationship between the temperature of a substance and the energy of the thermal motion of the molecules of this substance.
It is important to note that the average energy of thermal motion of molecules depends only on the temperature of the gas. At a given temperature, the average kinetic energy of the translational chaotic motion of molecules does not depend on either chemical composition gas, neither on the mass of molecules, nor on the pressure of the gas, nor on the volume occupied by the gas.
Examples of problem solving
EXAMPLE 1
| Exercise | What is the average kinetic energy of argon molecules if the gas temperature is C? |
| Solution | The average kinetic energy of gas molecules is determined by the formula: Boltzmann's constant. Let's calculate: |
| Answer | Average kinetic energy of argon molecules at a given temperature J. |
EXAMPLE 2
| Exercise | By what percentage will the average kinetic energy of gas molecules increase when its temperature changes from 7 to ? |
| Solution | The average kinetic energy of gas molecules is determined by the relation: Change in average kinetic energy due to temperature change: Percent change in energy: Let's convert the units to the SI system: . Let's calculate: |
| Answer | The average kinetic energy of gas molecules will increase by 10%. |
EXAMPLE 3
| Exercise | How many times is the root-mean-square velocity of a dust particle weighing kg, suspended in air, less than the root-mean-square velocity of air molecules? |
| Solution | Root-mean-square velocity of a dust particle:
RMS speed of an air molecule:
Air molecule mass: |
[Physics test 24] Forces of intermolecular interaction. Aggregate state of matter. The nature of the thermal motion of molecules in solid, liquid, gaseous bodies and its change with increasing temperature. Thermal expansion tel. Linear expansion of solids when heated. Volumetric thermal expansion of solids and liquids. Transitions between aggregate states. Heat of phase transition. Phase balance. Heat balance equation.
Forces of intermolecular interaction.
Intermolecular interaction is electrical in nature. Between themforces of attraction and repulsion act, which quickly decrease with increasingdistances between molecules.The repulsive forces actonly at very short distances.In practice, the behavior of matter andits physical statedetermined by what isdominant: forces of attractionor chaotic thermal motion.Forces dominate in solidsinteractions, so theyretains its shape.
Aggregate state of matter.
- the ability (solid body) or inability (liquid, gas, plasma) to maintain volume and shape,
- the presence or absence of long-range (solid body) and short-range order (liquid), and other properties.
Thermal motion in solids is mainly oscillatory. At high
temperatures, intense thermal motion prevents the molecules from approaching each other - gaseous
state, the movement of molecules is translational and rotational. . In gases less than 1% by volume
pertains to the volume of the molecules themselves. At intermediate temperatures
molecules will constantly move in space, exchanging places, however
the distance between them is not much greater than d - liquid. The nature of the movement of molecules
in a liquid is oscillatory and translational in nature (at the moment when they
jump to a new equilibrium position).
Thermal expansion of tel.
The thermal motion of molecules explains the phenomenon of thermal expansion of bodies. At
heating amplitude oscillatory motion molecules increase, resulting in
increase in body size.
Linear expansion of solids when heated.
The linear expansion of a rigid body is described by the formula: L=L0(1+at) , where a is the linear expansion coefficient ~10^-5 K^-1.
Volumetric thermal expansion of solids and liquids.
The volumetric expansion of bodies is described by a similar formula: V = V0(1+Bt), B is the coefficient of volumetric expansion, and B=3a.
Transitions between aggregate states.
The substance can be in solid, liquid, gaseous states. These
states are called aggregate states of matter. The substance can move from
one state to another. A characteristic feature of the transformation of matter is
the possibility of the existence of stable inhomogeneous systems, when the substance can
is in several states of aggregation at once. When describing such systems
use a broader concept of the phase of matter. For example, carbon in solid
aggregate state can be in two different phases - diamond and graphite. phase
called the totality of all parts of the system, which in the absence of an external
impact is physically homogeneous. If several phases of a substance at a given
temperature and pressure exist in contact with each other, and at the same time the mass of one
phase does not increase due to a decrease in the other, then one speaks of phase equilibrium.
Heat of phase transition.
Heat of phase transition- the amount of heat that must be imparted to the substance (or removed from it) during the equilibrium isobaric-isothermal transition of the substance from one phase to another (phase transition of the first kind - boiling, melting, crystallization, polymorphic transformation, etc.).
For phase transitions of the second kind, the heat of phase transformation is zero.
An equilibrium phase transition at a given pressure occurs at a constant temperature—the phase transition temperature. The phase transition heat is equal to the product of the phase transition temperature and the entropy difference in the two phases between which the transition occurs.
Phase balance.
Thermal motion of molecules.
The most convincing fact is the Brownian motion of molecules. Brownian motion of molecules confirms the chaotic nature of thermal motion and the dependence of the intensity of this motion on temperature. For the first time, the erratic movement of small solid particles was observed by the English botanist R. Brown in 1827, considering solid particles suspended in water - spores of the club moss. Draw students' attention to the fact that the movement of disputes occurs along straight lines that make up a broken line. Since then, the motion of particles in a liquid or gas has been called Brownian. Carry out a standard demonstration experiment "Observation of Brownian motion" using a round box with two glasses.
By changing the temperature of a liquid or gas, for example, by increasing it, one can increase the intensity of Brownian motion. A Brownian particle moves under the influence of molecular impacts. The explanation for the Brownian motion of a particle is that the impacts of liquid or gas molecules on the particle do not cancel each other out. The quantitative theory of Brownian motion was developed by Albert Einstein in 1905. Einstein showed that the mean square of the displacement of a Brownian particle is proportional to the temperature of the medium, depends on the shape and size of the particle, and is directly proportional to the observation time. The French physicist J. Perrin conducted a series of experiments that quantitatively confirmed the theory of Brownian motion.
Calculation of the number of impacts on the vessel wall. Consider an ideal monatomic gas in equilibrium in a vessel of volume V. Let us single out molecules with a velocity from v to v + dv. Then the number of molecules moving in the direction of the angles and with these velocities will be equal to:
dN v,, = dN v d/4. (14.8)
Let us single out an elementary surface with area dP., which we will take as part of the vessel wall. For a unit of time, this area will be reached by molecules enclosed in an oblique cylinder with a base dП and a height v cos (see Fig. 14.3). The number of intersections of the selected surface by the molecules chosen by us (the number of impacts on the wall) per unit time d v,, will be equal to the product of the concentration of molecules and the volume of this oblique cylinder:
d v,, = dП v cos dN v,, /V, (14.9)
where V is the volume of the vessel containing the gas.
Integrating expression (14.9) over the angles within the solid angle 2, which corresponds to a change in the angles and in the range from 0 to /2 and from 0 to 2, respectively, we obtain a formula for calculating the total number of impacts of molecules with velocities from v to v + dv against the wall.
Integrating the expression over all velocities, we obtain that the number of impacts of molecules on a wall with area dP per unit time will be equal to:
. (14.11)
Given the definition average speed we obtain that the number of impacts of molecules on a wall of unit area per unit time will be equal to:
= N/V
The Boltzmann distribution, i.e. the distribution of particles in an external potential field, can be used to determine the constants used in molecular physics. One of the most important and famous experiments in this area is Perrin's work on Avogadro's number. Since gas molecules are not visible even through a microscope, much larger Brownian particles were used in the experiment. These particles were placed in a solution in which a buoyant force acted on them. In this case, the force of gravity acting on the Brownian particles decreased, and thus the distribution of particles along the height seemed to be stretched. This made it possible to observe this distribution under a microscope.
One of the difficulties was to obtain suspended particles of exactly the same size and shape. Perrin used particles of gum and mastic. Rubbing gummigut in water. Perrin received a bright yellow emulsion, in which, when observed under a microscope, many spherical granules could be distinguished. Instead of mechanical grinding, Perrin also treated gum or mastic with alcohol, which dissolved these substances. When such a solution was diluted with a large amount of water, an emulsion was obtained from the same spherical grains as during mechanical grinding of gum. To select grains of exactly the same size, Perrin subjected particles suspended in water to repeated centrifugation and in this way obtained a very homogeneous emulsion consisting of spherical particles with a radius of the order of a micrometer. Having processed 1 kg of gummigut, Perrin received a fraction containing several decigrams of grains of the desired size after a few months. With this fraction, the experiments described here were carried out.
When studying the emulsion, it was necessary to make measurements at negligible height differences - only a few hundredths of a millimeter. Therefore, the height distribution of particles was studied using a microscope. A very thin glass with a wide hole drilled in it was glued to a microscope slide (shown in the figure). In this way, a flat bath (Zeiss (1816-1886) cuvette) was obtained, the height of which was about 100 µm (0.1 mm). A drop of emulsion was placed in the center of the bath, which was immediately flattened with a cover slip. To avoid evaporation, the edges of the coverslip were covered with paraffin or varnish. Then the drug could be observed for several days or even weeks. The preparation was placed on the stage of a microscope carefully set in a horizontal position. The lens was of very high magnification with a shallow depth of focus, so that only particles inside a very thin horizontal layer with a thickness of the order of a micrometer could be seen at a time. The particles performed intense Brownian motion. By focusing the microscope on a specific horizontal layer emulsion, it was possible to count the number of particles in this layer. Then the microscope was focused on another layer, and again the number of visible Brownian particles was counted. In this way it was possible to determine the ratio of the concentrations of Brownian particles at different heights. The height difference was measured with a micrometer screw of the microscope.
Now let's move on to specific calculations. Since Brownian particles are in the field of gravity and Archimedes, the potential energy of such a particle
In this formula, p is the density of the gum, p is the density of the liquid, V is the volume of the gum particle. The reference point for the potential energy is chosen at the bottom of the cell, that is, at h = 0. We write the Boltzmann distribution for such a field in the form
n(h) = n0e kT = n0e kT . Recall that n is the number of particles per unit volume at height h, and n0 is the number of particles per unit volume at height h = 0.
The number of balls AN visible through the microscope at height h is equal to n(h)SAh, where S is the area of the visible part of the emulsion, and Ah is the depth of field of the microscope (in Perrin's experiment, this value was 1 μm). Then we write the ratio of the numbers of particles at two heights h1 and h2 as follows:
AN1 = ((p-p")Vg(h2 _ h1) - exp
Calculating the logarithm of both sides of the equation and performing simple calculations, we obtain the value of the Boltzmann constant, and then the Avogadro number:
k(p_p")Vg(h2 _ h1)
When working in various conditions and with various emulsions, Perrin obtained values for the Avogadro constant ranging from 6.5 1023 to 7.2 1023 mol-1. This was one of the direct proofs of the molecular-kinetic theory, in the validity of which at that time not all scientists believed.
Average energy of molecules.
Topic: Forces of intermolecular interaction. Aggregate
state of matter. The nature of the thermal motion of molecules in solid,
liquid and gaseous bodies and its change with increasing temperature.
Thermal expansion of tel. Phase transitions. Heat phase
transitions. Phase balance.
Intermolecular interaction is electrical in nature. Between them
forces of attraction and repulsion act, which quickly decrease with increasing
distances between molecules.
Repulsive forces act only at very small distances.
In practice, the behavior of a substance and its state of aggregation is determined by what is dominant: attractive forces or chaotic thermal motion.
Solids are dominated by interaction forces, so they retain their shape. The interaction forces depend on the shape and structure of the molecules, so there is no single law for their calculation.
However, if we imagine that the molecules have a spherical shape - general character the dependence of the interaction forces on the distance between molecules –r is shown in Figure 1-a. Figure 1-b shows the dependence of the potential energy of the interaction of molecules on the distance between them. At a certain distance r0 (it is different for different substances) Fattract.= Fretract. The potential energy is minimal, at rr0 the repulsive forces predominate, and at rr0 it is vice versa.
Figure 1-c shows the transition of the kinetic energy of molecules into potential energy during their thermal motion (for example, vibrations). In all figures, the origin of coordinates is aligned with the center of one of the molecules. Approaching another molecule, its kinetic energy transforms into potential energy and reaches its maximum value at distances r=d. d is called the effective diameter of the molecules (the minimum distance that the centers of two molecules approach.
It is clear that the effective diameter depends, among other things, on temperature, since at a higher temperature the molecules can come closer together.
At low temperatures, when the kinetic energy of the molecules is small, they are attracted close and settled in a certain order - a solid state of aggregation.
Thermal motion in solids is mainly oscillatory. At high temperatures, intense thermal motion prevents the molecules from approaching each other - the gaseous state, the movement of molecules is translational and rotational .. In gases, less than 1% of the volume falls on the volume of the molecules themselves. At intermediate temperatures, the molecules will continuously move in space, exchanging places, but the distance between them is not much greater than d - liquid. The nature of the movement of molecules in a liquid is oscillatory and translational (at the moment when they jump to a new equilibrium position).
The thermal motion of molecules explains the phenomenon of thermal expansion of bodies. When heated, the amplitude of the vibrational motion of molecules increases, which leads to an increase in the size of the bodies.
The linear expansion of a rigid body is described by the formula:
l l 0 (1 t), where is the coefficient of linear expansion 10-5 K-1. The volumetric expansion of bodies is described by a similar formula: V V0 (1 t), is the coefficient of volumetric expansion, and =3.
The substance can be in solid, liquid, gaseous states. These states are called aggregate states of matter. Matter can change from one state to another. A characteristic feature of the transformation of a substance is the possibility of the existence of stable heterogeneous systems, when the substance can be in several states of aggregation at once.
When describing such systems, a broader concept of the phase of matter is used. For example, carbon in a solid state of aggregation can be in two different phases - diamond and graphite. The phase is the totality of all parts of the system, which in the absence of external influence is physically homogeneous. If several phases of a substance at a given temperature and pressure exist, in contact with each other, and at the same time the mass of one phase does not increase due to a decrease in the other, then they speak of phase equilibrium.
The transition of a substance from one phase to another is called a phase transition. During a phase transition, an abrupt (occurring in a narrow temperature range) qualitative change in the properties of a substance occurs. These transitions are accompanied by an abrupt change in energy, density, and other parameters. There are phase transitions of the first and second order. The phase transitions of the first kind include melting, solidification (crystallization), evaporation, condensation and sublimation (evaporation from the surface of a solid body). Phase transitions of this kind are always associated with the release or absorption of heat, called latent heat phase transition.
During phase transitions of the second kind, there is no abrupt change in energy and density. The phase transition heat is also equal to 0. Transformations during such transitions occur immediately in the entire volume as a result of a change crystal lattice at a certain temperature, called the Curie point.
Consider a transition of the first kind. When the body is heated, as noted, there is a thermal expansion of the body and, as a consequence, a decrease in the potential energy of particle interaction. A situation arises when, at a certain temperature, the relationship between potential and kinetic energies cannot ensure the equilibrium of the old phase state and the substance passes into a new phase.
Melting is the transition from a crystalline state to a liquid state. Q=m, specific heat melting, shows how much heat is needed to transfer 1 kg solid into liquid at the melting point, measured in J / kg. During crystallization, the released amount of heat is calculated using the same formula. Melting and crystallization occur at a specific temperature for a given substance, called the melting point.
Evaporation. Molecules in a liquid are bound by attractive forces, but some of the fastest molecules can leave the volume of the liquid. In this case, the average kinetic energy of the remaining molecules decreases and the liquid cools. To maintain evaporation, it is necessary to supply heat: Q=rm, r is the specific heat of vaporization, which shows how much heat must be spent to transfer 1 kg of liquid to a gaseous state at a constant temperature.
Unit: J/kg. During condensation, heat is released.
The calorific value of the fuel is calculated by the formula: Q=qm.
Under conditions of mechanical and thermal equilibrium, the states of inhomogeneous systems are determined by setting pressure and temperature, since these parameters are the same for each part of the system. Experience shows that when two phases are in equilibrium, pressure and temperature are interconnected by a dependence that is a phase equilibrium curve.
The points lying on the curve describe an inhomogeneous system in which there are two phases. The points lying inside the regions describe homogeneous states of matter.
If the curves of all phase equilibria of one substance are built on a plane, then they will divide it into separate regions, and they themselves will converge at one point, which is called the triple point. This point describes the state of matter in which all three phases can coexist. In Figure 2, diagrams of the state of water are constructed.
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One of the most important parameters characterizing a molecule is the minimum potential energy of interaction. Attractive forces acting between molecules tend to condense a substance, i.e., bring its molecules closer to a distance r 0 when their potential energy of interaction is minimal and equal, but this approach is hindered by the chaotic thermal motion of the molecules. The intensity of this movement is determined by the average kinetic energy of the molecule, which is of the order kT, where k is the Boltzmann constant. Aggregate states substances significantly depend on the ratio of quantities and kT.
Let us assume that the temperature of the considered system of molecules is so high that
kT>> In this case, intense chaotic thermal motion prevents the forces of attraction from connecting molecules into aggregates of several particles that have come close to a distance r 0: during collisions, the large kinetic energy of the molecules will easily break these aggregates into constituent molecules and, thus, the probability of formation of stable aggregates will be arbitrarily small. Under these circumstances, the molecules in question will obviously be in a gaseous state.
If the temperature of the particle system is very low, i.e. kT << молекулам, действующими силами притяжения, тепловое движение не может помешать приблизиться друг к другу на расстояние близкое к r 0 in a specific order. In this case, the system of particles will be in a solid state, and the small kinetic energy of thermal motion will force the molecules to make random small vibrations around certain equilibrium positions (crystal lattice nodes).
Finally, at the temperature of the system of particles determined from the approximate equality kT≈ the kinetic energy of the thermal motion of molecules, the value of which is approximately equal to the potential energy of attraction, will not be able to move the molecule to a distance significantly exceeding r 0 . Under these conditions, the substance will be in a liquid state of aggregation.
Thus, a substance, depending on its temperature and the size of its constituent molecules, will be in a gaseous, solid or liquid state.
Under normal conditions, the distance between molecules in a gas is dozens of times (see Example 1.1) greater than their size; most of the time they move in a straight line without interaction, and only a much smaller part of the time, when they are at close distances from other molecules, interact with them, changing the direction of their movement. Thus, in the gaseous state, the movement of a molecule looks like it is schematically shown in Fig. 7, a.
In the solid state, each molecule (atom) of a substance is in an equilibrium position (a node of the crystal lattice), near which it makes small vibrations, and the direction (for example, aa" in fig. 7, b) and the amplitude of these oscillations randomly change (for example, in the direction bb") after a time much longer than the period of these oscillations; the vibrational frequencies of molecules in the general case are not the same. Vibrations of an individual molecule of a solid body are shown in general terms in fig. 7, b.
The molecules of a solid are packed so tightly that the distance between them is approximately equal to their diameter, i.e. distance r 0 in fig. 3. It is known that the density of the liquid state is approximately 10% less than the density of the solid state, all other things being equal. Therefore, the distance between the molecules of the liquid state is somewhat larger r 0 . Considering that, in the liquid state, the molecules also have a greater kinetic energy of thermal motion, it should be expected that, unlike the solid state, they can easily change their location by making an oscillatory motion, moving over a distance not significantly exceeding the diameter of the molecule. The trajectory of the movement of a liquid molecule approximately looks like the one shown schematically in Fig. 7, in. Thus, the motion of a molecule in a liquid combines translational motion, as occurs in a gas, with oscillatory motion, which is observed in a solid.
