Let us consider how the projection of the resulting force of interaction between them on the straight line connecting the centers of the molecules changes depending on the distance between the molecules. If the molecules are located at distances exceeding their size by several times, then the forces of interaction between them practically do not affect. Interaction forces between molecules are short-range.
At distances exceeding 2-3 molecular diameters, the repulsive force is practically zero. Only the force of attraction is noticeable. As the distance decreases, the attractive force increases and at the same time the repulsive force begins to affect. This force increases very rapidly when the electron shells of the molecules begin to overlap.
Figure 2.10 graphically shows the dependence of the projection F r interaction forces of molecules on the distance between their centers. On distance r 0 , approximately equal to the sum of the radii of the molecules, F r = 0 , since the force of attraction is equal in absolute value to the force of repulsion. At r > r 0 there is an attractive force between molecules. The projection of the force acting on the right molecule is negative. At r < r 0 there is a repulsive force with a positive projection value F r .
Origin of elastic forces
The dependence of the interaction forces of molecules on the distance between them explains the appearance of an elastic force during compression and tension of bodies. If you try to bring the molecules closer to a distance less than r0, then a force begins to act that prevents the approach. On the contrary, when the molecules move away from each other, an attractive force acts, returning the molecules to their original positions after the cessation of external influence.
With a small displacement of molecules from equilibrium positions, the forces of attraction or repulsion grow linearly with increasing displacement. In a small section, the curve can be considered a straight line segment (the thickened section of the curve in Fig. 2.10). That is why, at small deformations, Hooke's law turns out to be valid, according to which the elastic force is proportional to the deformation. At large displacements of molecules, Hooke's law is no longer valid.
Since the distances between all molecules change when the body is deformed, the neighboring layers of molecules account for an insignificant part of the total deformation. Therefore, Hooke's law is fulfilled at deformations that are millions of times greater than the size of the molecules.
Atomic force microscope
The device of the atomic force microscope (AFM) is based on the action of repulsive forces between atoms and molecules at small distances. This microscope, in contrast to the tunnel microscope, allows you to obtain images of non-conductive surfaces. Instead of a tungsten tip, AFM uses a small piece of diamond sharpened to atomic size. This fragment is fixed on a thin metal holder. When the tip approaches the surface under study, the electron clouds of diamond atoms and the surface begin to overlap and repulsive forces arise. These forces deflect the tip of the diamond point. Deviation is registered by means of a laser beam reflected from a mirror fixed on a holder. The reflected beam drives a piezoelectric arm similar to that of a tunneling microscope. The feedback mechanism ensures that the height of the diamond needle above the surface is such that the curvature of the holder plate remains unchanged.
In Figure 2.11 you see an AFM image of the polymer chains of the amino acid alanine. Each tubercle represents one amino acid molecule.
At present, atomic microscopes have been designed, the device of which is based on the action of molecular forces of attraction at distances several times greater than the size of an atom. These forces are approximately 1000 times smaller than the repulsive forces in the AFM. Therefore, a more complex sensitive system is used to register forces.
Atoms and molecules are made up of electrically charged particles. Due to the action of electrical forces at short distances, the molecules attract, but begin to repel when the electron shells of the atoms overlap.
liquids, amorphous and crystalline bodies
gases and liquids
gases, liquids and crystalline bodies
approximately equal to the diameter of the molecule
less than the diameter of the molecule
about 10 times the diameter of the molecule
depends on gas temperature
liquids
crystalline bodies
amorphous bodies
only gas structure models
only models of the structure of amorphous bodies
models of the structure of gases and liquids
models of the structure of gases, liquids and solids
the distance between molecules increases
molecules begin to attract each other
increasing order in the arrangement of molecules
the distance between molecules decreases
hasn't changed
increased 5 times
decreased by 5 times
increased by the root of five times
The distances between molecules are comparable to the sizes of molecules (under normal conditions) for
In gases under normal conditions, the average distance between molecules
The least order in the arrangement of particles is typical for
The distance between adjacent particles of a substance, on average, is many times greater than the size of the particles themselves. This statement is consistent with the model
During the transition of water from a liquid to a crystalline state
At constant pressure, the concentration of gas molecules increased by 5 times, and its mass did not change. Average kinetic energy of translational motion of gas molecules
The table shows the melting and boiling points of some substances:
substance | Boiling temperature | substance | Melting temperature |
naphthalene |
Choose the correct statement.
The melting point of mercury is greater than the boiling point of ether
The boiling point of alcohol is less than the melting point of mercury
The boiling point of alcohol is greater than the melting point of naphthalene
The boiling point of ether is less than the melting point of naphthalene
The temperature of the solid body dropped by 17 ºС. On the absolute temperature scale, this change was
1) 290 K 2) 256 K 3) 17 K 4) 0 K
9. In a vessel of constant volume there is an ideal gas in the amount of 2 mol. How should the absolute temperature of a vessel with gas be changed when 1 mol of gas is released from the vessel so that the pressure of the gas on the walls of the vessel increases by 2 times?
1) increase by 2 times 3) increase by 4 times
2) decrease by 2 times 4) decrease by 4 times
10. At temperature T and pressure p, one mole of an ideal gas occupies a volume V. What is the volume of the same gas, taken in an amount of 2 mol, at a pressure of 2p and a temperature of 2T?
1) 4V 2) 2V 3) V 4) 8V
11. The temperature of hydrogen, taken in an amount of 3 mol, in a vessel is equal to T. What is the temperature of oxygen, taken in an amount of 3 mol, in a vessel of the same volume and at the same pressure?
1) T 2) 8T 3) 24 T 4) T/8
12. In a vessel closed by a piston, there is an ideal gas. A graph of the dependence of gas pressure on temperature with changes in its state is shown in the figure. Which state of the gas corresponds to the smallest value of volume?
1) A 2) B 3) C 4) D
13. In a vessel of constant volume there is an ideal gas, the mass of which is changed. The diagram shows the process of changing the state of the gas. At which point on the diagram is the mass of gas the greatest?
1) A 2) B 3) C 4) D
14. At the same temperature, saturated steam in a closed vessel differs from unsaturated steam in the same vessel
1) pressure
2) the speed of movement of molecules
3) the average energy of the chaotic movement of molecules
4) the absence of impurities of foreign gases
15. Which point on the diagram corresponds to the maximum gas pressure?
can't give an exact answer
17. A balloon with a volume of 2500 cubic meters with a shell mass of 400 kg has an opening at the bottom through which the air in the balloon is heated by a burner. To what minimum temperature must the air in the balloon be heated in order for the balloon to take off with a load (basket and aeronaut) weighing 200 kg? The ambient temperature is 7ºС, its density is 1.2 kg per cubic meter. The shell of the sphere is assumed to be inextensible.
MKT and thermodynamics
MKT and thermodynamics
For this section, each option included five tasks with a choice
response, of which 4 are basic and 1 is advanced. Based on exam results
The following elements of content were learned:
Application of the Mendeleev–Clapeyron equation;
Dependence of gas pressure on the concentration of molecules and temperature;
The amount of heat during heating and cooling (calculation);
Features of heat transfer;
Relative air humidity (calculation);
Work in thermodynamics (graph);
Application of the equation of state of a gas.
Among the tasks of the basic level of difficulty, the following questions were raised:
1) Change in internal energy in various isoprocesses (for example, when
isochoric increase in pressure) - 50% of completion.
2) Graphs of isoprocesses - 56%.
Example 5
The constant mass of an ideal gas is involved in the process shown
on the image. The highest gas pressure in the process is reached
1) at point 1
2) on the entire segment 1–2
3) at point 3
4) on the entire segment 2–3
Answer: 1
3) Determination of air humidity - 50%. These assignments included a photo
psychrometer, according to which it was necessary to take readings of dry and wet
thermometers, and then determine the humidity of the air using part
psychrometric table given in the task.
4) Application of the first law of thermodynamics. These tasks were the most
difficult among the tasks of the basic level in this section - 45%. Here
it was necessary to use the graph, determine the type of isoprocess
(either isotherms or isochores were used) and in accordance with this
determine one of the parameters given the other.
Among the tasks of an advanced level, there were presented computational tasks for
application of the equation of state of gas, with which an average of 54% coped
students, as well as previously used tasks to determine the change
parameters of an ideal gas in an arbitrary process. Dealing with them successfully
only a group of strong graduates, and the average percentage of completion was 45%.
One of these tasks is shown below.
Example 6
An ideal gas is contained in a vessel closed by a piston. Process
the change in the state of the gas is shown in the diagram (see figure). How
did the volume of the gas change during its transition from state A to state B?
1) increased all the time
2) decreased all the time
3) first increased, then decreased
4) first decreased, then increased
Answer: 1
Activities Quantity
jobs %
photos2 10-12 25.0-30.0
4. PHYSICS
4.1. Characteristics of control measuring materials in physics
2007
The examination paper for the unified state exam in 2007 had
the same structure as in the previous two years. It consisted of 40 tasks,
differing in form of presentation and level of complexity. In the first part of the work
30 tasks with a choice of answers were included, where each task was given
four possible answers, of which only one was correct. The second part contained 4
short answer questions. They were computational problems, after solving
which required the answer to be given as a number. The third part of the exam
work - these are 6 calculation tasks, to which it was necessary to bring a complete
expanded solution. The total time to complete the work was 210 minutes.
Education Content Elements Codifier and Specification
examination papers were compiled on the basis of the Mandatory Minimum
1999 No. 56) and took into account the Federal component of the state standard
secondary (complete) education in physics, profile level (Order of the Ministry of Defense dated 5
March 2004 No. 1089). The content element codifier has not changed since
compared with 2006 and included only those elements that are simultaneously
are present as in the Federal component of the state standard
(profile level, 2004), and in the Mandatory minimum maintenance
Education 1999
Compared to the 2006 control measuring materials in the options
The 2007 USE has been amended in two ways. The first of these was to redistribute
assignments in the first part of the work on a thematic basis. Regardless of the difficulty
(basic or advanced levels), first all tasks in mechanics followed, then
in MKT and thermodynamics, electrodynamics and, finally, in quantum physics. Second
the change concerned the purposeful introduction of tasks that check
formation of methodological skills. In 2007, A30 tasks tested skills
analyze the results of experimental studies expressed as
tables or graphs, as well as build graphs based on the results of the experiment. Selection
tasks for the A30 line was carried out based on the need for verification in this
series of variants of one type of activity and, accordingly, regardless of
thematic affiliation of a particular task.
In the examination paper, tasks of basic, advanced
and high levels of difficulty. The tasks of the basic level tested the assimilation of the most
important physical concepts and laws. Elevated tasks supervised
the ability to use these concepts and laws to analyze more complex processes or
the ability to solve problems for the application of one or two laws (formulas) for any of
topics of the school physics course. Tasks of a high level of complexity are calculated
tasks that reflect the level of requirements for university entrance exams and
require the application of knowledge from two or three sections of physics at once in a modified or
new situation.
KIM 2007 included assignments for all major content
sections of the physics course:
1) "Mechanics" (kinematics, dynamics, statics, conservation laws in mechanics,
mechanical vibrations and waves);
2) “Molecular physics. Thermodynamics";
3) "Electrodynamics" (electrostatics, direct current, magnetic field,
electromagnetic induction, electromagnetic oscillations and waves, optics);
4) "Quantum physics" (elements of SRT, corpuscular-wave dualism, physics
atom, nuclear physics).
Table 4.1 shows the distribution of tasks by content blocks in each
part of the examination paper.
Table 4.1
depending on the type of tasks
All work
(with choice
(with brief
Jobs % No.
Jobs % No.
jobs %
1 Mechanics 11-131 27.5-32.5 9-10 22.5-25.0 1 2.5 1-2 2.5-5.0
2 MKT and thermodynamics 8-10 20.0-25.0 6-7 15.0-17.5 1 2.5 1-2 2.5-5.0
3 Electrodynamics 12-14 30.0-35.5 9-10 22.5-15.0 2 5.0 2-3 5.0-7.5
4 Quantum physics and
STO 6-8 15.0-20.0 5-6 12.5-15.0 – – 1-2 2.5-5.0
Table 4.2 shows the distribution of tasks by content blocks in
depending on the level of difficulty.
Table4.2
Distribution of tasks by sections of the course of physics
depending on the level of difficulty
All work
A basic level of
(with choice
elevated
(with choice of answer
and brief
High level
(with extended
Answer section)
Jobs % No.
Jobs % No.
Jobs % No.
jobs %
1 Mechanics 11-13 27.5-32.5 7-8 17.5-20.0 3 7.5 1-2 2.5-5.0
2 MKT and thermodynamics 8-10 20.0-25.0 5-6 12.5-15.0 2 5.0 1-2 2.5-5.0
3 Electrodynamics 12-14 30.0-35.5 7-8 17.5-20.0 4 10.0 2-3 5.0-7.5
4 Quantum physics and
STO 6-8 15.0-20.0 4-5 10.0-12.5 1 2.5 1-2 2.5-5.0
When developing the content of the examination paper, it was taken into account
the need to check the mastery of various activities. Wherein
tasks of each of the series of options were selected taking into account the distribution by type
activities presented in table 4.3.
1 The change in the number of tasks for each of the topics is associated with different topics of complex tasks C6 and
tasks A30, testing methodological skills on the material of different sections of physics, in
different series of options.
Table4.3
Distribution of tasks by types of activity
Activities Quantity
jobs %
1 Understand the physical meaning of models, concepts, quantities 4-5 10.0-12.5
2 Explain physical phenomena, distinguish between the influence of various
factors on the course of phenomena, manifestations of phenomena in nature or
their use in technical devices and everyday life
3 Apply the laws of physics (formulas) to analyze processes on
quality level 6-8 15.0-20.0
4 Apply the laws of physics (formulas) to analyze processes on
calculated level 10-12 25.0-30.0
5 Analyze the results of experimental studies 1-2 2.5-5.0
6 Analyze information obtained from graphs, tables, diagrams,
photos2 10-12 25.0-30.0
7 Solve problems of various levels of complexity 13-14 32.5-35.0
All tasks of the first and second parts of the examination paper were evaluated at 1
primary score. Solutions to the problems of the third part (С1-С6) were checked by two experts in
in accordance with the generalized evaluation criteria, taking into account the correctness and
completeness of the answer. The maximum score for all tasks with a detailed answer was 3
points. The task was considered solved if the student scored at least 2 points for it.
Based on the points assigned for the completion of all tasks of the examination
work was translated into "test" scores on a 100-point scale and into marks
on a five-point scale. Table 4.4 reflects the relationship between primary,
test marks on a five-point system over the past three years.
Table4.4
Primary score ratio, test scores and school grades
Years, points 2 3 4 5
2007 primary 0-11 12-22 23-35 36-52
test 0-32 33-51 52-68 69-100
2006 primary 0-9 10-19 20-33 34-52
test 0-34 35-51 52-69 70-100
2005 primary 0-10 11-20 21-35 36-52
test 0-33 34-50 51-67 68-100
Comparison of the boundaries of primary scores shows that this year the conditions
the corresponding marks were more stringent than in 2006, but
approximately corresponded to the conditions of 2005. This was due to the fact that in the past
year, the unified exam in physics was passed not only by those who were going to enter universities
in the relevant profile, but also almost 20% of students (of the total number of applicants),
who studied physics at a basic level (for them, this exam was by decision
region is required).
In total, 40 options were prepared for the exam in 2007,
which were five series of 8 options, created according to different plans.
The series of variants differed in controlled content elements and types.
activities for the same line of tasks, but in general they all had approximately
2 In this case, we mean the form of presentation of information in the text of the task or distractors,
so the same job can check two activities.
the same average level of difficulty and corresponded to the plan of the examination
of the work given in Appendix 4.1.
4.2. Characteristics of USE participants in physics2007 of the year
The number of participants in the USE in physics this year amounted to 70,052 people, which
significantly lower than in the previous year, and approximately in line with the indicators
2005 (see table 4.5). The number of regions in which graduates took the USE in
physics, increased to 65. The number of graduates who chose physics in the format
USE, differs significantly for different regions: from 5316 people. in the Republic
Tatarstan up to 51 people in the Nenets Autonomous Okrug. As a percentage of
the total number of graduates, the number of participants in the USE in physics ranges from
0.34% in Moscow to 19.1% in the Samara region.
Table4.5
Number of Exam Participants
Year Number Girls Boys
regions
participants Number % Number %
2005 54 68 916 18 006 26,1 50 910 73,9
2006 61 90 3893 29 266 32,4 61 123 67,6
2007 65 70 052 17 076 24,4 52 976 75,6
The physics exam is chosen predominantly by young men, and only a quarter of
of the total number of participants are girls who chose to continue
education universities of physical and technical profile.
The distribution of exam participants by
types of settlements (see table 4.6). Nearly half of the graduates who took
Unified State Examination in Physics, lives in large cities, and only 20% are students who have completed
rural schools.
Table4.6
Distribution of exam participants by types of settlements, in which
their educational institutions are located
Number of examinees Percentage
Type of settlement examined
Settlement of rural type (village,
village, farm, etc.) 13,767 18,107 14,281 20.0 20.0 20.4
Urban settlement
(working settlement, urban settlement
type, etc.)
4 780 8 325 4 805 6,9 9,2 6,9
City with a population of less than 50 thousand people 7,427 10,810 7,965 10.8 12.0 11.4
City with a population of 50-100 thousand people 6,063 8,757 7,088 8.8 9.7 10.1
City with a population of 100-450 thousand people 16,195 17,673 14,630 23.5 19.5 20.9
City with a population of 450-680 thousand people 7,679 11,799 7,210 11.1 13.1 10.3
A city with a population of over 680,000.
people 13,005 14,283 13,807 18.9 15.8 19.7
St. Petersburg - 72 7 - 0.1 0.01
Moscow - 224 259 - 0.2 0.3
No data – 339 – – 0.4 –
Total 68,916 90,389 70,052 100% 100% 100%
3 In 2006, in one of the regions, entrance exams to universities in physics were held only in
USE format. This led to such a significant increase in the number of participants in the exam.
The composition of exam participants by types of educational institutions practically does not change.
institutions (see table 4.7). Like last year, the vast majority
of those tested graduated from general education institutions, and only about 2%
graduates came to the exam from educational institutions of primary or
secondary vocational education.
Table4.7
Distribution of exam participants by types of educational institutions
Number
examinees
Percent
Type of educational institution examined
2006 G. 2007 G. 2006 G. 2007 G.
General education institutions 86,331 66,849 95.5 95.4
Evening (shift) general education
institutions 487 369 0.5 0.5
General education boarding school,
cadet school, boarding school with
initial flight training
1 144 1 369 1,3 2,0
Educational institutions of primary and
secondary vocational education 1,469 1,333 1.7 1.9
No data 958 132 1.0 0.2
Total: 90,389 70,052 100% 100%
4.3. The main results of the examination work in physics
In general, the results of the examination work in 2007 were
slightly higher than last year, but about the same level as
figures for the previous year. Table 4.8 shows the results of the USE in physics in 2007.
on a five-point scale, and in table 4.9 and in fig. 4.1 - on test scores in 100-
point scale. For clarity of comparison, the results are presented in comparison with
the previous two years.
Table4.8
Distribution of exam participants by level
training(percentage of the total)
Years "2" Marks "n3o" 5 points "b4n" on the scale "5"
2005 10,5% 40,7% 38,1% 10,7%
2006 16,0% 41,4% 31,1% 11,5%
2007 12,3% 43,2% 32,5% 12,0%
Table4.9
Distribution of exam participants
based on test scores2005-2007 gg.
Year Test score scale interval
0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
2005 0,09% 0,57% 6,69% 19,62% 24,27% 24,44% 16,45% 6,34% 1,03% 0,50% 68 916
2006 0,10% 0,19% 6,91% 23,65% 23,28% 19,98% 15,74% 7,21% 2,26% 0,68% 90 389
2007 0,07% 1,09% 7,80% 19,13% 27,44% 20,60% 14,82% 6,76% 1,74% 0,55% 70 052
0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
Test score
Percentage of students who received
corresponding test score
Rice. 4.1 Distribution of exam participants by test scores received
Table 4.10 compares the scale in test scores in a 100-point
scale with the results of completing the tasks of the examination option in the primary
Table4.10
Comparison of intervals of primary and test scores in2007 year
Scale interval
test scores 0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
Scale interval
primary scores 0-3 4-6 7-10 11-15 16-22 23-29 30-37 38-44 45-48 49-52
To obtain 35 points (score 3, primary score - 13) the test-taker
it was enough to correctly answer the 13 simplest questions of the first part
work. To score 65 points (grade 4, primary score - 34), the graduate must
was, for example, correctly answer 25 tasks with a choice of answers, solve three out of four
short answer problems and two more high-level problems
difficulties. Those who received 85 points (score 5, primary score 46) practically
performed the first and second parts of the work perfectly and solved at least four tasks
third part.
The best of the best (range from 91 to 100 points) need not only
freely navigate in all matters of the school course of physics, but also in practice
avoid even technical errors. So, to get 94 points (primary score
– 49) it was possible to “not get” only 3 primary points, allowing, for example,
arithmetic errors in solving one of the problems of a high level of complexity
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An example of the simplest system studied in molecular physics is gas. According to the statistical approach, gases are considered as systems consisting of a very large number of particles (up to 1026 m–3) that are in constant random motion. In molecular kinetic theory, they use ideal gas model, according to which it is believed that:
1) the own volume of gas molecules is negligible compared to the volume of the vessel;
2) there are no interaction forces between gas molecules;
3) collisions of gas molecules with each other and with the walls of the vessel are absolutely elastic.
Let us estimate the distances between molecules in a gas. Under normal conditions (N.O.: р=1.03·10 5 Pa; t=0ºС), the number of molecules per unit volume: . Then the average volume per molecule is:
(m 3).
Average distance between molecules: 
m. The average diameter of the molecule: d»3 10 -10 m. The intrinsic dimensions of the molecule are small compared to the distance between them (10 times). Consequently, particles (molecules) are so small that they can be likened to material points.
In a gas, the molecules are so far apart most of the time that the interaction forces between them are practically zero. It can be considered that the kinetic energy of gas molecules is much greater than the potential energy, so the latter can be neglected.
However, at moments of short-term interaction ( clashes) interaction forces can be significant, which leads to the exchange of energy and momentum between molecules. Collisions serve as the mechanism by which a macrosystem can move from one energy state available to it under given conditions to another.
The ideal gas model can be used in the study of real gases, since under conditions close to normal (for example, oxygen, hydrogen, nitrogen, carbon dioxide, water vapor, helium), as well as at low pressures and high temperatures, they are close in their properties to the ideal gas.
The state of the body can change during heating, compression, shape change, that is, when changing any of the parameters. There are equilibrium and non-equilibrium states of the system. equilibrium state is a state in which all system parameters do not change with time (otherwise, it is non-equilibrium state), and there are no forces capable of changing the parameters.
The most important parameters of the state of the system are the density of the body (or the reciprocal of density - specific volume), pressure and temperature. Density (r) is the mass of a substance per unit volume. Pressure (R is the force acting per unit area of the surface of the body, directed along the normal to this surface. Difference temperatures (DT) is a measure of deviation of bodies from the state of thermal equilibrium. There is an empirical temperature and an absolute temperature. empirical temperature (t) is a measure of the deviation of bodies from the state of thermal equilibrium with melting ice under pressure of one physical atmosphere. The unit of measurement is 1 degree Celsius(1 o C), which is determined by the condition that 0 o C is attributed to ice melting under atmospheric pressure, and 100 o C to boiling water at the same pressure, respectively. The difference between absolute and empirical temperature is, first of all, that the absolute temperature is measured from the lowest temperature - absolute zero, which lies below the melting temperature of ice by 273.16 o, that is
| R= f(V,T). | (6.2.2,b) |
Note that any functional dependence that relates thermodynamic parameters to each other like (6.2.2, a), is also called the equation of state. The form of the dependence function between the parameters ((6.2.2, a), (6.2.2, b)) is determined experimentally for each substance. However, so far it has been possible to determine the equation of state only for gases in rarefied states, and, in an approximate form, for some compressed gases.
Many natural phenomena testify to the chaotic movement of microparticles, molecules and atoms of matter. The higher the temperature of the substance, the more intense this movement. Therefore, the heat of the body is a reflection of the random movement of its constituent molecules and atoms.
The proof that all atoms and molecules of a substance are in constant and random motion can be diffusion - the interpenetration of particles of one substance into another (see Fig. 20a). So, the smell quickly spreads around the room even in the absence of air movement. A drop of ink quickly turns the entire glass of water uniformly black, although it would seem that gravity should help color the glass only in the top-down direction. Diffusion can also be detected in solids if they are pressed tightly together and left for a long time. The phenomenon of diffusion demonstrates that the microparticles of a substance are able to spontaneously move in all directions. Such movement of microparticles of a substance, as well as its molecules and atoms, is called their thermal movement.
Obviously, all the water molecules in the glass are moving even if there is no ink drop in it. Simply, the diffusion of the ink makes the thermal movement of the molecules visible. Another phenomenon that makes it possible to observe thermal motion and even evaluate its characteristics can be Brownian motion, which is called the chaotic motion of any smallest particles in a completely calm liquid visible through a microscope. It was named Brownian in honor of the English botanist R. Brown, who in 1827, examining the pollen spores of one of the plants suspended in water under a microscope, found that they were continuously and chaotically moving.
Brown's observation was confirmed by many other scientists. It turned out that Brownian motion is connected neither with flows in a liquid, nor with its gradual evaporation. The smallest particles (they were also called Brownian ones) behaved as if they were alive, and this “dance” of particles accelerated with heating of the liquid and with a decrease in particle size, and, conversely, slowed down when water was replaced with a more viscous medium. Brownian motion was especially noticeable when it was observed in a gas, for example, following particles of smoke or fog droplets in the air. This amazing phenomenon never stopped, and it could be observed indefinitely.
An explanation of Brownian motion was given only in the last quarter of the 19th century, when it became obvious to many scientists that the motion of a Brownian particle is caused by random impacts of medium molecules (liquid or gas) that perform thermal motion (see Fig. 20b). On average, the molecules of the medium act on the Brownian particle from all sides with equal force, however, these impacts never exactly balance each other, and as a result, the speed of the Brownian particle randomly changes in magnitude and direction. Therefore, a Brownian particle moves along a zigzag path. In this case, the smaller the size and mass of a Brownian particle, the more noticeable its motion becomes.
In 1905, A. Einstein created the theory of Brownian motion, believing that at any given time the acceleration of a Brownian particle depends on the number of collisions with the molecules of the medium, which means that it depends on the number of molecules per unit volume of the medium, i.e. from Avogadro's number. Einstein derived a formula by which it was possible to calculate how the average square of the movement of a Brownian particle changes with time, if you know the temperature of the medium, its viscosity, particle size and the Avogadro number, which at that time was still unknown. The validity of this theory of Einstein was confirmed experimentally by J. Perrin, who was the first to obtain the value of Avogadro's number. Thus, the analysis of Brownian motion laid the foundations for the modern molecular-kinetic theory of the structure of matter.
Review questions:
· What is diffusion, and how is it related to the thermal motion of molecules?
What is called Brownian motion, and is it thermal?
How does the nature of Brownian motion change when heated?
Rice. 20. (a) - in the upper part, molecules of two different gases are shown, separated by a partition, which is removed (see lower part), after which diffusion begins; (b) the lower left shows a schematic representation of a Brownian particle (blue) surrounded by molecules in the medium, collisions with which cause the motion of the particle (see three trajectories of particle motion).
§ 21. INTERMOLECULAR FORCES: STRUCTURE OF GAS, LIQUID AND SOLID BODIES
We are accustomed to the fact that liquid can be poured from one vessel to another, and gas quickly fills the entire volume provided to it. Water can only flow along the riverbed, and the air above it knows no boundaries. If the gas did not seek to occupy all the space around, we would suffocate, because. the carbon dioxide we exhale would accumulate around us, preventing us from taking a breath of fresh air. Yes, and the cars would soon stop for the same reason. They also need oxygen to burn fuel.
Why does a gas, unlike a liquid, fill the entire volume provided to it? Intermolecular attractive forces act between all molecules, the magnitude of which decreases very quickly with the distance of the molecules from each other, and therefore, at a distance equal to several diameters of the molecules, they do not interact at all. It is easy to show that the distance between neighboring gas molecules is many times greater than that of a liquid. Using formula (19.3) and knowing the density of air (r=1.29 kg/m3) at atmospheric pressure and its molar mass (M=0.029 kg/mol), we can calculate the average distance between air molecules, which will be equal to 6.1.10- 9 m, which is twenty times the distance between water molecules.
Thus, between the molecules of a liquid, located almost close to each other, attractive forces act, preventing these molecules from scattering in different directions. On the contrary, the negligible forces of attraction between gas molecules are unable to hold them together, and therefore gases can expand, filling the entire volume provided to them. The existence of intermolecular forces of attraction can be verified by setting up a simple experiment - to press two lead bars against each other. If the contact surfaces are smooth enough, then the bars will stick together and it will be difficult to separate them.
However, intermolecular forces of attraction alone cannot explain all the differences between the properties of gaseous, liquid, and solid substances. Why, for example, is it very difficult to reduce the volume of a liquid or a solid, but it is relatively easy to compress a balloon? This is explained by the fact that between molecules there are not only attractive forces, but also intermolecular repulsive forces that act when the electron shells of atoms of neighboring molecules begin to overlap. It is these repulsive forces that prevent one molecule from penetrating into a volume already occupied by another molecule.
When external forces do not act on a liquid or solid body, the distance between their molecules is such (see r0 in Fig. 21a) at which the resultant forces of attraction and repulsion are equal to zero. If you try to reduce the volume of the body, then the distance between the molecules decreases, and from the side of the compressed body, the resultant of the increased repulsive forces begins to act. On the contrary, when a body is stretched, the elastic forces that arise are associated with a relative increase in the forces of attraction, since when the molecules move away from each other, the repulsive forces fall much faster than the attractive forces (see Fig. 21a).
Gas molecules are located at distances tens of times greater than their size, as a result of which these molecules do not interact with each other, and therefore gases are much easier to compress than liquids and solids. Gases do not have any specific structure and are a collection of moving and colliding molecules (see Fig. 21b).
A liquid is a collection of molecules that are almost closely adjacent to each other (see Fig. 21c). Thermal motion allows a liquid molecule to change its neighbors from time to time, jumping from one place to another. This explains the fluidity of liquids.
Atoms and molecules of solids are deprived of the ability to change their neighbors, and their thermal motion is only small fluctuations relative to the position of neighboring atoms or molecules (see Fig. 21d). The interaction between atoms can lead to the fact that a solid becomes a crystal, and the atoms in it occupy positions at the nodes of the crystal lattice. Since the molecules of solids do not move relative to their neighbors, these bodies retain their shape.
Review questions:
Why do gas molecules not attract each other?
What properties of bodies determine the intermolecular forces of repulsion and attraction?
How is fluid flow explained?
Why do all solid bodies retain their shape?
§ 22. IDEAL GAS. BASIC EQUATION OF THE MOLECULAR-KINETIC THEORY OF GAS.
The molecular kinetic theory explains that all substances can be in three states of aggregation: solid, liquid and gaseous. For example, ice, water and water vapor. Plasma is often considered the fourth state of matter.
Aggregate states of matter(from Latin aggrego- attach, bind) - states of the same substance, the transitions between which are accompanied by a change in its physical properties. This is the change in the aggregate states of matter.
In all three states, the molecules of the same substance do not differ from each other in any way, only their location, the nature of thermal motion and the forces of intermolecular interaction change.
Movement of molecules in gases
In gases, the distance between molecules and atoms is usually much larger than the size of the molecules, and the attractive forces are very small. Therefore, gases do not have their own shape and constant volume. Gases are easily compressed because the repulsive forces at large distances are also small. Gases have the property of expanding indefinitely, filling the entire volume provided to them. Gas molecules move at very high speeds, collide with each other, bounce off each other in different directions. Numerous impacts of molecules on the walls of the vessel create gas pressure.
Movement of molecules in liquids
In liquids, molecules not only oscillate around the equilibrium position, but also jump from one equilibrium position to the next. These jumps happen periodically. The time interval between such jumps is called average time of settled life(or average relaxation time) and is denoted by the letter ?. In other words, the relaxation time is the time of oscillations around one specific equilibrium position. At room temperature, this time is on average 10 -11 s. The time of one oscillation is 10 -12 ... 10 -13 s.
The time of settled life decreases with increasing temperature. The distance between liquid molecules is smaller than the size of the molecules, the particles are close to each other, and the intermolecular attraction is large. However, the arrangement of liquid molecules is not strictly ordered throughout the volume.
Liquids, like solids, retain their volume but do not have their own shape. Therefore, they take the form of the vessel in which they are located. The liquid has the property fluidity. Due to this property, the liquid does not resist a change in shape, it compresses little, and its physical properties are the same in all directions inside the liquid (isotropy of liquids). For the first time, the nature of molecular motion in liquids was established by the Soviet physicist Yakov Ilyich Frenkel (1894 - 1952).
Movement of molecules in solids
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.
Physics
Interaction between atoms and molecules of matter. The structure of solid, liquid and gaseous bodies
Attractive and repulsive forces act simultaneously between the molecules of a substance. These forces are largely dependent on the distances between molecules.
According to experimental and theoretical studies, intermolecular forces of interaction are inversely proportional to the nth power of the distance between molecules:
where for attractive forces n = 7, and for repulsive forces .
The interaction of two molecules can be described using a plot of the projection of the resultant forces of attraction and repulsion of molecules on the distance r between their centers. Let us direct the r axis from molecule 1, whose center coincides with the origin of coordinates, to the center of molecule 2 located at a distance from it (Fig. 1).
Then the projection of the repulsive force of molecule 2 from molecule 1 onto the r axis will be positive. The projection of the attractive force of molecule 2 to molecule 1 will be negative.
The repulsive forces (Fig. 2) are much greater than the attractive forces at small distances, but decrease much faster with increasing r. Attractive forces also decrease rapidly with increasing r, so that, starting from a certain distance , the interaction of molecules can be neglected. The largest distance rm at which the molecules still interact is called the radius of molecular action. 
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The repulsive forces are equal in modulus to the attractive forces.
The distance corresponds to the stable equilibrium mutual position of the molecules.
In various aggregate states of a substance, the distance between its molecules is different. Hence the difference in the force interaction of molecules and the essential difference in the nature of the motion of the molecules of gases, liquids and solids.
In gases, the distances between molecules are several times the size of the molecules themselves. As a result, the forces of interaction between gas molecules are small and the kinetic energy of the thermal motion of molecules far exceeds the potential energy of their interaction. Each molecule moves freely from other molecules at huge speeds (hundreds of meters per second), changing direction and velocity modulus when colliding with other molecules. The mean free path of gas molecules depends on the pressure and temperature of the gas. under normal conditions.
In liquids, the distance between molecules is much smaller than in gases. The forces of interaction between molecules are large, and the kinetic energy of the movement of molecules is commensurate with the potential energy of their interaction, as a result of which the molecules of the liquid oscillate around a certain equilibrium position, then abruptly move to new equilibrium positions after very short time intervals, which leads to liquid fluidity. Thus, in a liquid, the molecules perform mainly oscillatory and translational motions. In solids, the forces of interaction between molecules are so great that the kinetic energy of the motion of molecules is much less than the potential energy of their interaction. Molecules perform only vibrations with a small amplitude around a certain constant equilibrium position - a node of the crystal lattice.
This distance can be estimated by knowing the density of the substance and the molar mass. Concentration - the number of particles per unit volume is related to density, molar mass and Avogadro's number by the relation.
