Let's consider the properties of a molecule using the example of a substance such as sugar. If you grind it into the smallest grains, it will still contain many identical sugar molecules. Each grain will preserve all the properties of this substance. Even if you break sugar into separate molecules, for example, dissolve it in water, the substance will not disappear anywhere and will exhibit its properties. You can check this by testing whether the water has become sweet. Of course, if you continue crushing sugar further, destroying the molecules or taking away several atoms from them, the substance will be destroyed. It is worth noting that the atoms will not disappear, but will become part of other molecules. Sugar itself as a substance will no longer exist and will turn into another substance.

There are no eternal substances. Just as there are no eternal molecules. However, atoms are considered practically eternal.

Although the molecules are very small in size, their structure can still be elucidated using various chemical and physical methods. Some substances exist in pure form. These are substances that contain molecules of the same type. If the physical body contains different types of molecules, in this case we are dealing with a mixture of substances.

Today, the structure of substance molecules is determined by diffraction methods. Such methods include neutron diffraction, as well as X-ray diffraction analysis. There is also an electronic paramagnetic method and a vibrational spectroscopy method. Depending on the substance and its state, one or another method of analyzing molecules is determined.

Now you know what is called a molecule and what it consists of.

For example, a water molecule is the smallest representative of a substance such as water.

Why don't we notice that substances are made up of molecules? The answer is simple: the molecules are so small that they are simply invisible to the human eye. So what size are they?

An experiment to determine the size of a molecule was carried out by the English physicist Rayleigh. Water was poured into a clean vessel, and a drop of oil was placed on its surface. The oil spread over the surface of the water and formed a round film. Gradually, the area of ​​the film increased, but then the spreading stopped and the area stopped changing. Rayleigh suggested that the thickness of the film became equal to the size of one molecule. Through mathematical calculations it was established that the size of the molecule is approximately 16 * 10 -10 m.

Molecules are so small that small volumes of matter contain huge amounts of them. For example, one drop of water contains the same number of molecules as there are such drops in the Black Sea.

Molecules cannot be seen with an optical microscope. You can take photographs of molecules and atoms using an electron microscope, invented in the 30s of the 20th century.

Molecules of different substances differ in size and composition, but molecules of the same substance are always the same. For example, the water molecule is always the same: in water, in a snowflake, and in steam.

Although molecules are very small particles, they are also divisible. The particles that make up molecules are called atoms. Atoms of each type are usually designated by special symbols. For example, an oxygen atom is O, a hydrogen atom is H, a carbon atom is C. In total, there are 93 different atoms in nature, and scientists have created about 20 more in their laboratories. The Russian scientist Dmitry Ivanovich Mendeleev ordered all the elements and placed them in the periodic table, which we will learn more about in chemistry lessons.

An oxygen molecule consists of two identical oxygen atoms, a water molecule consists of three atoms - two hydrogen atoms and one oxygen atom. By themselves, hydrogen and oxygen do not have the properties of water. On the contrary, water only becomes water when such a bond is formed.

The sizes of atoms are very small. For example, if you enlarge an apple to the size of the globe, the size of the atom will increase to the size of an apple. In 1951, Erwin Müller invented the ion microscope, which made it possible to see the atomic structure of a metal in detail.

In our time, unlike the times of Democritus, the atom is no longer considered indivisible. At the beginning of the 20th century, scientists managed to study its internal structure.

It turned out that an atom consists of a nucleus and electrons rotating around the nucleus. Later it turned out that core in turn consists of protons and neutrons.

Thus, experiments are in full swing at the Large Hadron Collider - a huge structure built underground on the border between France and Switzerland. The Large Hadron Collider is a 30-kilometer closed tube through which hadrons (the so-called proton, neutron or electron) are accelerated. Having accelerated almost to the speed of light, the hadrons collide. The force of the impact is so great that the protons are “broken” into pieces. It is assumed that in this way it is possible to study the internal structure of hadrons

It is obvious that the further a person goes in studying the internal structure of matter, the greater difficulties he encounters. It is possible that the indivisible particle that Democritus imagined does not exist at all and particles can be divided ad infinitum. Research in this area is one of the fastest growing topics in modern physics.

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Electricity: general concepts

Electrical phenomena became known to man first in the formidable form of lightning - discharges of atmospheric electricity, then electricity obtained through friction (for example, skin on glass, etc.) was discovered and studied; finally, after the discovery of chemical current sources (galvanic cells in 1800), electrical engineering arose and quickly developed. In the Soviet state we witnessed the brilliant flourishing of electrical engineering. Russian scientists contributed greatly to such rapid progress.

However, it is difficult to give a simple answer to the question: “What is electricity?" We can say that “electricity is electrical charges and associated electromagnetic fields.” But such an answer requires detailed further explanation: “What are electric charges and electromagnetic fields?” We will gradually show how essentially complex the concept of “electricity” is, although extremely diverse electrical phenomena have been studied in great detail, and in parallel with their deeper understanding, the field of practical application of electricity has expanded.

The inventors of the first electric machines imagined electric current as the movement of a special electrical fluid in metal wires, but to create vacuum tubes it was necessary to know the electronic nature of electric current.

The modern doctrine of electricity is closely connected with the doctrine of the structure of matter. The smallest particle of a substance that retains its chemical properties is a molecule (from the Latin word “moles” - mass).

This particle is very small, for example, a water molecule has a diameter of about 3/1000,000,000 = 3/10 8 = 3*10 -8 cm and a volume of 29.7*10 -24.

To imagine more clearly how small such molecules are, what a huge number of them fit in a small volume, let us mentally carry out the following experiment. Let's somehow mark all the molecules in a glass of water (50 cm 3) and pour this water into the Black Sea. Let us imagine that the molecules contained in these 50 cm 3, evenly distributed throughout the vast oceans, which occupy 71% of the globe's area; Let us then scoop up another glass of water from this ocean, at least in Vladivostok. Is there a probability of finding at least one of the molecules we labeled in this glass?

The volume of the world's oceans is enormous. Its surface is 361.1 million km 2. Its average depth is 3795 m. Therefore, its volume is 361.1 * 10 6 * 3.795 km 3, i.e. about 1,370 LLC LLC km 3 = 1,37*10 9 km 3 - 1,37*10 24 cm 3.

But at 50 cm 3 water contains 1.69 * 10 24 molecules. Consequently, after mixing, each cubic centimeter of ocean water will contain 1.69/1.37 labeled molecules, and about 66 labeled molecules will end up in our glass in Vladivostok.

No matter how small molecules are, they are made up of even smaller particles - atoms.

An atom is the smallest part of a chemical element, which is the carrier of its chemical properties. A chemical element is usually understood as a substance consisting of identical atoms. Molecules can form identical atoms (for example, a molecule of hydrogen gas H2 consists of two atoms) or different atoms (a molecule of water H20 consists of two hydrogen atoms H2 and an oxygen atom O). In the latter case, when molecules are divided into atoms, the chemical and physical properties of the substance change. For example, when the molecules of a liquid body, water, decompose, two gases are released - hydrogen and oxygen. The number of atoms in molecules varies: from two (in a hydrogen molecule) to hundreds and thousands of atoms (in proteins and high-molecular compounds). A number of substances, in particular metals, do not form molecules, that is, they consist directly of atoms not connected internally by molecular bonds.

For a long time, an atom was considered the smallest particle of matter (the name atom itself comes from the Greek word atomos - indivisible). It is now known that the atom is a complex system. Most of the mass of the atom is concentrated in its nucleus. The lightest electrically charged elementary particles - electrons - revolve around the nucleus in certain orbits, just as the planets revolve around the Sun. Gravitational forces hold the planets in their orbits, and electrons are attracted to the nucleus by electrical forces. Electrical charges can be of two different types: positive and negative. From experience we know that only opposite electric charges attract each other. Consequently, the charges of the nucleus and electrons must also have different signs. It is conventionally accepted to consider the charge of electrons to be negative and the charge of the nucleus to be positive.

All electrons, regardless of the method of their production, have the same electrical charges and a mass of 9.108 * 10 -28 G. Consequently, the electrons that make up the atoms of any element can be considered the same.

At the same time, the electron charge (usually denoted e) is elementary, i.e., the smallest possible electric charge. Attempts to prove the existence of smaller charges were unsuccessful.

The belonging of an atom to a particular chemical element is determined by the magnitude of the positive charge of the nucleus. Total negative charge Z electrons of an atom is equal to the positive charge of its nucleus, therefore, the value of the positive charge of the nucleus must be eZ. The Z number determines the place of an element in Mendeleev’s periodic table of elements.

Some electrons in an atom are in inner orbits, and some are in outer orbits. The former are relatively firmly held in their orbits by atomic bonds. The latter can relatively easily separate from an atom and move to another atom, or remain free for some time. These outer orbital electrons determine the electrical and chemical properties of the atom.

As long as the sum of the negative charges of the electrons is equal to the positive charge of the nucleus, the atom or molecule is neutral. But if an atom has lost one or more electrons, then due to the excess positive charge of the nucleus it becomes a positive ion (from the Greek word ion - moving). If an atom has captured excess electrons, then it serves as a negative ion. In the same way, ions can be formed from neutral molecules.

The carriers of positive charges in the nucleus of an atom are protons (from the Greek word “protos” - first). The proton serves as the nucleus of hydrogen, the first element in the periodic table. Its positive charge e + is numerically equal to the negative charge of the electron. But the mass of a proton is 1836 times greater than the mass of an electron. Protons, together with neutrons, form the nuclei of all chemical elements. The neutron (from the Latin word “neuter” - neither one nor the other) has no charge and its mass is 1838 times greater than the mass of the electron. Thus, the main parts of atoms are electrons, protons and neutrons. Of these, protons and neutrons are firmly held in the nucleus of an atom and only electrons can move inside the substance, and positive charges under normal conditions can only move together with atoms in the form of ions.

The number of free electrons in a substance depends on the structure of its atoms. If there are a lot of these electrons, then this substance allows moving electric charges to pass through it well. It is called a conductor. All metals are considered conductors. Silver, copper and aluminum are especially good conductors. If, under one or another external influence, the conductor has lost some of the free electrons, then the predominance of the positive charges of its atoms will create the effect of a positive charge of the conductor as a whole, i.e. the conductor will attract negative charges - free electrons and negative ions. Otherwise, with an excess of free electrons, the conductor will be negatively charged.

A number of substances contain very few free electrons. Such substances are called dielectrics or insulators. They transmit electrical charges poorly or practically not. Dielectrics include porcelain, glass, hard rubber, most plastics, air, etc.

In electrical devices, electrical charges move along conductors, and dielectrics serve to direct this movement.

STRUCTURE OF MATTER

All substances consist of individual tiny particles: molecules and atoms.
The founder of the idea of ​​a discrete structure of matter (i.e., consisting of individual particles) is considered to be the ancient Greek philosopher Democritus, who lived around 470 BC. Democritus believed that all bodies consist of a countless number of ultra-small, invisible to the eye, indivisible particles. “They are infinitely varied, have depressions and convexities with which they interlock, forming all material bodies, but in nature there are only atoms and emptiness.
Democritus' guess was forgotten for a long time. However, his views on the structure of matter have come to us thanks to the Roman poet Lucretius Caru: “... all things, as we notice, become smaller, And they seem to melt over the course of a long century...”
Atoms.
Atoms are very small. They cannot be seen not only with the naked eye, but also with the help of even the most powerful optical microscope.
The human eye is not able to discern atoms and the spaces between them, so any substance seems solid to us.
In 1951, Erwin Müller invented the ion microscope, which made it possible to see the atomic structure of a metal in detail.
The atoms of different chemical elements differ from each other. The differences between the atoms of elements can be determined from the periodic table.
Molecules.
A molecule is the smallest particle of a substance that has the properties of that substance. So, a sugar molecule is sweet, and a salt molecule is salty.
Molecules are made up of atoms.
The sizes of molecules are negligible.

How to see a molecule? - using an electron microscope.

How to extract a molecule from a substance? - mechanical crushing of the substance. Each substance has a specific type of molecule. For different substances, molecules can consist of one atom (inert gases) or of several identical or different atoms, or even of hundreds of thousands of atoms (polymers). Molecules of various substances can have the shape of a triangle, pyramid and other geometric shapes, as well as be linear.

Molecules of the same substance are identical in all states of aggregation.

There are gaps between molecules in a substance. Evidence of the existence of gaps is a change in the volume of the substance, i.e. expansion and contraction of matter with temperature changes

Homework.
Exercise. Answer the questions:
№ 1.
1. What do substances consist of?
2. What experiments confirm that substances consist of tiny particles?
3. How does the volume of a body change when the distance between particles changes?
4. What experience shows that particles of matter are very small?
5. What is a molecule?
6. What do you know about the sizes of molecules?
7. What particles does a water molecule consist of?
8. How is a water molecule represented schematically?
№ 2.
1. Is the composition of water molecules the same in hot tea and in a chilled Cola drink?
2. Why do the soles of shoes wear out and the elbows of jackets wear down to holes?
3. How to explain the drying of nail polish?
4. You pass by a bakery. From it comes the delicious smell of fresh bread... How could this happen?

Robert Rayleigh's experiment.

The sizes of molecules have been determined in many experiments. One of them was carried out by the English scientist Robert Rayleigh.
Water was poured into a clean wide vessel and a drop of olive oil was placed on its surface. The drop spread over the surface of the water and formed a round film. Gradually, the area of ​​the film increased, but then the spreading stopped and the area stopped changing. Rayleigh assumed that the molecules were arranged in one row, i.e. The thickness of the film became equal to exactly the size of one molecule, and I decided to determine its thickness. In this case, of course, it is necessary to take into account that the volume of the film is equal to the volume of the drop.
Using the data obtained in Rayleigh's experiment, we calculate the thickness of the film and find out what the linear size of the oil molecule is. The drop had a volume of 0.0009 cm3, and the area of ​​the film formed from the drop was 5500 cm2. Hence the film thickness:

Experimental task:

Do an experiment at home to determine the size of oil molecules.
For experimentation, it is convenient to use clean machine oil. First, determine the volume of one drop of oil. Figure out how to do this yourself using a pipette and a beaker (you can use a beaker that is used to measure medications).
Pour water into a plate and place a drop of oil on its surface. When the drop has spread, measure the diameter of the film with a ruler, placing it on the edges of the plate. If the surface of the film does not have the shape of a circle, then either wait until it takes this shape, or take several measurements and determine its average diameter. Then calculate the area of ​​the film and its thickness.
What number did you get? How many times does it differ from the actual size of an oil molecule?

Molecular structure of matter. Speeds of gas molecules.

1. 
   The molecular kinetic theory of MKT is a theory that explains the properties of a substance based on its molecular structure. The main provisions of the molecular kinetic theory: all bodies consist of molecules; molecules are constantly moving; molecules interact with each other.
2. 
   Molecule– the smallest particle of a substance that retains the properties of a given substance.
3. 
   Atoms– the smallest particle of a chemical element. Molecules are made up of atoms.
4. 
   Molecules are constantly moving. The proof of this position is diffusion- the phenomenon of penetration of molecules of one substance into another. Diffusion occurs in gases, liquids, and solids. As temperature increases, the rate of diffusion increases. The movement of paint particles in a solution discovered by Brown is called Brownian motion and also proves the movement of molecules.
5. 
   Atomic structure. An atom consists of a positively charged nucleus around which electrons orbit.
6. 
   Atomic nucleus consists of nucleons (proton, neutron). The charge of the nucleus is determined by the number of protons. The mass number is determined by the number of nucleons. Isotopes are atoms of the same element whose nuclei contain different numbers of neutrons.
7. 
   Relative atomic mass M – mass of one atom in units atomic mass (1/12 the mass of a carbon atom). Relative molecular weight– M is the mass of the molecule in atomic mass units.
8. 
   Quantity of substance determined by the number of molecules. A mole is a unit of measurement for the amount of a substance. Mole- the amount of a substance whose mass, expressed in grams, is numerically equal to the relative molecular mass. 1 mole substance contains N A molecules. N A = 6,022∙10 23 1/mol – Avogadro’s number. The mass of one mole in kilograms is called molar mass – μ =M·10 -3 . 1 mol – 12gC – N A -22.4 l. gas
9. 
   Number moles is determined by the formulas : ν = m / μ , ν = N / N A , ν = V / V 0 .
10. 
    Basic MKT model– a set of moving and interacting molecules of a substance. Aggregate states of matter.
    1. 
       Solid: W n >> W k, the packing is dense, the molecules vibrate around the equilibrium position, the equilibrium positions are stationary, the arrangement of the molecules is ordered, i.e. a crystal lattice is formed, and both shape and volume are preserved.
    2. 
       Liquid:W n ≈ W k , the packing is dense, the molecules vibrate around the equilibrium position, the equilibrium positions are mobile, the arrangement of molecules is ordered within 2, 3 layers (short-range order), the volume is preserved, but the shape is not preserved (fluidity).
    3. 
       Gas: W n W k , molecules are located far from each other, move in a straight line until they collide with each other, the collisions are elastic, they easily change both shape and volume. Ideal gas conditions: W n =0, collisions are perfectly elastic, Diameter of molecule distances between them.
       
    4. 
       Plasma – electrically neutral collection of neutral and charged particles . Plasma(gas) molecules are located far from each other, move rectilinearly until they collide with each other, easily change both shape and volume, collisions are inelastic, ionization occurs during collisions, and reacts to electric and magnetic fields.
11. 
    Phase transitions: evaporation, condensation, sublimation, melting, crystallization.
12. 
    Statistical patterns– laws of behavior of a large number of particles. Microparameters– small-scale parameters – mass, size, speed and other characteristics of molecules and atoms. Macro parameters – parameters of large scales - mass, volume, pressure, temperature of physical bodies.
13. 
    R
    Z =2 N
    distribution of ideal gas particles over two halves of a vessel:

• 
  Number of possible statesZwith the number of particlesN is found by the formula
• 
  H
  Z = N! / n!∙(N-n)!
  number of ways to implement staten/ (N – n) is found by the formula
• 
  Analysis of the answers leads to the conclusion that there is the greatest probability that the molecules will be distributed equally across the two halves of the vessels.

1. 
   The most probable speed is the speed that most molecules have
2. 
   How to calculate the average speed of molecules V av = (V 1 ∙ N 1 + V 2 ∙ N 2 + V 3 ∙ N 3)/N. The average speed is usually higher than the most likely speed.
3. 
   Communication: speed – energy – temperature. E cf ~ T.
4. 
   T
   E=3 kT /2
   temperature determines the degree of body heating. Temperature the main characteristic of bodies in thermal equilibrium. Thermal equilibrium when there is no heat exchange between bodies
5. 
   Temperature is a measure of the average kinetic energy of gas molecules. With increasing temperature, the rate of diffusion increases and the speed of Brownian motion increases. The formula for the relationship between the average kinetic energy of molecules and temperature is expressed by the formula gdk k = 1.38∙10 -23 J/K – Boltzmann’s constant, expressing the relationship between Kelvin and Joule as units of temperature.

• 
  T
  T = t + 273.
  thermodynamic temperature cannot be negative.
• 
  Absolute temperature scale– Kelvin scale (273K – 373K).

• 
  Temperature scales: Celsius (0 o C – 100 o C), Fahrenheit (32 o F – 212 o F), Kelvin (273K – 373K).

1. 
   Speed ​​of thermal movement of molecules: m 0 v 2 = 3 kT, v 2 = 3 kT / m 0 , v 2 = 3 kN A T / μ

Gas laws

1. 
   Pressure is a macroscopic parameter of the system . Pressure is numerically equal to the force acting per unit surface perpendicular to this surface.P= F/ S. Pressure is measured in Pascals (Pa), atmospheres (atm.), bars (bar), mmHg. The pressure of a column of gas or liquid in a gravitational field is found by the formula P = ρgh, where ρ is the density of the gas or liquid, h is the height of the column. In communicating vessels, a homogeneous liquid is established at the same level. The ratio of the heights of columns of inhomogeneous liquids is inverse to the ratio of their densities.
2. 
   Atmospheric pressure– pressure created by the air shell of the Earth. Normal atmospheric pressure is 760 mmHg. or 1.01∙10 5 Pa, or 1 bar, or 1 atm.
3. 
   Gas pressure is determined the number of molecules hitting the wall of the container and their speed.

• 
  Arithmetic average speed the movement of gas molecules is zero, because there is no advantage to movement in any particular direction due to the fact that the movement of molecules is equally probable in all directions. Therefore, to characterize the movement of molecules we take root mean square speed. The mean squares of the speed along the X, Y, Z axes are equal to each other and amount to 1/3 of the mean square speed.

For one mole of gas

Isobars

P 1
Gay-Lussac's law

1. 
   V = const – isochoric process,

V 1
Charles's law.

Tasks: Task № 1 . Determine the total number of microstates of six particles of an ideal gas in two halves of a vessel not separated by a partition. What is the number of ways to realize states 1/5, 2/4? At what state will the number of implementation methods be maximum?

Solution. Z =2 N = 2 6 = 64. For state 1/5 Z = N! / n!∙(N-n)! = 1∙2∙3∙4∙5∙6 / 1∙1∙2∙3∙4∙5= 6

On one's own. What is the number of ways to implement states 2/4?

Task No. 2. Find the number of molecules in a glass of water (m=200g). Solution. N = m∙ N A /μ = 0.2 ∙ 6.022∙10 23 / 18 ∙ 10 -3 =67∙ 10 23 .

On one's own. Find the number of molecules in 2 g of copper. Find the number of molecules in 1 m 3 of carbon dioxide CO 2 .

Task No. 3. The figure shows a closed loop in coordinates P V. What processes occurred with the gas? How did macro parameters change? Draw this diagram in VT coordinates.

WITH
independently draw the diagram in PT coordinates.

R
decision.

Task No. 4."Magdeburg Hemispheres" stretched 8 horses on each side. How will the traction force change if one hemisphere is attached to a wall and the other is pulled by 16 horses?

Z
task number 5. An ideal gas exerts a pressure of 1.01∙10 5 Pa on the walls of the vessel. The thermal speed of molecules is 500 m/s. Find the gas density. (1.21kg/m3). Solution.. Let's divide both sides of the equation by V. We get

μ we find from the formula for the speed of molecules

Task No. 6. What pressure is oxygen under if the thermal speed of its molecules is 550 m/s, and their concentration 10 25 m -3 ? (54kPa.) Solution. P = nkT, R=N A k,P=nv 2 μ /3N A , We find T from the formula

Task No. 7. Nitrogen occupies a volume of 1 liter at normal atmospheric pressure. Determine the energy of translational motion of gas molecules.

Solution. Energy of one molecule - E o = 5 kT / 2 , energy of all molecules in a given volume of gas – E = N 5 kT / 2 = nV 5 kT / 2, P = nkT , E = 5 PV /2 = 250 J.

Task № 8. Air consists of a mixture of nitrogen, oxygen and argon. Their concentrations are respectively 7.8 ∙ 10 24 m -3 , 2.1 ∙ 10 24 m -3 , 10 23 m -3 . The average kinetic energy of the molecules of the mixture is the same and equal to 3 ∙10 -21 J. Find the air pressure. (20kPa). On one's own.

Task No. 9. How will the gas pressure change when its volume decreases by 4 times and the temperature increases by 1.5 times? (Increases 6 times). On one's own.

Task No. 10. The gas pressure in a fluorescent lamp is 10 3 Pa, and its temperature is 42 o C. Determine the concentration of atoms in the lamp. Estimate the average distance between molecules.

(2.3∙10 23 m -3, 16.3 nm). On one's own.

Task No. 11. Find the volume of one mole of an ideal gas of any chemical composition under normal conditions. (22.4l). On one's own.

Z
problem number 12. A vessel with a volume of 4 liters contains molecular hydrogen and helium. Assuming the gases are ideal, find the pressure of the gases in the vessel at a temperature of 20 o C if their masses are 2g and 4g, respectively. (1226kPa).

Solution. According to Dalton's law P = P 1 + R 2 . We find the partial pressure of each gas using the formula. Both hydrogen and helium occupy the entire volume V=4l.

Problem No. 13. Determine the depth of the lake if the volume of the air bubble doubles as it rises from the bottom to the surface. The temperature of the bubble does not have time to change. (10.3m).

Solution. The process is isothermal P 1 V 1 = P 2 V 2

The pressure in a bubble on the surface of the water is equal to atmospheric pressure P 2 = P o The pressure at the bottom of the reservoir is the sum of the pressure inside the bubble and the pressure of the water column R 1 = P O + ρ gh, where ρ = 1000 kg/m 3 is the density of water, h is the depth of the reservoir. R O = (R O + ρ gh) V 1 / 2 V 1 = (R O + ρ gh)/ 2

Problem No. 14. The cylinder is divided by an impenetrable fixed partition into two parts, the volumes of which are V 1, V 2. The air pressure in these parts of the cylinder is P 1, P 2, respectively. When the fastening is removed, the partition can move like a weightless piston. How much and in which direction will the partition move?

R
P 1 V 1

P 2 V 2

decision . If P 2 > P 1 Pressure in both parts

P 1 V 1 = P (V 1 -∆ V)

P 2 V 2 = P (V 2 + ∆ V)

the cylinder will be set to the same - R. The process is isothermal.

Let's divide the right and left sides of the equations into each other. And then we solve the equation for ∆ V.

Answer: ((P 1 – P 2 ) V 1 V 2 )/(P 1 V 1 + P 2 V 2 .

Problem No. 15. Car tires are inflated to a pressure of 2∙10 4 Pa ​​at a temperature of 7 o C. A few hours after driving, the air temperature in the tires rose to 42 o C. What was the pressure in the tires? (2.25∙10 4 Pa). On one's own.