School Encyclopedia. Gas pressure on the vessel wall Consolidation of the material covered in the lesson

Wherever the gas is: in a balloon, a car tire, or a metal cylinder - it fills the entire volume of the vessel in which it is located.

The pressure of a gas arises for a completely different reason than the pressure of a solid body. It is formed as a result of impacts of molecules on the walls of the vessel.

The pressure of the gas on the walls of the vessel

Moving randomly in space, gas molecules collide with each other and with the walls of the vessel in which they are located. The impact force of one molecule is small. But since there are a lot of molecules, and they collide with great frequency, then, acting together on the walls of the vessel, they create significant pressure. If a solid body is placed in a gas, then it is also subjected to impacts by gas molecules.

Let's do a simple experiment. Under the bell of the air pump we place a tied up balloon, not completely filled with air. Since there is little air in it, the ball has an irregular shape. When we begin to pump out air from under the bell, the balloon will begin to inflate. After a while, it will take the form of a regular ball.

What happened to our ball? After all, it was tied, therefore, the amount of air in it remained the same.

Everything is explained quite simply. During the movement, the gas molecules collide with the shell of the ball outside and inside it. If the air is pumped out of the bell, the molecules become smaller. The density decreases, and hence the frequency of impacts of molecules on the outer shell also decreases. Consequently, the pressure outside the shell drops. And since the number of molecules inside the shell remains the same, the internal pressure exceeds the external one. The gas presses on the shell from the inside. And for this reason, it gradually swells and takes the form of a ball.

Pascal's law for gases

Gas molecules are very mobile. Due to this, they transmit pressure not only in the direction of the force that causes this pressure, but evenly in all directions. The pressure transfer law was formulated by the French scientist Blaise Pascal: Pressure applied to a gas or liquid is transmitted unchanged to any point in all directions". This law is called the basic law of hydrostatics - the science of liquid and gas in a state of equilibrium.

Pascal's law is confirmed by experience with a device called Pascal's ball . This device is a ball of solid matter with tiny holes made in it, connected to a cylinder along which a piston moves. The balloon is filled with smoke. When compressed by a piston, smoke is pushed out of the holes of the ball in equal streams.

The gas pressure is calculated by the formula:

where e lin - average kinetic energy of translational motion of gas molecules;

n - concentration of molecules

partial pressure. Dalton's law

In practice, most often we have to meet not with pure gases, but with their mixtures. We breathe air, which is a mixture of gases. Car exhaust is also a mixture. Pure carbon dioxide has not been used in welding for a long time. Instead, gas mixtures are also used.

A gas mixture is a mixture of gases that do not enter into chemical reactions with each other.

The pressure of an individual component of a gas mixture is called partial pressure .

If we assume that all gases of the mixture are ideal gases, then the pressure of the mixture is determined by Dalton's law: "The pressure of a mixture of ideal gases that do not interact chemically is equal to the sum of the partial pressures."

Its value is determined by the formula:

Each gas in the mixture creates a partial pressure. Its temperature is equal to the temperature of the mixture.

The pressure of a gas can be changed by changing its density. The more gas is pumped into a metal cylinder, the more molecules it will hit the walls, and the higher its pressure will become. Accordingly, pumping out the gas, we rarefy it, and the pressure decreases.

But the pressure of a gas can also be changed by changing its volume or temperature, that is, by compressing the gas. Compression is carried out by exerting a force on a gaseous body. As a result of such an impact, the volume occupied by it decreases, pressure and temperature increase.

The gas is compressed in the engine cylinder as the piston moves. In production, high gas pressure is created by compressing it with the help of complex devices - compressors that are capable of creating pressure up to several thousand atmospheres.

Behavior of Atmospheric Molecules The atmosphere consists of gases, and why don't molecules fly away into the world space? The atmosphere consists of gases, and why don't molecules fly away into the world space? Like all bodies, the gas molecules that make up the Earth's air envelope are attracted to the Earth. Like all bodies, the gas molecules that make up the Earth's air envelope are attracted to the Earth. To leave the Earth, they must have a speed of at least 11.2 km / s, this is the second cosmic speed. Most molecules have a speed less than 11.2 km/s. To leave the Earth, they must have a speed of at least 11.2 km / s, this is the second cosmic speed. Most molecules have a speed less than 11.2 km/s. Why doesn't the atmosphere settle on the Earth's surface? Why doesn't the atmosphere settle on the Earth's surface? The molecules of the gases that make up the atmosphere move continuously and randomly. The molecules of the gases that make up the atmosphere move continuously and randomly.

Under the influence of gravity, the upper layers of the air of the atmosphere compress the lower ones. Under the influence of gravity, the upper layers of the air of the atmosphere compress the lower ones. The layer adjacent to the Earth is compressed the most. The layer adjacent to the Earth is compressed the most. The earth's surface and the bodies on it experience the pressure of the entire thickness of the air (according to Pascal's law) - atmospheric pressure. The earth's surface and the bodies on it experience the pressure of the entire thickness of the air (according to Pascal's law) - atmospheric pressure.

Historical fact For the first time, the weight of the air confused people in 1638, when the idea of ​​the Duke of Tuscany to decorate the gardens of Florence with fountains failed - the water did not rise above 10.3 m. For the first time, the weight of the air confused people in 1638, when the idea of ​​the Duke of Tuscany to decorate the gardens of Florence with fountains failed - the water did not rise above 10.3 m. The search for the causes of the stubbornness of water and experiments with a heavier liquid - mercury, undertaken in 1643. Torricelli, led to the discovery of atmospheric pressure. The search for the causes of the stubbornness of water and experiments with a heavier liquid - mercury, undertaken in 1643. Torricelli, led to the discovery of atmospheric pressure.

Experience of Otto von Guericke In 1654, Magdeburg burgomaster and physicist Otto von Guericke showed one experiment at the Reichstag in Regensburg, which is now called the experiment with the Magdeburg hemispheres all over the world. In 1654, the Magdeburg burgomaster and physicist Otto von Guericke showed one experiment at the Reichstag in Regensburg, which is now called the experience with the Magdeburg hemispheres all over the world.

Atmospheric pressure and man Atmospheric pressure is not felt by man and animals. Atmospheric pressure is not felt by humans and animals. Tissues, blood vessels and walls of other body cavities are exposed to the external pressure of the atmosphere. Tissues, blood vessels and walls of other body cavities are exposed to the external pressure of the atmosphere. The blood and other liquids and gases that fill these cavities exert the same pressure from within. The blood and other liquids and gases that fill these cavities exert the same pressure from within.

Breathing The mechanism of inhalation is as follows: with muscle effort, we increase the volume of the chest, while the air pressure inside the lungs becomes less than atmospheric pressure, and atmospheric pressure pushes a portion of air into an area of ​​\u200b\u200blower pressure. The mechanism of inhalation is as follows: with muscle effort, we increase the volume of the chest, while the air pressure inside the lungs becomes less than atmospheric pressure, and atmospheric pressure pushes a portion of air into an area of ​​\u200b\u200blower pressure. How does exhalation take place? How does exhalation take place?

Homework Interesting information on the site Cool physics You can answer questions for a separate assessment Interesting information on the site Cool physics You can answer questions for a separate assessment §40 §40 Fill in the card Fill in the card Perform and explain in writing one of the experiments Perform and explain in writing one of the experiments

Why are airplane passengers advised to remove ink from fountain pens before taking off? Why are airplane passengers advised to remove ink from fountain pens before taking off? How do you fill a glass tube with water? How do you fill a glass tube with water? Why are there not one, but two holes in the lids of cans for lubricating oils? Why are there not one, but two holes in the lids of cans for lubricating oils? Why is there a hole in the lid of a porcelain teapot? Why is there a hole in the lid of a porcelain teapot? Why is it difficult to pull out legs stuck in soaked clay? Why is it difficult to pull out legs stuck in soaked clay? Who is easier to walk in the mud? It is very difficult for a horse with a solid hoof to get his foot out of deep mud. Under the leg, when she raises it, a rarefied space is formed and atmospheric pressure prevents the leg from being pulled out. In this case, the leg works like a piston in a cylinder. It is very difficult for a horse with a solid hoof to get his foot out of deep mud. Under the leg, when she raises it, a rarefied space is formed and atmospheric pressure prevents the leg from being pulled out. In this case, the leg works like a piston in a cylinder. External, huge in comparison with the arisen, atmospheric pressure does not allow to raise the leg. At the same time, the pressure force on the leg can reach 1000 N. External, huge in comparison with the arisen, atmospheric pressure does not allow lifting the leg. At the same time, the pressure force on the leg can reach 1000 N. It is much easier for ruminants to move through such mud, in which the hooves consist of several parts and when pulling the legs out of the mud they are compressed, passing air into the formed depression. It is much easier to move through such mud for ruminants, in which the hooves consist of several parts and, when pulled out of the mud, the legs are compressed, letting air into the resulting depression.

Atmospheric pressure and weather Atmospheric pressure helps to predict the weather, which is necessary for people of different professions - pilots, agronomists, radio operators, polar explorers, doctors, scientists. If atmospheric pressure rises, then the weather will be good: cold in winter, hot in summer; if it falls sharply, then we can expect the appearance of clouds, saturation of the air with moisture. A decrease in pressure in summer portends a cold snap, in winter - warming. Atmospheric pressure helps to predict the weather, which is necessary for people of different professions - pilots, agronomists, radio operators, polar explorers, doctors, scientists. If atmospheric pressure rises, then the weather will be good: cold in winter, hot in summer; if it falls sharply, then we can expect the appearance of clouds, saturation of the air with moisture. A decrease in pressure in summer portends a cold snap, in winter - warming. Atmospheric pressure increases if air masses move downwards (downdrafts). Dry air descends from high altitudes, so the weather will be good, without precipitation. Atmospheric pressure decreases with ascending air currents. Air rises up, richly saturated with water vapor. At the top, it cools, which leads to the appearance of clouds, precipitation - the weather worsens. Atmospheric pressure increases if air masses move downwards (downdrafts). Dry air descends from high altitudes, so the weather will be good, without precipitation. Atmospheric pressure decreases with ascending air currents. Air rises up, richly saturated with water vapor. At the top, it cools, which leads to the appearance of clouds, precipitation - the weather worsens.

What would happen on Earth if the air atmosphere suddenly disappeared? on Earth, a temperature of approximately C would be established on Earth, a temperature of approximately C would be established, all water spaces would freeze, and the land would be covered with an ice crust, all water spaces would freeze, and the land would be covered with an ice crust, there would be complete silence, since sound does not propagate in the void there would be complete silence, since sound does not propagate in the void, the sky would turn black, since the color of the firmament depends on the air; there would be no twilight, dawn, white nights, the sky would turn black, since the color of the firmament depends on the air; there would be no twilight, dawns, white nights, the twinkling of stars would stop, and the stars themselves would be visible not only at night, but also during the day (during the day we do not see them due to the scattering of sunlight by air particles), the twinkling of stars would stop, and the stars themselves would be visible not only at night, but also during the day (during the day we do not see them due to the scattering of sunlight by air particles) animals and plants would die animals and plants would die

When deriving the equation of state for an ideal gas, we will consider the molecules as small solid balls enclosed in a box with a volume V(Fig. 8.2) . The assumption of hard balls means that elastic collisions occur between molecules. Consider first one such molecule reflected from the left wall of the box. The average force acting on the wall over time is equal to

As a result of the collision, the momentum changes by the amount

Since the time between collisions of the molecule with this wall

then the average force acts on the wall from one molecule

Rice. 8.2 Particle in a vessel of volume lS after reflection from the left wall

The full strength with which everything N molecules in the box act on the wall, is given by

where is the square of the velocity averaged over all particles.

This value is called the rms speed in the direction of the axis X. Dividing both parts of this ratio by the area of ​​the wall S, we get the pressure

Let's replace Sl per volume V; then

It is already seen from here that for a given amount of gas, the product pV remains constant provided that the kinetic energy of the particles is kept unchanged. The right side of formula (8.16) can be written in terms of . Really,

Since the molecules are reflected in exactly the same way from all six faces, then

Let us now substitute into (8.16) the value :

We will define the absolute temperature as a quantity directly proportional to the average kinetic energy of the molecules in the vessel:

(determination of temperature), where is the average kinetic energy per particle.

Proportionality factor (2 / 3k) is a constant. The value of the constant k (Boltzmann constant) depends on the choice of temperature scale. One way to choose a scale is based on the fact that the temperature interval between the boiling and freezing points of water at normal pressure is assumed to be 100 degrees (=100 To). Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, magnitude k determined by measuring the properties of water. It has been experimentally found that

(Boltzmann's constant). If using (8.18) we exclude the value from (8.17), then we obtain

(ideal gas equation of state).

Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, by applying the equations of Newtonian mechanics to individual molecules, i.e. using them at the microscopic level, we have introduced an important relationship between macroscopic quantities p, V and T(cf.
Hosted on ref.rf
(8.20) with (8.7)).

Taking into account equality (8.20), the ideal gas equation of state can be rewritten in the form

where n is the concentration of molecules. Since for a monatomic gas the average kinetic energy coincides with the average translational energy , equation (8.21) can be represented as

The product gives the total energy of translational motion n molecules. Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, the pressure is equal to two-thirds of the energy of the translational motion of the molecules contained in a unit volume of gas.

We have already said (§ 220) that gases always completely fill the volume bounded by gas-impermeable walls. So, for example, a steel cylinder used in technology for storing compressed gases (Fig. 375), or a car tire chamber is completely and almost evenly filled with gas.

Rice. 375. Steel cylinder for storage of highly compressed gases

In an effort to expand, the gas exerts pressure on the walls of the cylinder, tire chamber or any other body, solid or liquid, with which it comes into contact. If we do not take into account the action of the Earth's gravity field, which, with the usual dimensions of vessels, only negligibly changes the pressure, then at equilibrium, the pressure of the gas in the vessel seems to us to be completely uniform. This remark refers to the macrocosm. If we imagine what happens in the microcosm of the molecules that make up the gas in the vessel, then there can be no question of any uniform distribution of pressure. In some places on the surface of the walls, gas molecules hit them, while in other places there are no impacts; this picture changes all the time in a disorderly way.

For simplicity, let us assume that all molecules fly at the same speed before hitting the wall, directed along the normal to the wall. We also assume that the impact is absolutely elastic. Under these conditions, the velocity of the molecule upon impact will change direction to the opposite, remaining unchanged in absolute value. Therefore, the velocity of the molecule after the impact will be equal to . Accordingly, the momentum of the molecule before the impact is , and after the impact it is equal to ( - the mass of the molecule). By subtracting its initial value from the final value of the momentum, we find the increment in the momentum of the molecule imparted by the wall. It is equal. According to Newton's third law, the momentum equal to is imparted to the wall upon impact.

If per unit time per unit area of ​​the wall there are impacts, then during the time molecules hit the surface of the wall. Molecules report to the site during the time the total impulse, equal in modulus. By virtue of Newton's second law, this impulse is equal to the product of the force acting on the site and the time. In this way,

Where .

Dividing the force by the area of ​​the wall section, we obtain the gas pressure on the wall:

It is easy to see that the number of impacts per unit time depends on the speed of the molecules, because the faster they fly, the more often they hit the wall, and on the number of molecules per unit volume, because the more molecules, the greater the number of impacts they inflict. Therefore, we can assume that it is proportional to and, i.e., proportionally

In order to calculate the pressure of a gas using molecular theory, we must know the following characteristics of the microcosm of molecules: mass, velocity, and the number of molecules per unit volume. In order to find these microcharacteristics of molecules, we must establish on what characteristics of the macrocosm the pressure of a gas depends, i.e., establish by experience the laws of gas pressure. By comparing these experimental laws with the laws calculated using molecular theory, we will be able to determine the characteristics of the microcosm, for example, the speed of gas molecules.

So, let's establish what the pressure of a gas depends on?

First, the pressure depends on the degree of compression of the gas, that is, on how many gas molecules are in a given volume. For example, by forcing more and more air into a car tire or by compressing (reducing the volume ) closed chamber, we force the gas to press harder and harder on the walls of the chamber.

Secondly, the pressure depends on the temperature of the gas. It is known, for example, that the ball becomes more elastic if it is held near a heated furnace.

Usually, a change in pressure is caused by both causes at once: both a change in volume and a change in temperature. But it is possible to carry out the process in such a way that when the volume changes, the temperature will change negligibly little, or when the temperature changes, the volume will practically remain unchanged. We will deal with these cases first, after making the following remark beforehand. We will consider the gas in equilibrium. This means that both mechanical and thermal equilibrium have been established in the gas.

Mechanical equilibrium means that there is no movement of individual parts of the gas. For this, it is necessary that the pressure of the gas be the same in all its parts, if we neglect the insignificant pressure difference in the upper and lower layers of the gas, which occurs under the action of gravity.

Thermal equilibrium means that there is no transfer of heat from one section of the gas to another. To do this, it is necessary that the temperature in the entire volume of the gas be the same.

DEFINITION

Pressure in a vessel with gas is created by impacts of molecules on its wall.

Due to thermal motion, gas particles from time to time hit the walls of the vessel (Fig. 1a). With each impact, the molecules act on the vessel wall with some force. Adding each other, the impact forces of individual particles form a certain pressure force that constantly acts on the vessel wall. When colliding with the vessel walls, gas molecules interact with them according to the laws of mechanics as elastic bodies and transfer their impulses to the vessel walls (Fig. 1b).

Fig.1. Gas pressure on the wall of the vessel: a) the occurrence of pressure due to impacts on the wall of randomly moving particles; b) pressure force as a result of elastic impact of particles.

In practice, most often they deal not with a pure gas, but with a mixture of gases. For example, atmospheric air is a mixture of nitrogen, oxygen, carbon dioxide, hydrogen, and other gases. Each of the gases that make up the mixture contributes to the total pressure that the mixture of gases exerts on the walls of the vessel.

For a gas mixture, dalton's law:

the pressure of the gas mixture is equal to the sum of the partial pressures of each component of the mixture:

DEFINITION

Partial pressure is the pressure that would be occupied by the gas that is part of the gas mixture if it alone occupied a volume equal to the volume of the mixture at a given temperature (Fig. 2).

Fig.2. Dalton's law for a gas mixture

From the point of view of molecular kinetic theory, Dalton's law is satisfied because the interaction between molecules of an ideal gas is negligible. Therefore, each gas exerts pressure on the wall of the vessel, as if there were no other gases in the vessel.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2

Exercise

A closed vessel contains a mixture of 1 mole of oxygen and 2 moles of hydrogen. Compare the partial pressures of both gases (oxygen pressure) and (hydrogen pressure):

Answer

The pressure of a gas is due to the impact of molecules on the walls of the vessel, it does not depend on the type of gas. Under conditions of thermal equilibrium, the temperature of the gases that make up the gas mixture, in this case oxygen and hydrogen, is the same. This means that the partial pressures of gases depend on the number of molecules of the corresponding gas. One mole of any substance contains