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 momentum is equal to the product force acting on the site for 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.
Class: 7
Presentation for the lesson
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Textbook"Physics. Grade 7" A.V. Peryshkin - M. : Bustard, 2011
Lesson type: combined on the basis of research activities.
Goals:
- establish the reason for the existence of pressure in gases from the point of view of the molecular structure of matter;
- to find out:
- what does the pressure of a gas depend on
- how can i change it.
Tasks:
- to form knowledge about gas pressure and the nature of the occurrence of pressure on the walls of the vessel in which the gas is located;
- to form the ability to explain gas pressure on the basis of the doctrine of the movement of molecules, the dependence of pressure on volume at a constant mass and temperature, as well as with a change in temperature;
- develop general educational knowledge and skills: observe, draw conclusions;
- to promote the instillation of interest in the subject, the development of attention, scientific and logical thinking of students.
Equipment and materials for the lesson: a computer, a screen, a multimedia projector, a presentation for the lesson, a flask with a stopper, a tripod, a spirit lamp, a syringe, a balloon, a plastic bottle with a stopper.
Lesson plan:
- Checking homework.
- Knowledge update.
- Explanation of new material.
- Consolidation of the material covered in the lesson.
- Summary of the lesson. Homework.
DURING THE CLASSES
I prefer what can be seen, heard and studied. (Heraclitus)(Slide 2)
- This is the motto of our lesson
- In the last lessons, we learned about the pressure of solids, on what physical quantities the pressure depends.
1. Repetition of the material covered
1. What is pressure?
2. What does the pressure of a solid body depend on?
3. How does the pressure depend on the force applied perpendicular to the support? What is the nature of this dependency?
4. How does the pressure depend on the area of support? What is the nature of this dependency?
5. What is the reason for the pressure of a solid body on a support?
quality task.
Are the forces acting on the support and the pressure the same in both cases? Why?
Check of knowledge. Testing (verification and mutual verification)
Test
1. Physical quantity, which has the dimension of pascal (Pa), is called:
a) strength; b) mass; c) pressure; d) density.
2. The pressure force was increased by 2 times. How will the pressure change?
a) will decrease by 2 times; b) stay the same c) will increase by 4 times; d) will double.
4. What pressure does a 200 N carpet with an area of 4 m 2 exert on the floor?
a) 50 Pa; b) 5 Pa; c) 800Pa; d) 80 Pa.
5. Two bodies of equal weight are placed on the table. Do they exert the same pressure on the table?
2. Updating knowledge(in the form of a conversation)
Why are balloons and soap bubbles round?
Students inflate balloons.
What did we fill the balloons with? (by air) What else can fill the balls? (by gases)
- I suggest squeezing the balls. What's stopping you from squeezing the balls? What acts on the shell of the sphere?
- Take plastic bottles, close the cork and try to squeeze.
- What will be discussed in the lesson?
– Lesson topic: Gas pressure
3. Explanation of new material
Gases, unlike solids and liquids, fill the entire vessel in which they are located.
In an effort to expand, the gas exerts pressure on the walls, bottom and lid of any body with which it comes into contact.
(Slide 9) Pictures of steel cylinders containing gas; car tire chambers; ball
Gas pressure is due to other reasons than the pressure of a solid body on a support.
Conclusion: the pressure of the gas on the walls of the vessel (and on the body placed in the gas) is caused by impacts of the gas molecules.
For example, the number of impacts of air molecules in a room on a surface of 1 cm 2 in 1 s is expressed as a twenty-three-digit number. Although the impact force of an individual molecule is small, the action of all molecules on the walls of the vessel is significant, and it creates gas pressure.
Students work independently with the textbook. Read the experience with a rubber ball under the bell. How to explain this experience? (p.83 fig. 91)
The students explain the experience.
(Slide 11) Watching a video clip explaining the experience to consolidate the material.
(Slide 12) A moment of rest. Eye charger.
“The feeling of mystery is the most beautiful experience available to us. It is this feeling that stands at the cradle of true science.
Albert Einstein
(Slide 14) DO GASES HAVE VOLUME? IS IT EASY TO CHANGE THE VOLUME OF GASES? DO GASES TAKEN THE ENTIRE VOLUME SUPPLIED TO THEM? WHY? WHY? DO GASES HAVE A CONSTANT VOLUME AND OWN SHAPE? WHY?
rice. 92 p. 84
(Slide 15) Students made models from syringes. Execution of experience.
Students conclude that when the volume of a gas decreases, its pressure increases, and when the volume increases, the pressure decreases, provided that the mass and temperature of the gas remain unchanged.
(Slide 16) Experience with a flask
How will the pressure of a gas change if it is heated at a constant volume?
When heated, the pressure of the gas in the flask will gradually increase until the cork flies out of the flask.
Students conclude: the pressure of a gas in a closed vessel is the greater, the higher the temperature of the gas, provided that the mass of the gas and volume do not change. (Slide 17)
Gases contained in a vessel can be compressed or squeezed, while reducing their volume. The compressed gas is evenly distributed in all directions. The more you compress a gas, the higher its pressure will be.
Students conclude: the pressure of the gas is greater, the more often and stronger the molecules hit the walls of the vessel
4. Consolidation of the material covered in the lesson.
(Slide 18) Think about it
What happens to gas molecules when the volume of the vessel containing the gas decreases?
- molecules move faster
- molecules move more slowly
- the average distance between gas molecules decreases,
- the average distance between gas molecules increases.
(Slide 19) Compare your answers
- What causes gas pressure?
- Why does the pressure of a gas increase when it is compressed and decrease when it expands?
- When is the gas pressure greater: cold or hot? Why?
Answer 1. Gas pressure is caused by impacts of gas molecules on the walls of the vessel or on a body placed in the gas
Answer 2. When compressed, the density of the gas increases, which increases the number of impacts of molecules on the walls of the vessel. Consequently, the pressure also increases. With expansion, the density of the gas decreases, which entails a decrease in the number of impacts of molecules on the walls of the vessel. Therefore, the pressure of the gas decreases
Answer 3. Gas pressure is greater when hot. This is due to the fact that gas molecules begin to move faster as the temperature rises, which is why their impacts become more frequent and stronger.
(Slide 20) Qualitative tasks. (Collection of problems in physics V.I. Lukashik, E.V. Ivanova, Moscow "Enlightenment" 2007, p. 64)
1. Why does it become more and more difficult to move the pump handle each time you inflate a car tire with air?
2. The masses of the same gas in different closed vessels at the same temperature are the same. Which vessel has the highest gas pressure? Least? Explain answer
3. Explain the appearance of a dent on the ball
Ball at room temperature
Ball on the snow on a frosty day
Riddles can be solved forever.
The universe is, after all, infinite.
Thank you all for the lesson
And most importantly, that he was for the future!
Reflection.
5. Summary of the lesson
Homework:§35
Myakishev G.Ya. Gas pressure in a vessel // Kvant. - 1987. - No. 9. - S. 41-42.
By special agreement with the editorial board and the editors of the journal "Kvant"
Does the gas pressure on the vessel wall depend on the material of the wall and its temperature? Let's try to answer this question.
When deriving the basic equation of the molecular-kinetic theory of an ideal gas in the textbook "Physics 9" (§ 7), it is assumed that the wall is absolutely smooth and the collisions of molecules with the wall occur according to the law of absolutely elastic impact. In other words, the kinetic energy of the molecule does not change upon impact, and the angle of incidence of the molecule equal to the angle reflections. Is this assumption justified and necessary?
Briefly, we can say this: the assumption is justified, but not necessary.
At first glance, it seems that it is impossible to consider the wall absolutely smooth in any case - the wall itself consists of molecules and, therefore, cannot be smooth. Because of this, the angle of incidence cannot be equal to the angle of reflection in any collision. In addition, the wall molecules perform chaotic oscillations around the equilibrium positions (they participate in random thermal motion). Therefore, when colliding with any wall molecule, a gas molecule can transfer part of the energy to the wall or, conversely, increase its kinetic energy due to the wall.
Nevertheless, the assumption of an absolutely elastic nature of the collision of a gas molecule with a wall is justified. The fact is that when calculating pressure, the average values of the corresponding quantities are ultimately important. On condition thermal equilibrium between the gas and the wall of the vessel, the kinetic energy of the gas molecules remains on average unchanged, i.e., collisions with the wall do not change the average energy of the gas molecules. If this were not so, then the thermal equilibrium would be spontaneously violated. And this is impossible according to the second law of thermodynamics. Also, there can be no predominant reflection of molecules in any particular direction - otherwise the vessel with gas would begin to move, which contradicts the law of conservation of momentum. This means that the average number of molecules falling on the wall at a certain angle is equal to the average number of molecules flying off the wall at the same angle. Assumption about mirror reflection from the wall of each individual molecule corresponds to this condition.
Thus, assuming that the collisions of gas molecules with the wall are elastic, we obtain the same result for the average pressure as without this assumption. This means that the gas pressure does not depend on the quality of the wall processing (its smoothness). However, the assumption of an absolutely elastic nature of the impact greatly simplifies the calculation of the gas pressure, and therefore it is justified.
Does the pressure of a gas on a wall depend on its temperature? At first glance, it must depend. If, for example, there is no thermal equilibrium, then molecules from a cold wall should bounce off with less energy than from a hot one.
However, even if one wall is kept cold by means of a refrigeration unit, the pressure on it still cannot be less than the pressure on the opposite hot wall. After all, then the vessel would begin to move rapidly without external forces, and this contradicts the laws of mechanics: by releasing a fixed vessel with walls of different temperatures, we will not cause its displacement. The point here is that for a given nonequilibrium state of the gas in the vessel, the concentration of molecules near the cold wall is greater than near the hot one. A decrease in the kinetic energy of molecules near the cold wall is compensated by an increase in the concentration of molecules and vice versa. As a result, the pressure on the cold and hot walls is the same.
Let's consider another version of the experiment. Let's cool one of the walls very quickly. At the first moment, the pressure on it will decrease, and the vessel will move a little; then the pressures equalize and the vessel stops. But with this movement, the center of mass of the system will remain in place due to the fact that the gas density at the cold wall will become slightly higher than that at the hot one.
It should be noted that in fact the pressure does not remain a strictly fixed value. It experiences fluctuations, and therefore the vessel slightly "trembles" in place. But the amplitude of the trembling of the vessel is extremely small.
So, finally, we came to the conclusion that the pressure of the gas on the walls in the vessel does not depend on the quality of the processing of the walls, nor on their temperature.
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. Gas molecules in collisions with the walls of the vessel interact with them according to the laws of mechanics as elastic bodies and transmit their impulses to the walls of the vessel (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 gas mixture fair 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  |
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 placed in a gas solid, then it is also subjected to impacts of gas molecules.
Let's do a simple experiment. Under the bell of the air pump we place a tied balloon not completely filled with air. Since there is little air in it, the balloon has 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. When welding, pure carbon dioxide. Instead, gas mixtures are also used.
A gas mixture is a mixture of gases that do not enter into chemical reactions between themselves.
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.
