Therefore, by changing the temperature of the body, we change its internal energy. When a body is heated, its internal energy increases, when it is cooled, it decreases.
Let's do an experiment. We fix a thin-walled brass tube on the stand. Pour a little ether into it and close it tightly with a cork. Now we wrap the pipe with a rope and begin to rub the pipe with it, quickly pulling it into the rope in one direction or the other. After some time, the internal energy of the tube with ether will increase so much that the ether will boil and the resulting vapor will push out the cork (Fig. 60).
This experience shows that the internal energy of the body can be changed by doing work on the body, in particular by friction.
By changing the internal energy of a piece of wood through friction, our ancestors made fire. The ignition temperature of wood is 250 °C. Therefore, to get fire, you need to rub one piece of wood over another until their temperature reaches this value. Is it easy? When the heroes of Jules Verne's novel "The Mysterious Island" tried to make fire in this way, they did not succeed.
“If the energy that Neb and Pencroff spent could be turned into heat, it would probably be enough to heat the boiler of an ocean steamer. But the result of their efforts was zero. Pieces of wood, however, warmed up, but much less than the participants themselves this operation.
After an hour of work, Pencroff was covered in sweat and angrily threw away the pieces of wood, saying:
"Don't tell me that savages make fire this way!" I would rather believe that it snows in summer. It is easier, perhaps, to light your own palms by rubbing them one against the other.
The reason for their failure was that fire had to be made not by simply rubbing one piece of wood against another, but by drilling into a plank with a pointed stick (Fig. 61). Then, with a certain skill, it is possible to increase the temperature in the nest of the stick by 20 ° C in 1 s. And it takes only 250/20=12.5 seconds to bring the stick to the point of burning! 
Many people in our time "produce" fire by friction - by rubbing matches against a matchbox. How long have matches been around? The production of the first (phosphorus) matches began in the 1930s. 19th century Phosphorus ignites at rather low heating - only up to 60 °C. Therefore, in order to light a phosphorus match, it was enough to strike it on almost any surface (starting from the nearest wall and ending with the bootleg). However, these matches were very dangerous: they were poisonous and, due to easy ignition, often caused a fire. Safety matches (which we still use today) were invented in 1855 in Sweden (hence their name "Swedish matches"). The phosphorus in these matches has been replaced by other combustible substances.
Thus, friction can raise the temperature of a substance. Doing work on the body(for example, striking a piece of lead with a hammer, bending and unbending a wire, moving one object over the surface of another, or compressing a gas in a cylinder with a piston), we increase its internal energy. If the body itself does the work " (due to its internal energy), then the internal energy of the body decreases and the body cools.
Let's observe this in experience. Take a thick-walled glass vessel and tightly close it with a rubber stopper with a hole. Through this hole, with the help of a pump, we will begin to pump air into the vessel. After some time, the cork will fly out of the vessel with noise, and fog will appear in the vessel itself (Fig. 62). The appearance of fog means that the air in the vessel has become colder and, consequently, its internal energy has decreased. This is explained by the fact that the compressed air in the vessel, pushing out the cork, did the work by reducing its internal energy. Therefore, the air temperature has dropped.
The internal energy of the body can be changed without doing work. So, for example, it can be increased by heating a kettle of water on the stove or by lowering a spoon into a glass of hot tea. The fireplace in which the fire is kindled, the roof of the house illuminated by the sun, etc. are heated. An increase in the temperature of bodies in all these cases means an increase in their internal energy, but this increase occurs without doing work.
The change in the internal energy of a body without doing work is called heat exchange. Heat transfer occurs between bodies (or parts of the same body) that have different temperatures.
How, for example, does heat transfer occur when a cold spoon comes into contact with hot water? First, the average speed and kinetic energy of the hot water molecules exceed the average speed and kinetic energy of the metal particles from which the spoon is made. But in those places where the spoon comes into contact with water, the hot water molecules begin to transfer part of their kinetic energy to the particles of the spoon, and they begin to move faster. In this case, the kinetic energy of water molecules decreases, and the kinetic energy of the particles of the spoon increases. Along with the energy, the temperature also changes: the water gradually cools down, and the spoon heats up. The change in their temperature occurs until it becomes the same for both the water and the spoon.
Part of the internal energy transferred from one body to another during heat transfer is denoted by a letter and is called amount of heat.
Q is the amount of heat.
The amount of heat should not be confused with temperature. Temperature is measured in degrees, and the amount of heat (like any other energy) is measured in joules.
When bodies with different temperatures come into contact, the hotter body gives off a certain amount of heat, and the colder body receives it.
So, there are two ways to change the internal energy: 1) doing work and 2) heat exchange. When implementing the first of these methods, the internal energy of the body changes by the amount of perfect work A, and when implementing the second of them, by an amount equal to the amount of transferred heat Q
Interestingly, both considered methods can lead to exactly the same results. Therefore, according to the final result, it is impossible to determine which of these methods it was achieved. So, taking a heated steel needle from the table, we will not be able to say in what way it was heated - by friction or by contact with a hot body. In principle, it could be either one or the other.
1. Name two ways to change the internal energy of the body. 2. Give examples of increasing the internal energy of the body by doing work on it. 3. Give examples of the increase and decrease in the internal energy of the body as a result of heat transfer. 4. What is the amount of heat? How is it designated? 5. In what units is the amount of heat measured? 6. In what ways can fire be made? 7. When did the production of matches begin?
Press a coin or piece of foil against cardboard or some kind of board. Having made first 10, then 20, etc. movements in one direction or the other, notice what happens to the temperature of the bodies in the process of friction. How does the change in the internal energy of a body depend on the amount of work done?
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Lesson content lesson summary support frame lesson presentation accelerative methods interactive technologies Practice tasks and exercises self-examination workshops, trainings, cases, quests homework discussion questions rhetorical questions from students Illustrations audio, video clips and multimedia photographs, pictures graphics, tables, schemes humor, anecdotes, jokes, comics parables, sayings, crossword puzzles, quotes Add-ons abstracts articles chips for inquisitive cheat sheets textbooks basic and additional glossary of terms other Improving textbooks and lessonscorrecting errors in the textbook updating a fragment in the textbook elements of innovation in the lesson replacing obsolete knowledge with new ones Only for teachers perfect lessons calendar plan for the year methodological recommendations of the discussion program Integrated LessonsThe internal energy of a body is not some kind of constant. In the same body, it can change.
When the temperature rises, the internal energy of the body increases, as the average velocity of the molecules increases.
Consequently, the kinetic energy of the molecules of this body increases. Conversely, as the temperature decreases, the internal energy of the body decreases..
In this way, the internal energy of the body changes with a change in the speed of movement of molecules.
Let's try to figure out how to increase or decrease the speed of the molecules. To do this, we will do the following experiment. We fix the thin-walled brass tube on the stand (Fig. 3). Pour a little ether into the tube and close the cork. Then we wrap the tube with a rope and begin to quickly move it first in one direction, then in the other. After a while, the ether will boil, and the steam will push the cork out. Experience shows that the internal energy of the ether has increased: after all, it has heated up and even boiled.
Rice. 3. An increase in the internal energy of the body when doing work on it
The increase in internal energy occurred as a result of the work done when rubbing the tube with a rope.
Heating of bodies also occurs during impacts, extension and bending, i.e., during deformation. The internal energy of the body in all the above examples increases.
Consequently, the internal energy of a body can be increased by doing work on the body.
If the work is done by the body itself, then it internal, energy decreases.
Let's do the following experiment.
Into a thick-walled glass vessel, closed with a cork, we pump air through a special hole in it (Fig. 4).
Rice. 4. Reducing the internal energy of the body when doing work by the body itself
After a while, the cork will pop out of the vessel. At the moment when the cork pops out of the vessel, fog is formed. Its appearance means that the air in the vessel has become colder. The compressed air in the vessel pushes out the cork and does work. He does this work at the expense of his internal energy, which at the same time decreases. You can judge the decrease in internal energy by cooling the air in the vessel. So, the internal energy of a body can be changed by doing work.
The internal energy of the body can be changed in another way, without doing work. For example, water in a kettle put on the stove boils. The air and various objects in the room are heated by a central heating radiator, the roofs of houses are heated by the rays of the sun, etc. In all these cases, the temperature of the bodies rises, which means that their internal energy increases. But the work is not done.
Means, change in internal energy can occur not only as a result of doing work.
How can the increase in internal energy be explained in these cases?
Consider the following example.
Dip a metal needle into a glass of hot water. The kinetic energy of hot water molecules is greater than the kinetic energy of cold metal particles. Hot water molecules, when interacting with cold metal particles, will transfer part of their kinetic energy to them. As a result, the energy of water molecules will decrease on average, while the energy of metal particles will increase. The temperature of the water will decrease and the temperature of the metal spoke will gradually increase. After a while, their temperatures will even out. This experience demonstrates the change in the internal energy of bodies.
So, internal energy of bodies can be changed by heat transfer.
The process of changing internal energy without doing work on the body or the body itself is called heat transfer.
Heat transfer always occurs in a certain direction: from bodies with a higher temperature to bodies with a lower one.
When the temperatures of the bodies equalize, heat transfer stops.
The internal energy of a body can be changed in two ways: by doing mechanical work or by heat transfer.
Heat transfer, in turn, can be carried out: 1) thermal conductivity; 2) convection; 3) radiation.
Questions
- Using Figure 3, describe how the internal energy of a body changes when work is done on it.
- Describe an experiment showing that a body can do work due to internal energy.
- Give examples of changes in the internal energy of a body by means of heat transfer.
- Explain, on the basis of the molecular structure of a substance, the heating of a knitting needle dipped in hot water.
- What is heat transfer?
- What are two ways to change the internal energy of a body?
Exercise 2
- The force of friction does work on the body. Does this change the internal energy of the body? By what signs can one judge this?
- When you go down the rope quickly, your hands get hot. Explain why this is happening.
Exercise
Place the coin on a sheet of plywood or a wooden board. Press the coin against the board and move it quickly in one direction or the other. Notice how many times you need to move the coin to make it warm, hot. Make a conclusion about the relationship between the work done and the increase in the internal energy of the body.
Physics lesson in the 8th grade on the topic: "Internal energy. Ways to change internal energy"
Lesson Objectives:
- Formation of the concept of "internal energy of the body" on the basis of the MKT of the structure of matter.
- Familiarization with ways to change the internal energy of the body.
- Formation of the concept of "heat transfer" and the ability to apply knowledge of the MKT of the structure of matter in explaining thermal phenomena.
- Development of interest in physics through the demonstration of interesting examples of the manifestation of thermal phenomena in nature and technology.
- Justification of the need to study thermal phenomena for the application of this knowledge in everyday life.
- Development of information and communication competencies of students.
Lesson type. Combined lesson.
Lesson type. Lesson - presentation
Lesson form.Interactive conversation, demonstration experiment, storytelling, self-study
Forms of student work.Collective work, individual work, work in groups.
Equipment: electronic presentation “Internal energy. Ways to change internal energy”, computer, projector.
During the classes
Organizing time.Good afternoon! Today in the lesson we will get acquainted with another type of energy, find out what it depends on and how it can be changed.
Knowledge update.
- Repetition of basic concepts: energy, kinetic and potential energy, mechanical work.
Learning new material.
Teacher . In addition to the above concepts, it should be remembered that two typesmechanical energycan turn (pass) into each other, for example, when the body falls. Consider a freely falling ball. Obviously, when falling, its height above the surface decreases, and the speed increases, which means that its potential energy decreases, and its kinetic energy increases. It should be understood that these two processes do not occur separately, they are interrelated, and it is said thatpotential energy is converted into kinetic.
To understand what the internal energy of a body is, it is necessary to answer the following question: what do all bodies consist of?
Students . Bodies are composed of particles that are constantly moving randomly and interacting with each other.
Teacher . And if they move and interact, then they have kinetic and potential energy, which constitute the internal energy.
Students. It turns out that all bodies have the same internal energy, which means that the temperature must be the same. And this is not so.
Teacher. Of course not. Bodies have different internal energy, and we will try to find out what the internal energy of the body depends on and what does not depend on.
Definition.
Kinetic energyparticle motion andpotential energytheir interactions areinternal energy of the body.
The internal energy isand it is measured, like all other types of energy, in J (joules).
Therefore, we have a formula for the internal energy of the body:. Where under is understood as the kinetic energy of the particles of the body, and underis their potential energy.
Recall the previous lesson, where we talked about the fact that the movement of particles of a body is characterized by its temperature, on the other hand, the internal energy of a body is related to the nature (activity) of the movement of particles. Therefore, internal energy and temperature are interrelated concepts. When the body temperature rises, its internal energy also increases, and when it decreases, it decreases.
We found out that the internal energy of a body can change. Consider ways to change the internal energy of the body.
You are already familiar with the concept of the mechanical work of the body, it is associated with the movement of the body when a certain force is applied to it. If mechanical work is performed, then the energy of the body changes, and the same can be said specifically about the internal energy of the body. It is convenient to depict this in a diagram:
Teacher The method of increasing the internal energy of the body during friction has been known to people since ancient times. This is how people made fire. Working in workshops, for example, turning parts with a file, what can be observed? (Parts heated up). When a person is cold, he begins to shiver involuntarily. Why do you think? (Trembling causes muscle contractions. Due to the work of the muscles, the internal energy of the body increases, it becomes warmer). What conclusion can be drawn from what has been said?
Students . The internal energy of a body changes when work is done. If the body itself does work, its internal energy decreases, and if work is done on it, then its internal energy increases.
Teacher . In technology, industry, everyday practice, we constantly encounter a change in the internal energy of a body when doing work: heating of bodies during forging, upon impact; work with compressed air or steam.
Let's take a break and at the same time learn some interesting facts from the history of thermal phenomena (two students give short presentations prepared in advance).
Message 1 . How did miracles happen?
The ancient Greek mechanic Heron of Alexandria, the inventor of the fountain that bears his name, left us a description of two ingenious ways in which the Egyptian priests deceived the people, inspiring them to believe in miracles.
In figure 1 you see a hollow metal altar, and underneath it is a mechanism hidden in the dungeon that sets the doors of the temple in motion. The altar stood outside it. When a fire is kindled, the air inside the altar, due to the heating, presses harder on the water in the vessel hidden under the floor; water is forced out of the vessel through a tube and poured into a bucket, which, descending, activates a mechanism that rotates the doors (Fig. 2). The astonished spectators, unaware of the installation hidden under the floor, see a “miracle” in front of them: as soon as the fire blazes on the altar, the doors of the temple, “hearing the prayers of the priest”, dissolve as if by themselves...
Exposing the "miracle" of the Egyptian priests: the doors of the temple are opened by the action of the sacrificial fire.
Message 2. How did miracles happen?
Another imaginary miracle arranged by the priests is depicted in fig. 3. When a flame blazes on the altar, the air, expanding, takes the oil from the lower reservoir into the tubes hidden inside the figures of the priests, and then the oil miraculously pours itself into the fire ... But as soon as the priest in charge of this altar quietly removes the cork tank - and the outpouring of oil stopped (because excess air freely escaped through the hole); the priests resorted to this trick when the offering of the worshipers was too scarce.
Teacher. We all know morning tea! It is so nice to make tea, pour sugar into a cup and drink a little, with a small spoon. Only one thing is bad - the spoon is too hot! What happened to the spoon? Why did her temperature rise? Why did her internal energy increase? Did we work on it?
Students . No, they didn't.
Teacher . Let's find out why there was a change in internal energy.
Initially, the temperature of the water is higher than the temperature of the spoon, and therefore the speed of the water molecules is greater. This means that water molecules have more kinetic energy than the metal particles from which the spoon is made. When colliding with metal particles, water molecules transfer part of their energy to them, and the kinetic energy of metal particles increases, and the kinetic energy of water molecules decreases. This way of changing the internal energy of bodies is called heat transfer . In our daily life, we often encounter this phenomenon. For example, in the water, when lying on the ground or in the snow, the body cools down, which can lead to colds or frostbite. In severe frost, ducks willingly climb into the water. Why do you think? (In severe frost, the water temperature is much higher than the ambient temperature, so the bird will cool less in the water than in the air).Heat transfer is carried out in several ways, but we will talk about this in the next lesson.
Thus, two ways of changing the internal energy are possible. Which?
Students . Work done and heat transfer.
Consolidation of the studied material.Now let's see how well you learned the new material of today's lesson.. I will ask questions and you will try to answer them.
Question 1 . Cold water is poured into one glass, the same amount of boiling water is poured into the other. Which glass has more internal energy? (In the second, because its temperature is higher).
Question 2. Two copper bars have the same temperature, but the mass of one is 1 kg, and the other is 0.5 kg. Which of the two given bars has more internal energy? (First, because its mass is greater).
Question 3. The hammer heats up when it is struck, for example, on an anvil, and when it lies in the sun on a hot summer day. Name the ways of changing the internal energy of the hammer in both cases. (In the first case, work is done, and in the second, heat transfer).
Question 4 . Water is poured into a metal mug. Which of the following actions changes the internal energy of water? (13)
- Heating water on a hot stove.
- Performing work on water, bringing it into translational motion along with the mug.
- Making work on water by mixing it with a mixer.
Teacher . And now I suggest you work on your own. (Students are divided into 6 groups, and further work will be carried out in groups). In front of you is a piece of paper with three tasks.
Exercise 1. What is the reason for the change in the internal energy of bodies in the following phenomena:
- heating water with a boiler;
- cooling food placed in the refrigerator;
- ignition of a match when struck by it on the box;
- strong heating and combustion of artificial satellites of the earth when they enter the lower dense layers of the atmosphere;
- if you quickly bend the wire in the same place, then in one direction, then in the other direction, then this place becomes very hot;
- cooking food;
- if you quickly slide down a pole or rope, you can burn your hands;
- heating the water in the pool on a hot summer day;
- when hammering a nail, its hat heats up;
- A match ignites when placed in a candle flame.
For two groups - during friction; the other two groups - on impact and two more groups - on compression.
Reflection.
- What new, interesting things did you learn at the lesson today?
- How did you get the material you learned?
- What were the difficulties? Have you managed to overcome them?
- Will the knowledge gained in the lesson today be useful to you?
Summing up the lesson.Today we got acquainted with the basic concepts of the section "Thermal phenomena" internal energy and heat transfer and got acquainted with the methods of changing the internal energy of bodies. The knowledge gained will help you explain and predict the course of thermal processes that you will meet in your life.
Homework. § 2, 3. Experimental tasks:
- Measure the temperature of water poured into a jar or bottle with a home thermometer.
Close the vessel tightly and shake it vigorously for 10–15 minutes, after which measure the temperature again.
To prevent heat transfer from your hands, put on mittens or wrap the vessel in a towel.
What method of changing internal energy did you use? Explain. - Take a rubber band tied with a ring, put the tape on your forehead and note its temperature. Holding the rubber with your fingers, vigorously stretch several times and, in a stretched form, press it again to the forehead. Make a conclusion about the temperature and the reasons that caused the change.
Preview:
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Internal energy can be changed in two ways.
If work is done on a body, its internal energy increases.
If the work is done by the body itself, its internal energy decreases.
In total, there are three simple (elementary) types of heat transfer:
Thermal conductivity
· Convection
Convection is the phenomenon of heat transfer in liquids or gases, or granular media by flows of matter. There is a so-called. natural convection, which occurs spontaneously in a substance when it is heated unevenly in a gravitational field. With such convection, the lower layers of matter heat up, become lighter and float, while the upper layers, on the contrary, cool down, become heavier and sink down, after which the process repeats again and again.
Thermal radiation or radiation is the transfer of energy from one body to another in the form of electromagnetic waves due to their thermal energy.
Internal energy of an ideal gas
Based on the definition of an ideal gas, there is no potential component of internal energy in it (there are no forces of interaction of molecules, except for shock). Thus, the internal energy of an ideal gas is only the kinetic energy of the movement of its molecules. Previously (Equation 2.10) it was shown that the kinetic energy of the translational motion of gas molecules is directly proportional to its absolute temperature.
Using the expression for the universal gas constant (4.6), one can determine the value of the constant α.
Thus, the kinetic energy of the translational motion of one molecule of an ideal gas will be determined by the expression.
In accordance with the kinetic theory, the distribution of energy over degrees of freedom is uniform. Translational motion has 3 degrees of freedom. Therefore, one degree of freedom of motion of a gas molecule will account for 1/3 of its kinetic energy. 
For two, three and polyatomic gas molecules, in addition to the degrees of freedom of translational motion, there are degrees of freedom of rotational motion of the molecule. For diatomic gas molecules, the number of degrees of freedom of rotational motion is 2, for three and polyatomic molecules - 3.
Since the distribution of the energy of motion of a molecule over all degrees of freedom is uniform, and the number of molecules in one kilomol of a gas is Nμ, the internal energy of one kilomol of an ideal gas can be obtained by multiplying expression (4.11) by the number of molecules in one kilomol and by the number of degrees of freedom of motion of a molecule of a given gas .
where Uμ is the internal energy of a kilomole of gas in J/kmol, i is the number of degrees of freedom of motion of a gas molecule.
For 1 - atomic gas i = 3, for 2 - atomic gas i = 5, for 3 - atomic and polyatomic gases i = 6.
Electricity. Conditions for the existence of an electric current. EMF. Ohm's law for a complete circuit. Work and current power. Joule-Lenz law.
Among the conditions necessary for the existence of an electric current, there are: the presence of free electric charges in the environment and the creation of an electric field in the environment. The electric field in the medium is necessary to create a directed movement of free charges. As is known, a charge q in an electric field of strength E is affected by a force F = qE, which forces the free charges to move in the direction of the electric field. A sign of the existence of an electric field in the conductor is the presence of a non-zero potential difference between any two points of the conductor.
However, electric forces cannot sustain an electric current for a long time. The directed movement of electric charges after some time leads to equalization of the potentials at the ends of the conductor and, consequently, to the disappearance of the electric field in it. To maintain the current in the electric circuit, the charges, in addition to the Coulomb forces, must be affected by non-electrical forces (external forces). A device that creates external forces, maintains a potential difference in a circuit and converts various types of energy into electrical energy, is called a current source.
Conditions for the existence of an electric current:
The presence of free charge carriers
the presence of a potential difference. these are the conditions for the occurrence of current. for the current to exist
a closed circuit
a source of external forces that maintains a potential difference.
Any forces acting on electrically charged particles, with the exception of electrostatic (Coulomb) forces, are called external forces.
Electromotive force.
Electromotive force (EMF) is a scalar physical quantity that characterizes the work of external (non-potential) forces in direct or alternating current sources. In a closed conducting circuit, the EMF is equal to the work of these forces in moving a single positive charge along the circuit.
The unit of EMF, like voltage, is the volt. We can talk about the electromotive force in any part of the circuit. The electromotive force of a galvanic cell is numerically equal to the work of external forces when moving a single positive charge inside the cell from its negative pole to the positive one. The sign of the EMF is determined depending on the arbitrarily chosen direction of bypassing that section of the circuit on which the given current source is turned on.
Ohm's law for a complete circuit.
Consider the simplest complete circuit, consisting of a current source and a resistor with a resistance R. A current source having an EMF ε has a resistance r, it is called the internal resistance of the current source. To obtain Ohm's law for a complete circuit, we use the law of conservation of energy.
Let a charge q pass through the cross section of the conductor in time Δt. Then, according to the formula, the work of external forces when moving the charge q is equal to . From the definition of current strength, we have: q = IΔt. Consequently, .
Due to the work of external forces during the passage of current in the circuit, an amount of heat is released on its external and internal sections of the circuit, according to the Joule-Lenz law equal to:
According to the law of conservation of energy A st \u003d Q, therefore Hence Thus, the EMF of the current source is equal to the sum of the voltage drops in the external and internal sections of the circuit.
According to MKT, all substances are composed of particles that are in continuous thermal motion and interact with each other. Therefore, even if the body is motionless and has zero potential energy, it has energy (internal energy), which is the total energy of motion and interaction of the microparticles that make up the body. The composition of internal energy includes:
- kinetic energy of translational, rotational and vibrational motion of molecules;
- potential energy of interaction of atoms and molecules;
- intraatomic and intranuclear energy.
In thermodynamics, processes are considered at temperatures at which the oscillatory motion of atoms in molecules is not excited, i.e. at temperatures not exceeding 1000 K. Only the first two components of the internal energy change in these processes. That's why
under internal energy in thermodynamics, they understand the sum of the kinetic energy of all molecules and atoms of a body and the potential energy of their interaction.
The internal energy of a body determines its thermal state and changes during the transition from one state to another. In a given state, the body has a well-defined internal energy, independent of the process as a result of which it passed into this state. Therefore, the internal energy is very often called body state function.
\(~U = \dfrac (i)(2) \cdot \dfrac (m)(M) \cdot R \cdot T,\)
where i- degree of freedom. For a monatomic gas (for example, inert gases) i= 3, for diatomic - i = 5.
From these formulas it can be seen that the internal energy of an ideal gas depends only on temperature and number of molecules and does not depend on volume or pressure. Therefore, the change in the internal energy of an ideal gas is determined only by a change in its temperature and does not depend on the nature of the process in which the gas passes from one state to another:
\(~\Delta U = U_2 - U_1 = \dfrac (i)(2) \cdot \dfrac(m)(M) \cdot R \cdot \Delta T ,\)
where ∆ T = T 2 - T 1 .
- Molecules of real gases interact with each other and therefore have potential energy W p , which depends on the distance between the molecules and, consequently, on the volume occupied by the gas. Thus, the internal energy of a real gas depends on its temperature, volume, and molecular structure.
*Derivation of the formula
Average kinetic energy of a molecule \(~\left\langle W_k \right\rangle = \dfrac (i)(2) \cdot k \cdot T\).
The number of molecules in the gas \(~N = \dfrac (m)(M) \cdot N_A\).
Therefore, the internal energy of an ideal gas
\(~U = N \cdot \left\langle W_k \right\rangle = \dfrac (m)(M) \cdot N_A \cdot \dfrac (i)(2) \cdot k \cdot T .\)
Given that k⋅N A= R is the universal gas constant, we have
\(~U = \dfrac (i)(2) \cdot \dfrac (m)(M) \cdot R \cdot T\) is the internal energy of an ideal gas.
Change in internal energy
To solve practical issues, it is not the internal energy itself that plays a significant role, but its change Δ U = U 2 - U one . The change in internal energy is calculated based on the laws of conservation of energy.
The internal energy of a body can change in two ways:
- When making mechanical work. a) If an external force causes deformation of the body, then the distances between the particles of which it consists change, and consequently, the potential energy of the interaction of particles changes. With inelastic deformations, in addition, the temperature of the body changes, i.e. the kinetic energy of the thermal motion of particles changes. But when the body is deformed, work is done, which is a measure of the change in the internal energy of the body. b) The internal energy of a body also changes during its inelastic collision with another body. As we saw earlier, during inelastic collision of bodies, their kinetic energy decreases, it turns into internal energy (for example, if you hit a wire lying on an anvil several times with a hammer, the wire will heat up). The measure of change in the kinetic energy of a body is, according to the kinetic energy theorem, the work of the acting forces. This work can also serve as a measure of changes in internal energy. c) The change in the internal energy of the body occurs under the action of the force of friction, since, as is known from experience, friction is always accompanied by a change in the temperature of rubbing bodies. The work of the friction force can serve as a measure of the change in internal energy.
- With help heat transfer. For example, if a body is placed in a burner flame, its temperature will change, and therefore its internal energy will also change. However, no work was done here, because there was no visible movement of either the body itself or its parts.
The change in the internal energy of a system without doing work is called heat exchange(heat transfer).
There are three types of heat transfer: conduction, convection and radiation.
a) thermal conductivity is the process of heat exchange between bodies (or body parts) in their direct contact, due to the thermal chaotic movement of body particles. The amplitude of oscillations of the molecules of a solid body is greater, the higher its temperature. The thermal conductivity of gases is due to the exchange of energy between gas molecules during their collisions. In the case of liquids, both mechanisms work. The thermal conductivity of a substance is maximum in the solid state and minimum in the gaseous state.
b) Convection is the transfer of heat by heated flows of liquid or gas from one part of the volume they occupy to another.
c) Heat transfer at radiation carried out at a distance by means of electromagnetic waves.
Let us consider in more detail how to change the internal energy.
mechanical work
When considering thermodynamic processes, the mechanical movement of macrobodies as a whole is not considered. The concept of work here is associated with a change in the volume of the body, i.e. moving parts of the macrobody relative to each other. This process leads to a change in the distance between the particles, and also often to a change in the speed of their movement, therefore, to a change in the internal energy of the body.
isobaric process
Consider first the isobaric process. Let there be gas in a cylinder with a movable piston at a temperature T 1 (Fig. 1).
We will slowly heat the gas to a temperature T 2. The gas will expand isobarically and the piston will move from position 1 into position 2 distance Δ l. In this case, the pressure force of the gas will do work on external bodies. Because p= const, then the pressure force F = p⋅S also constant. Therefore, the work of this force can be calculated by the formula
\(~A = F \cdot \Delta l = p \cdot S \cdot \Delta l = p \cdot \Delta V,\)
where ∆ V- change in gas volume.
- If the volume of the gas does not change (isochoric process), then the work done by the gas is zero.
- The gas does work only in the process of changing its volume.
When expanding (Δ V> 0) positive work is done on the gas ( BUT> 0); under compression (Δ V < 0) газа совершается отрицательная работа (BUT < 0).
- If we consider the work of external forces A " (BUT " = –BUT), then with the expansion (Δ V> 0) gas BUT " < 0); при сжатии (ΔV < 0) BUT " > 0.
Let's write the Clapeyron-Mendeleev equation for two gas states:
\(~p \cdot V_1 = \nu \cdot R \cdot T_1, \; \; p \cdot V_2 = \nu \cdot R \cdot T_2,\)
\(~p \cdot (V_2 - V_1) = \nu \cdot R \cdot (T_2 - T_1) .\)
Therefore, at isobaric process
\(~A = \nu \cdot R \cdot \Delta T .\)
If ν = 1 mol, then at Δ Τ = 1 K we get that R is numerically equal to A.
Hence follows physical meaning of the universal gas constant: it is numerically equal to the work done by 1 mole of an ideal gas when it is heated isobarically by 1 K.
Not an isobaric process
On the chart p (V) in an isobaric process, the work is equal to the area of the rectangle shaded in Figure 2, a.
If the process not isobaric(Fig. 2, b), then the function curve p = f(V) can be represented as a broken line consisting of a large number of isochores and isobars. Work on isochoric sections is equal to zero, and the total work on all isobaric sections will be equal to
\(~A = \lim_(\Delta V \to 0) \sum^n_(i=1) p_i \cdot \Delta V_i\), or \(~A = \int p(V) \cdot dV,\ )
those. will be equal to area of the shaded figure.
At isothermal process (T= const) the work is equal to the area of the shaded figure shown in Figure 2, c.
It is possible to determine the work using the last formula only if it is known how the gas pressure changes with a change in its volume, i.e. the form of the function is known p = f(V).
Thus, it is clear that even with the same change in gas volume, the work will depend on the method of transition (i.e., on the process: isothermal, isobaric ...) from the initial state of the gas to the final one. Therefore, it can be concluded that
- Work in thermodynamics is a process function and not a state function.
Quantity of heat
As you know, during various mechanical processes, there is a change in mechanical energy W. The measure of change in mechanical energy is the work of forces applied to the system:
\(~\DeltaW = A.\)
During heat transfer, a change in the internal energy of the body occurs. The measure of change in internal energy during heat transfer is the amount of heat.
Quantity of heat is a measure of the change in internal energy during heat transfer.
Thus, both work and the amount of heat characterize the change in energy, but are not identical to internal energy. They do not characterize the state of the system itself (as internal energy does), but determine the process of energy transition from one form to another (from one body to another) when the state changes and essentially depend on the nature of the process.
The main difference between work and heat is that
- the work characterizes the process of changing the internal energy of the system, accompanied by the transformation of energy from one type to another (from mechanical to internal);
- the amount of heat characterizes the process of transfer of internal energy from one body to another (from more heated to less heated), not accompanied by energy transformations.
Heating (cooling)
Experience shows that the amount of heat required to heat a body with a mass m temperature T 1 to temperature T 2 is calculated by the formula
\(~Q = c \cdot m \cdot (T_2 - T_1) = c \cdot m \cdot \Delta T,\)
where c- specific heat capacity of a substance (table value);
\(~c = \dfrac(Q)(m \cdot \Delta T).\)
The SI unit of specific heat is the joule per kilogram-Kelvin (J/(kg K)).
Specific heat c is numerically equal to the amount of heat that must be imparted to a body of mass 1 kg in order to heat it by 1 K.
In addition to the specific heat capacity, such a quantity as the heat capacity of the body is also considered.
Heat capacity body C numerically equal to the amount of heat required to change the body temperature by 1 K:
\(~C = \dfrac(Q)(\Delta T) = c \cdot m.\)
The SI unit of heat capacity of a body is the joule per Kelvin (J/K).
Vaporization (condensation)
To change a liquid into a vapor at a constant temperature, the amount of heat required is
\(~Q = L\cdot m,\)
where L- specific heat of vaporization (table value). When steam condenses, the same amount of heat is released.
The SI unit for specific heat of vaporization is the joule per kilogram (J/kg).
Melting (crystallization)
In order to melt a crystalline body with a mass m at the melting point, it is necessary for the body to report the amount of heat
\(~Q = \lambda \cdot m,\)
where λ - specific heat of fusion (table value). During the crystallization of a body, the same amount of heat is released.
The SI unit for specific heat of fusion is the joule per kilogram (J/kg).
fuel combustion
The amount of heat that is released during the complete combustion of fuel mass m,
\(~Q = q \cdot m,\)
where q- specific heat of combustion (table value).
The SI unit for specific heat of combustion is the joule per kilogram (J/kg).
Literature
Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 129-133, 152-161.
