Temperature is a measure of the average kinetic energy of a gas. Temperature is a measure of the average kinetic energy of molecules

LESSON

Subject . Temperature is a measure of the average kinetic energy of molecular motion.

Target: develop knowledge about temperature as one of the thermodynamic parametersand to the extentthe average kinetic energy of molecular motion, the Kelvin and Celsius temperature scales and the relationship between them, and the measurement of temperature using thermometers.

Lesson type: lesson in learning new knowledge.

Equipment: liquid thermometer demonstration.

Lesson progress

1. 1. 1. 1. Organizational stage
        Update background knowledge
        
        Do gases have their own volume?
        Do gases have shape?
        Do gases form jets? are they leaking?
        Is it possible to compress gases?
        How are molecules located in gases? How do they move?
        What can be said about the interaction of molecules in gases?

Questions for the class

1. Why gases when high temperature can be considered ideal?

( The higher the gas temperature, the more kinetic energy thermal movement of molecules, which means the gas is closer to ideal .)

2. Why when high blood pressure Do the properties of real gases differ from those of ideal gases? (As pressure increases, the distance between gas molecules decreases and their interaction can no longer be neglected .)

1. 1. 1. 1. Communicating the topic, purpose and objectives of the lesson

We inform you about the topic of the lesson.

IV. Motivation educational activities

Why is it important to study gases and be able to describe the processes that occur in them? Justify your answer using the knowledge you have acquired in physics and your own life experience.

V. Learning new material

3. Temperature as a thermodynamic parameter of an ideal gas. The state of a gas is described using certain quantities called state parameters. There are:

Molecular kinetic theory allows us to understand what the physical essence of such complex concept like the temperature.

Are you familiar with the word "temperature"? early childhood. Now let's get acquainted with temperature as a parameter.

We know that different bodies may have different temperatures. Therefore, temperature characterizes internal state bodies. As a result of the interaction of two bodies with different temperatures, as experience shows, their temperatures will become equal after some time. Numerous experiments indicate that the temperatures of bodies in thermal contact are equalized, i.e. thermal equilibrium is established between them.

Thermal or thermodynamic equilibrium called a state in which all macroscopic parameters in the system remain unchanged for an arbitrarily long time . This means that the volume and pressure in the system do not change, the aggregate states of the substance and the concentration of substances do not change. But microscopic processes inside the body do not stop even in thermal equilibrium: the positions of the molecules and their speeds during collisions change. In a system of bodies in a state of thermodynamic equilibrium, volumes and pressures can be different, but the temperatures are necessarily the same.Thus, temperature characterizes the state of thermodynamic equilibrium of an isolated system of bodies .

The faster the molecules in the body move, the stronger the feeling of warmth when touched. Higher molecular speed corresponds to higher kinetic energy. Therefore, based on the temperature, one can get an idea of the kinetic energy of molecules.

Temperature is a measure of the kinetic energy of thermal motion of molecules .

Temperature is a scalar quantity; in SI measured inKehlwines (K).

2 . Temperature scales. Temperature measurement

Temperature is measured using thermometers, the action of which is based on the phenomenon of thermodynamic equilibrium, i.e. A thermometer is a device for measuring temperature by contact with the body being examined. In the manufacture of thermometers different types takes into account the temperature dependence of different physical phenomena: thermal expansion, electrical and magnetic phenomena etc.

Their action is based on the fact that when temperature changes, other physical parameters of the body, such as pressure and volume, also change.

In 1787, J. Charles established a direct line from an experiment proportional dependence gas pressure versus temperature. From the experiments it followed that with the same heating, the pressure of any gases changes equally. The use of this experimental fact formed the basis for the creation of a gas thermometer.

There are suchtypes of thermometers : liquid, thermocouples, gas, resistance thermometers.

Main types of scales:

In physics, in most cases they use the one introduced by the English scientist W. Kelvin absolute scale temperatures (1848), which has two main points.

First main point - 0 K, or absolute zero.

Physical meaning absolute zero: is the temperature at which thermal motion of molecules stops .

At absolute zero, molecules do not move forward. The thermal motion of molecules is continuous and infinite. Consequently, absolute zero temperature is unattainable in the presence of molecules of a substance. Absolute zero Temperature is the lowest temperature limit; there is no upper limit.

Second main point - This is the point at which water exists in all three states (solid, liquid and gas), it is called the triple point.

In everyday life, another temperature scale is used to measure temperature - the Celsius scale, named after the Swedish astronomer A. Celsius and introduced by him in 1742.

There are two main points on the Celsius scale: 0°C (the point at which ice melts) and 100°C (the point at which water boils). Temperature, which is determined on the Celsius scale, is designated t . The Celsius scale has both positive and negative values.

P Using the figure, we will trace the connection between temperatures on the Kelvin and Celsius scales.

The division value on the Kelvin scale is the same as on the Celsius scale:

ΔT = T 2 - T 1 =( t 2 +273) - ( t 1 +273) = t 2 - t 1 = Δt .

So,ΔT= Δt, those. a change in temperature on the Kelvin scale is equal to a change in temperature on the Celsius scale.

TK = t° C+ 273

0 K = -273°C

0°C =273 K

Class assignment .

Describe a liquid thermometer as a physical device according to the characteristics of a physical device plan.

Characteristics of a liquid thermometer as a physical device

Temperature measurement.

A sealed glass capillary with a liquid reservoir in the lower part filled with mercury or tinted alcohol. The capillary is attached to the scale and is usually placed in a glass case.

As the temperature increases, the liquid inside the capillary expands and rises, and as the temperature decreases, it falls.

Used to measure. temperature of air, water, human body, etc.

The range of temperatures that can be measured using liquid thermometers is wide (mercury from -35 to 75 °C, alcohol from -80 to 70 °C). The disadvantage is that when heated, different liquids expand differently; at the same temperature, readings may differ slightly.

3. Temperature is a measure of the average kinetic energy of molecular motion

ABOUT It was experimentally established that at constant volume and temperature, the pressure of a gas is directly proportional to its concentration. Combining the experimentally obtained dependences of pressure on temperature and concentration, we obtain the equation:

p = nkT , Where -k=1.38×10 -23 J/C , the proportionality coefficient is Boltzmann's constant.Boltzmann's constant relates temperature to the average kinetic energy of motion of molecules in a substance. This is one of the most important constants in MCT. Temperature is directly proportional to the average kinetic energy of thermal motion of particles of a substance. Consequently, temperature can be called a measure of the average kinetic energy of particles, characterizing the intensity of thermal motion of molecules. This conclusion is in good agreement with experimental data showing an increase in the speed of particles of matter with increasing temperature.

The reasoning we carried out to find out physical entity temperatures refer to an ideal gas. However, the conclusions we obtained are valid not only for ideal gases, but also for real gases. They are also valid for liquids and solids. In any state, the temperature of a substance characterizes the intensity of thermal motion of its particles.

VII. Summing up the lesson

We summarize the lesson and evaluate the students’ activities.

Homework

Teacher highest category L.A.Donets

Page 5

Topic: “Temperature. Absolute temperature. Temperature is a measure of the average kinetic energy of molecules. Measuring the velocities of gas molecules"

Macroscopic parameters

Quantities characterizing the state of macroscopic bodies without taking them into account molecular structure(V, p, t) are called macroscopic parameters.

TEMPERATURE

Temperature- quantity characterizing the state thermal equilibrium.

Temperature measurement

It is necessary to bring the body into thermal contact with the thermometer;

The thermometer must have a mass significantly less than body weight;

The thermometer readings should be taken after the onset of thermal equilibrium.

Thermal equilibrium is a state of bodies in which all macroscopic parameters remain unchanged for an arbitrarily long time

PHYSICAL MEANING OF TEMPERATURE

Temperature called scalar quantity, characterizing the intensity of thermal motion of molecules of an isolated system under conditions of thermal equilibrium, proportional to the average kinetic energy of the translational motion of molecules.

Problem solving

Find the number of molecules in 1 kg of gas whose root mean square velocity at absolute temperature T is equal to v = √v2.
Find how many times the mean square speed of a dust particle weighing 1.75 ⋅ 10-12 kg suspended in the air is less than the mean square speed of air molecules.
Determine the average kinetic energy and concentration of molecules of a monatomic gas at a temperature of 290 K and a pressure of 0.8 MPa.

Problem solving

When the Stern device was rotated with a frequency of 45 s -1, the average displacement of the silver strip due to rotation was 1.12 cm. The radii of the inner and outer cylinders are 1.2 and 16 cm, respectively. Find the root mean square velocity of the silver atoms from the experimental data and compare it With theoretical value, if the filament temperature of the platinum filament is 1500 K.

Homework

Paragraphs: 60-61

In practice, to describe the processes occurring in gases, macroscopic parameters are used - pressure r, volume V and temperature T. These quantities characterize the state of the gas and are easily measured by various instruments. Relations between them are established in the form gas laws, which we will look at later.

The concept of temperature is closely related to the concept of thermal equilibrium . Thermal equilibrium is a state of a system of bodies in thermal contact in which there is no heat transfer from one body to another, and all macroscopic parameters of the bodies remain unchanged. Temperature is a physical parameter that is the same for all bodies in thermal equilibrium.

To measure temperature, physical instruments are used - thermometers, in which the temperature value is judged by a change in any physical parameter. IN various designs A variety of thermometers are used physical properties substances (for example, a change in the linear dimensions of solids or a change electrical resistance conductors when heated). Thermometers must be calibrated. To do this, they are brought into thermal contact with bodies whose temperatures are considered known. On the Celsius temperature scale, the melting point of ice is assigned a temperature of 0 °C, and the boiling point of water is assigned a temperature of 100 °C.

The English physicist W. Kelvin in 1848 proposed using the point of zero gas pressure to construct a new temperature scale - Kelvin scale. In this scale, the unit of temperature is the same as in the Celsius scale, but zero point shifted:

T = t + 273.15. (7.10)

In the SI system, the unit of temperature measured on the Kelvin scale is called kelvin and denoted by the letter K.

The Kelvin temperature scale is called the absolute temperature scale. It turns out to be most convenient when constructing physical theories.

It has been experimentally proven that the pressure of a rarefied gas in a vessel of constant volume V changes in direct proportion to its absolute temperature: p ~ T. On the other hand, experience shows that with constant volume V and temperature T, the gas pressure changes in direct proportion to the concentration n gas molecules, i.e. number of gas molecules per unit volume. For any rarefied gas the following relation is valid:

where k is some universal value for all gases constant. It is called the Boltzmann constant, in honor of the Austrian physicist L. Boltzmann, one of the creators of the molecular kinetic theory. Boltzmann's constant is one of the fundamental physical constants. Her numerical value in SI it is equal to:

k = 1.38·10 -23 J/K. (7.12)

Comparing relations (7.11) and (7.9), we can obtain:

The average kinetic energy of the chaotic movement of gas molecules is directly proportional to the absolute temperature. Thus, temperature is a measure of the average kinetic energy of translational motion of molecules.

It should be noted that the average kinetic energy of the translational motion of a molecule does not depend on its mass. A Brownian particle suspended in a liquid or gas has the same average kinetic energy as an individual molecule, the mass of which is many orders of magnitude less than the mass of the Brownian particle. This conclusion also applies to the case when the vessel contains a mixture of chemically non-interacting gases, the molecules of which have different masses. In a state of equilibrium, molecules of different gases will have the same average kinetic energies of thermal motion, determined only by the temperature of the mixture. The pressure of the gas mixture on the walls of the vessel will consist of partial pressures each gas:

In this ratio, n 1, n 2, n 3, ... are the concentrations of molecules of various gases in the mixture. This relationship is expressed in the language of molecular kinetic theory, experimentally established in early XIX century Dalton's law: the pressure in a mixture of chemically non-interacting gases is equal to the sum of their partial pressures .

It represents the energy that is determined by the speed of movement of various points belonging to this system. In this case, it is necessary to distinguish between the energy that characterizes forward movement and the movement is rotational. At the same time, the average kinetic energy is the average difference between the total energy of the entire system and its rest energy, that is, in essence, its value is average size potential energy.

Her physical quantity is determined by the formula 3 / 2 kT, which indicates: T - temperature, k - Boltzmann constant. This value can serve as a kind of criterion for comparison (standard) for the energies contained in various types thermal movement. For example, the average kinetic energy for gas molecules when studying translational motion is 17 (- 10) nJ at a gas temperature of 500 C. As a rule, the greatest energy during translational motion, electrons have, but the energy of neutral atoms and ions is much less.

This value, if we consider any solution, gas or liquid at a given temperature, has constant value. This statement is also true for colloidal solutions.

The situation is somewhat different with solids. In these substances, the average kinetic energy of any particle is too small to overcome the forces of molecular attraction, and therefore it can only move around a certain point, which conventionally fixes a certain equilibrium position particles over a long period of time. This property allows solid be sufficiently stable in shape and volume.

If we consider the conditions: translational motion and an ideal gas, then here the average kinetic energy is not a quantity dependent on molecular weight, and therefore is defined as a value directly proportional to the absolute temperature.

We have presented all these judgments with the aim of showing that they are valid for all types of aggregate states of matter - in any of them, temperature acts as the main characteristic, reflecting the dynamics and intensity of the thermal movement of elements. And this is the essence of molecular kinetic theory and the content of the concept of thermal equilibrium.

As is known, if two physical bodies come into interaction with each other, then a heat exchange process occurs between them. If the body is closed system, that is, does not interact with any bodies, then its heat exchange process will last as long as it takes to equalize the temperatures of this body and environment. This state is called thermodynamic equilibrium. This conclusion has been repeatedly confirmed by experimental results. To determine the average kinetic energy, one should refer to the characteristics of the temperature of a given body and its heat transfer properties.

It is also important to take into account that microprocesses inside bodies do not end when the body enters thermodynamic equilibrium. In this state, molecules move inside bodies, change their speeds, impacts and collisions. Therefore, only one of our several statements is true - body volume, pressure (if we're talking about about gas), may differ, but the temperature will still remain constant. This once again confirms the statement that the average kinetic energy of thermal motion in isolated systems determined solely by temperature.

This pattern was established during experiments by J. Charles in 1787. While conducting experiments, he noticed that when bodies (gases) are heated by the same size, their pressure changes in accordance with the direct proportional law. This observation made it possible to create many useful instruments and things, in particular a gas thermometer.

So far we have not dealt with temperature; we deliberately avoided talking about this topic. We know that if we compress a gas, the energy of the molecules increases, and we usually say that the gas heats up. Now we need to understand what this has to do with temperature. We know what adiabatic compression is, but how can we carry out an experiment so that we can say that it was carried out at a constant temperature? If you take two identical boxes of gas, put them next to each other and hold them like that for quite a long time, then even if at first these boxes had what we called different temperatures, then eventually their temperatures will become the same. What does this mean? Only that the boxes have reached the state that they would eventually reach if they were left to their own devices for a long time! The state in which the temperatures of two bodies are equal is precisely the final state that is achieved after prolonged contact with each other.

Let us see what happens if a box is divided into two parts by a moving piston and each compartment is filled with a different gas, as shown in Fig. 39.2 (for simplicity, assume that there are two monatomic gases, say helium and neon). In compartment 1, atoms of mass move at a speed, and there are a lot of them per unit volume; in compartment 2, these numbers are respectively equal to , and . Under what conditions is equilibrium achieved?

Fig. 39.2. Atoms of two different monatomic gases separated by a movable piston.

Of course, the bombardment on the left forces the piston to move to the right and compresses the gas in the second compartment, then the same thing happens on the right and the piston moves back and forth until the pressure on both sides is equal, and then the piston stops. We can arrange it so that the pressure on both sides is equal, for this we need to: internal energies, per unit volume, were the same, or so that the product of the number of particles per unit volume and the average kinetic energy was the same in both compartments. Now we will try to prove that in equilibrium the individual factors must be identical. So far we only know that the products of the numbers of particles in unit volumes and the average kinetic energies are equal

;

this follows from the condition of equality of pressures and from (39.8). We have to establish that as we gradually approach equilibrium, when the temperatures of the gases become equal, not only this condition is satisfied, but something else happens.

To make it clearer, let's assume that the required pressure on the left side of the box is achieved by very high density, but at low speeds. With large and small, you can get the same pressure as with small and large. The atoms, if they are tightly packed, may move slowly, or there may be very few atoms, but they hit the piston with greater strength. Will equilibrium be established forever? At first it seems that the piston will not move anywhere and will always be so, but if you think about it again, it will become clear that we have missed one very important thing. The fact is that the pressure on the piston is not at all uniform; the piston swings just like the eardrum, which we talked about at the beginning of the chapter, because every new blow not similar to the previous one. The result is not a constant, uniform pressure, but rather something like a drum roll - the pressure is constantly changing, and our piston seems to be constantly trembling. Let us assume that the atoms on the right side strike the piston more or less uniformly, while on the left there are fewer atoms, and their impacts are rare but very energetic. Then the piston will continually receive a very strong impulse from the left and move to the right, towards slower atoms, and the speed of these atoms will increase. (When colliding with a piston, each atom gains or loses energy depending on which direction the piston is moving at the moment of collision.) After several collisions, the piston will swing, then again, again and again..., there will be gas in the right compartment from time to time shake, and this will lead to an increase in the energy of its atoms, and their movement will accelerate. This will continue until the piston swings are balanced. And equilibrium will be established when the speed of the piston becomes such that it will take energy from the atoms as quickly as it gives it back. So, the piston moves with some average speed, and we have to find her. If we succeed, we will come closer to solving the problem, because the atoms must adjust their speeds so that each gas receives through the piston exactly as much energy as it loses.

It is very difficult to calculate the movement of the piston in all details; Although all this is very easy to understand, it turns out that it is somewhat more difficult to analyze. Before proceeding with such an analysis, let us solve another problem: let a box be filled with molecules of two types with masses and , velocities, etc.; Now the molecules will be able to get to know each other better. If at first all molecules No. 2 are at rest, then this cannot continue for long, because molecules No. 1 will hit them and impart some kind of speed to them. If molecules No. 2 can move much faster than molecules No. 1, then sooner or later they will still have to give up part of their energy to slower molecules. Thus, if a box is filled with a mixture of two gases, then the problem is to determine relative speed molecules of both types.

This is also very difficult task, but we will still solve it. First we will have to solve the “sub-problem” (again, this is one of those cases where, no matter how the problem is solved, the final result is easy to remember, but the conclusion requires a lot of skill). Let us assume that we have two colliding molecules with different masses; to avoid complications, we observe the collision from the system of their center of mass (cm), from where it is easier to follow the impact of the molecules. According to the laws of collisions, derived from the laws of conservation of momentum and energy, after a collision, molecules can only move in such a way that each retains the value of its original speed, and they can only change the direction of movement. A typical collision looks like it is depicted in Fig. 39.3. Let us assume for a moment that we are observing collisions whose center of mass systems are at rest. In addition, we must assume that all molecules move horizontally. Of course, after the first collision, some of the molecules will move at some angle to the original direction. In other words, if at first all the molecules moved horizontally, then after some time we will find molecules moving vertically. After a series of other collisions, they will again change direction and turn another angle. Thus, even if someone manages to first restore order among the molecules, they will still very soon scatter in different directions and each time they will become more and more dispersed. What will this ultimately lead to? Answer: Any pair of molecules will move in a randomly chosen direction just as willingly as in any other. After this, further collisions will no longer be able to change the distribution of molecules.

Fig. 39. 3. The collision of two unequal molecules, as viewed from the center of mass system.

What do they mean when they talk about equally probable movement in any direction? Of course, one cannot talk about the probability of movement along a given straight line - the straight line is too thin for probability to be attributed to it, but one should take the unit of “something”. The idea is that the same number of molecules pass through a given portion of a sphere centered at the collision point as through any other portion of the sphere. As a result of collisions, molecules are distributed in directions so that any two areas of equal area will correspond to spheres equal probabilities(i.e. same number molecules passing through these sections).

By the way, if we compare the original direction and the direction forming some angle with it, it is interesting that the elementary area on a sphere of unit radius is equal to the product of , or, which is the same thing, the differential. This means that the cosine of the angle between two directions is equally likely to take any value between and .

Now we need to remember what actually exists; after all, we do not have collisions in the center of mass system, but two atoms collide with arbitrary vector velocities and . What happens to them? We will do this: we will again move to the center of mass system, only now it moves with a “mass-averaged” speed. If you monitor the collision from the center of mass system, it will look like it is shown in Fig. 39.3, you just need to think about the relative speed of the collision. The relative speed is . The situation, therefore, is as follows: the system of the center of mass moves, and in the system of the center of mass the molecules approach each other with a relative speed; having collided, they move in new directions. While all this is happening, the center of mass is always moving at the same speed without changes.

So what will happen in the end? From the previous arguments we draw the following conclusion: in equilibrium, all directions are equally probable relative to the direction of movement of the center of mass. This means that eventually there will be no correlation between the direction of the relative velocity and the movement of the center of mass. Even if such a correlation existed at the beginning, collisions would destroy it and it would eventually disappear completely. Therefore, the average value of the cosine of the angle between and is equal to zero. This means that

The dot product can be easily expressed in terms of and :

Let's do it first; what is the average? In other words, what is the average of the projection of the velocity of one molecule onto the direction of the velocity of another molecule? It is clear that the probabilities of a molecule moving both in one direction and in the opposite direction are the same. The average speed in any direction is zero. Therefore, in the direction the average value is also zero. So the average is zero! Therefore, we came to the conclusion that the average should be equal to . This means that the average kinetic energies of both molecules must be equal:

If a gas consists of two types of atoms, then it can be shown (and we even believe that we have succeeded in doing this) that the average kinetic energies of each type of atom are equal when the gas is in a state of equilibrium. This means that heavy atoms move slower than light ones; this can be easily verified by performing an experiment with “atoms” various masses in the air channel.

Now we will take the next step and show that if there are two gases in a box, separated by a partition, then as equilibrium is reached, the average kinetic energies of the atoms of different gases will be the same, although the atoms are enclosed in different boxes. The reasoning can be structured in different ways. For example, you can imagine that a small hole is made in the partition (Fig. 39.4), so that the molecules of one gas pass through it, but the molecules of the second are too large and do not fit through. When equilibrium is established, then in the compartment where the mixture of gases is located, the average kinetic energies of molecules of each type will be equal. But among the molecules that penetrated through the hole, there are also those that did not lose energy, therefore the average kinetic energy of the molecules of a pure gas must be equal to the average kinetic energy of the molecules of the mixture. This is not a very satisfactory proof, because there might not be such a hole through which the molecules of one gas can pass and the molecules of another cannot pass.

Fig. 39.4. Two gases in a box separated by a semi-permeable partition.

Let's return to the piston problem. It can be shown that the kinetic energy of the piston must also be equal to . In fact, the kinetic energy of the piston is associated only with its horizontal movement. Neglecting the possible up and down motion of the piston, we find that horizontal motion corresponds to kinetic energy. But in the same way, based on the equilibrium on the other side, it can be shown that the kinetic energy of the piston should be equal to . Although we repeat the previous argument, some additional difficulties arise due to the fact that as a result of collisions the average kinetic energies of the piston and the gas molecule are compared, because the piston is not located inside the gas, but is displaced to one side.

If this proof does not satisfy you, then you can come up with an artificial example when equilibrium is ensured by a device in which the molecules of each gas hit from both sides. Let us assume that a short rod passes through the piston, at the ends of which a ball is mounted. The rod can move through the piston without friction. Each of the balls is hit by molecules of the same type from all sides. Let the mass of our device be equal to , and the masses of gas molecules, as before, be equal to and . As a result of collisions with molecules of the first type, the kinetic energy of a body of mass is equal to the average value (we have already proven this). Similarly, collisions with second-class molecules cause the body to have a kinetic energy equal to the average value. If the gases are in thermal equilibrium, then the kinetic energies of both balls must be equal. Thus, the result proved for the case of a mixture of gases can be immediately generalized to the case of two different gases at the same temperature.

So, if two gases have the same temperature, then the average kinetic energies of the molecules of these gases in the center of mass system are equal.

The average kinetic energy of molecules is a property of "temperature" only. And being a property of “temperature” rather than a gas, it can serve as a definition of temperature. The average kinetic energy of a molecule is thus some function of temperature. But who can tell us on what scale to measure the temperature? We can define the temperature scale ourselves so that average energy will be proportional to temperature. The best way to do this is to call the average energy itself “temperature.” This would be the most simple function, but, unfortunately, this scale has already been chosen differently and instead of calling the energy of a molecule simply “temperature”, they use constant factor, which relates the average energy of a molecule and the degree of absolute temperature, or degree Kelvin. This multiplier is J for every degree Kelvin. Thus, if absolute temperature gas is equal to , then the average kinetic energy of the molecule is equal (the factor is introduced only for convenience, due to which the factors in other formulas will disappear).

Note that the kinetic energy associated with the component of motion in any direction is only . Three independent directions of movement bring it to .