Ideal gas. Basic MKT equation

Temperature.

The basic equation of molecular kinetic theory for ideal gas establishes a connection between an easily measured macroscopic parameter - pressure - and such microscopic parameters of a gas as average kinetic energy and concentration of molecules.

But by measuring only the gas pressure, we cannot find out the average value kinetic energy molecules individually, nor their concentration. Consequently, to find the microscopic parameters of a gas, measurements of some other physical quantity related to

average kinetic energy of molecules. Such a quantity in physics is temperature.

From everyday experience, everyone knows that there are hot and cold bodies. When two bodies come into contact, one of which we perceive as hot and the other as cold, changes in the physical parameters of both the first and second bodies occur. For example, solids and liquids usually expand when heated. Some time after establishing contact between the bodies, changes in the macroscopic parameters of the bodies stop. This state of bodies is called thermal equilibrium. A physical parameter that is the same in all parts of a system of bodies in a state of thermal equilibrium is called body temperature. If, when two bodies come into contact, none of their physical parameters, for example volume, pressure, change, then there is no heat transfer between the bodies and the temperature of the bodies is the same.

Thermometers.

In everyday practice, the most common method of measuring temperature is using a liquid thermometer.

The liquid thermometer uses the property of liquids to expand when heated. Mercury, alcohol, and glycerin are usually used as working fluids. To measure body temperature, the thermometer is brought into contact with that body; Heat transfer will take place between the body and the thermometer until thermal equilibrium is established. The mass of the thermometer should be significantly less than body weight, since otherwise the measurement process can significantly change body temperature.

Changes in the volume of liquid in the thermometer stop when heat exchange between the body and the thermometer stops. In this case, the temperature of the liquid in the thermometer is equal to body temperature.

By marking on the thermometer tube the position of the end of the liquid column when placing the thermometer in melting ice, and then in boiling water at normal pressure and dividing the segment between these marks by 100 equal parts, obtain a temperature scale in Celsius. The temperature of melting ice is assumed to be equal (Fig. 83), boiling water - (Fig. 84). The change in the length of the liquid column in the thermometer by one hundredth of the length between the 0 marks corresponds to a change in temperature by

A significant disadvantage of the method of measuring temperature using liquid thermometers is that the temperature scale is associated with specific physical properties a certain substance used as a working fluid in a thermometer - mercury, glycerin, alcohol. The change in volume of different liquids under the same heating turns out to be somewhat different. Therefore, mercury and glycerin thermometers, whose readings are the same at 0 and 100 °C, give different readings at other temperatures.

Gases are in a state of thermal equilibrium.

In order to find a more perfect way to determine temperature, it is necessary to find a value that would be the same for any bodies in a state of thermal equilibrium.

Experimental studies of the properties of gases have shown that for any gases in a state of thermal equilibrium, the ratio of the product of the gas pressure and its volume to the number of molecules is the same:

This experimental fact allows us to accept the value 0 as a natural measure of temperature.

Since, taking into account the basic equation of molecular kinetic theory (24.2), we obtain

Consequently, the average kinetic energy of the molecules of any gases that are in thermal equilibrium is the same. The value 0 is equal to two-thirds of the average kinetic energy of the random thermal motion of gas molecules and is expressed in joules.

In physics, temperature is usually expressed in degrees, assuming that the temperature T in degrees and the value 0 are related by the equation

where is a proportionality coefficient depending on the choice of temperature unit.

From here we get

The last equation shows that it is possible to choose a temperature scale that does not depend on the nature of the gas used as the working fluid.

In practice, temperature measurement based on the use of equation (25.4) is carried out using a gas thermometer (Fig. 85). Its structure is as follows: there is gas in a vessel of constant volume, the amount of gas remains unchanged. At constant values of the volume V and the number of molecules, the gas pressure measured by a manometer can serve as a measure of the temperature of the gas, and therefore of any body with which the gas is in thermal equilibrium.

Absolute temperature scale.

The temperature measurement scale in accordance with equation (25.4) is called the absolute scale. It was proposed by the English physicist W. Kelvia (Thomson) (1824-1907), which is why the scale is also called the Kelvin scale.

Before the introduction of the absolute temperature scale, the Celsius temperature scale became widespread in practice. Therefore, the unit of temperature on the absolute scale, called the kelvin, is chosen to be equal to one degree on the Celsius scale:

Absolute zero temperature.

On the left side of equation (25.4) all quantities can only have positive values or be equal to zero. Therefore, the absolute temperature T can only be positive or equal to zero. The temperature at which the pressure of an ideal gas at constant volume should be equal to zero is called absolute zero temperature.

Boltzmann's constant.

The value of the constant k in equation (25.4) can be found from known values pressure and volume of a gas with a known number of molecules at two temperatures

As is known, 1 mole of any gas contains approximately molecules and at normal pressure Pa occupies a volume

Experiments have shown that when any gas is applied at a constant volume from 0 to 100 ° C, its pressure increases from up to Pa. Substituting these values into equation (25.6), we get

The coefficient is called Boltzmann's constant, in honor of the Austrian physicist Ludwig Boltzmann (1844-1906), one of the creators of molecular kinetic theory.

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.

During the classes

1. 1. 1. 1. Organizational stage
        Updating of reference 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 temperature of the gas, the greater the kinetic energy of the 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 a complex concept as temperature is.

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. When manufacturing thermometers of various types, the dependence on the temperature 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 experimentally established a direct proportional relationship between gas pressure and 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 absolute temperature scale introduced by the English scientist W. Kelvin (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.

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, the 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 that we carried out to clarify the physical essence of temperature applies 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

It represents the energy that is determined by the speed of movement of various points belonging to this system. In this case, one should distinguish between the energy that characterizes translational motion and rotational motion. 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 the average value

Its physical value 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 in a study forward motion, is equal to 17 (- 10) nJ at a gas temperature of 500 C. As a rule, electrons have the greatest energy during translational motion, 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 a 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 conditionally fixes a certain equilibrium position of the particle over a long period of time. This property allows the solid to be quite stable in shape and volume.

If we consider the conditions: translational motion and then here the average kinetic energy is not a quantity dependent on and therefore is defined as a value directly proportional to the value

We have given all these judgments with the aim of showing that they are valid for all types states of aggregation substances - 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 a closed system, that is, it 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 - the volume of the body, the pressure (if we are talking 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 is determined solely by the temperature indicator.

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 amount, 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.

In this lesson we will analyze a physical quantity that is already familiar to us from the eighth grade course - temperature. We will supplement its definition as a measure of thermal equilibrium and a measure of average kinetic energy. We will describe the disadvantages of some and the advantages of other methods of measuring temperatures, introduce the concept of an absolute temperature scale and, finally, derive the dependence of the kinetic energy of gas molecules and gas pressure on temperature.

There are two reasons for this:

Various thermometers use various substances as an indicator, therefore thermometers react differently to the same temperature change depending on the properties of a particular substance;
Arbitrariness in choosing the starting point for the temperature scale.

Therefore, such thermometers are not suitable for any accurate temperature measurements. And since the eighteenth century, more accurate thermometers have been used, which are gas thermometers (see Fig. 2)

Rice. 2. Gas thermometer ()

The reason for this is the fact that gases expand the same when the temperature changes by the same amount. The following applies to gas thermometers:

That is, to measure temperature, either the change in pressure is recorded at a constant volume, or the volume at a constant pressure.

Gas thermometers often use rarefied hydrogen, which, as we remember, fits the ideal gas model very well.

In addition to the imperfection of household thermometers, there is also the imperfection of many scales that are used in everyday life. In particular, the Celsius scale, as the most familiar to us. As with thermometers, these scales select a random starting level (for the Celsius scale, this is the melting point of ice). Therefore, to work with physical quantities another, absolute scale is needed.

This scale was introduced in 1848 by the English physicist William Thompson (Lord Kelvin) (Fig. 3). Knowing that as temperatures increase, the thermal speed of movement of molecules and atoms also increases, it is not difficult to establish that as temperatures decrease, the speed will fall and at a certain temperature will sooner or later become zero, as will the pressure (based on the basic MKT equation). This temperature was chosen as the starting point. It is obvious that the temperature cannot reach a value less than this value, which is why it is called “absolute zero temperature”. For convenience, 1 degree on the Kelvin scale was given in accordance with 1 degree on the Celsius scale.

So, we get the following:

Temperature designation - ;

Unit of measurement - K, "kelvin"

Translation to the Kelvin scale:

Therefore, absolute zero temperature is the temperature

Rice. 3. William Thompson ()

Now, to determine temperature as a measure of the average kinetic energy of molecules, it makes sense to generalize the reasoning that we gave in defining the absolute temperature scale:

So, as we see, temperature is indeed a measure of the average kinetic energy of translational motion. The specific formulaic relationship was derived by the Austrian physicist Ludwig Boltzmann (Fig. 4):

Here is the so-called Boltzmann coefficient. This is a constant numerically equal to:

As we see, the dimension of this coefficient is , that is, it is a kind of conversion factor from the temperature scale to the energy scale, because we now understand that, in fact, we had to measure temperature in energy units.

Now let's look at how the pressure of an ideal gas depends on temperature. To do this, we write the basic MKT equation in the following form:

and substitute into this formula the expression for the relationship between the average kinetic energy and temperature. We get:

Rice. 4. Ludwig Boltzmann ()

In the next lesson we will formulate the equation of state of an ideal gas.

Bibliography

Myakishev G.Ya., Sinyakov A.Z. Molecular physics. Thermodynamics. - M.: Bustard, 2010.
Gendenshtein L.E., Dick Yu.I. Physics 10th grade. - M.: Ilexa, 2005.
Kasyanov V.A. Physics 10th grade. - M.: Bustard, 2010.

Great Encyclopedia of Oil and Gas ().
youtube.com().
E-science.ru ().

Homework

Page 66: No. 478-481. Physics. Problem book. 10-11 grades. Rymkevich A.P. - M.: Bustard, 2013. ()
How is the Celsius temperature scale determined?
Indicate the temperature range on the Kelvin scale for your city in summer and winter.
Air consists mainly of nitrogen and oxygen. The kinetic energy of which gas molecules is greater?
*How does the expansion of gases differ from the expansion of liquids and solids?

When the absolute temperature of an ideal gas decreases by 1.5 times, the average kinetic energy of thermal motion of molecules

1) will increase by 1.5 times

2) will decrease by 1.5 times

3) will decrease by 2.25 times

4) will not change

Solution.

When the absolute temperature decreases by 1.5 times, the average kinetic energy will also decrease by 1.5 times.

Correct answer: 2.

Answer: 2

When the absolute temperature of an ideal gas decreases by 4 times, the mean square speed of thermal motion of its molecules

1) will decrease by 16 times

2) will decrease by 2 times

3) will decrease by 4 times

4) will not change

Solution.

The absolute temperature of an ideal gas is proportional to the square of the mean square speed: Thus, when the absolute temperature decreases by 4 times, the mean square speed of its molecules will decrease by 2 times.

Correct answer: 2.

Vladimir Pokidov (Moscow) 21.05.2013 16:37

We were sent such a wonderful formula as E = 3/2kT. The average kinetic energy of the thermal motion of the molecules of an ideal gas is directly proportional to its temperature, as the temperature changes, so does the average kinetic energy of the thermal motion of the molecules.

Alexei

Good afternoon

That's right, in fact, temperature and average energy of thermal motion are one and the same. But in this problem we are asked about speed, not about energy

When the absolute temperature of an ideal gas increases by 2 times, the average kinetic energy of thermal motion of molecules

1) will not change

2) will increase 4 times

3) will decrease by 2 times

4) will increase by 2 times

Solution.

The average kinetic energy of thermal motion of molecules of an ideal gas is directly proportional to the absolute temperature, for example, for a monatomic gas:

When the absolute temperature increases by 2 times, the average kinetic energy will also increase by 2 times.

Correct answer: 4.

Answer: 4

When the absolute temperature of an ideal gas decreases by 2 times, the average kinetic energy of thermal motion of molecules

1) will not change

2) will decrease by 4 times

3) will decrease by 2 times

4) will increase by 2 times

Solution.

The average kinetic energy of thermal motion of molecules of an ideal gas is directly proportional to the absolute temperature:

When the absolute temperature decreases by 2 times, the average kinetic energy will also decrease by 2 times.

Correct answer: 3.

Answer: 3

When the root mean square speed of thermal motion of molecules increases by 2 times, the average kinetic energy of thermal motion of molecules

1) will not change

2) will increase 4 times

3) will decrease by 4 times

4) will increase by 2 times

Solution.

Consequently, an increase in the mean square speed of thermal motion by 2 times will lead to an increase in the average kinetic energy by 4 times.

Correct answer: 2.

Answer: 2

Alexey (St. Petersburg)

Good afternoon

Both formulas hold. The formula used in the solution (the first equality) is simply a mathematical notation for the definition of average kinetic energy: that you need to take all the molecules, calculate their kinetic energies, and then take the arithmetic mean. The second (identical) equality in this formula is just a definition of what the root mean square speed is.

Your formula is actually much more serious, it shows that average energy thermal motion can be used as a measure of temperature.

When the root mean square speed of thermal motion of molecules decreases by 2 times, the average kinetic energy of thermal motion of molecules

1) will not change

2) will increase 4 times

3) will decrease by 4 times

4) will increase by 2 times

Solution.

The average kinetic energy of thermal motion of molecules is proportional to the square of the root mean square speed of thermal motion of molecules:

Consequently, a decrease in the root mean square speed of thermal motion by 2 times will lead to a decrease in the average kinetic energy by 4 times.

Correct answer: 3.

Answer: 3

When the average kinetic energy of thermal motion of molecules increases by 4 times, their root mean square speed

1) will decrease by 4 times

2) will increase 4 times

3) will decrease by 2 times

4) will increase by 2 times

Solution.

Consequently, with an increase in the average kinetic energy of the thermal motion of molecules by 4 times, their root mean square speed will increase by 2 times.

Correct answer: 4.

Answer: 4

Alexey (St. Petersburg)

Good afternoon

A sign is an identical equality, that is, an equality that is always satisfied; in fact, when such a sign appears, this means that the quantities are equal by definition.

Yana Firsova (Gelendzhik) 25.05.2012 23:33

Yuri Shoitov (Kursk) 10.10.2012 10:00

Hello, Alexey!

There is an error in your solution that does not affect the answer. Why did you need to talk about the square of the average value of the velocity module in your solution? There is no such term in the assignment. Moreover, it is not at all equal to the root mean square value, but only proportional. Therefore your identity is false.

Yuri Shoitov (Kursk) 10.10.2012 22:00

Good evening, Alexey!

If this is so, what is the joke that you denote the same quantity differently in the same formula?! Perhaps to make it more scientific. Believe me, in our method of teaching physics, this “good” is enough without you.

Alexey (St. Petersburg)

I just can’t understand what’s bothering you. I have written that the square of the root mean square speed, by definition, is the average value of the square of the speed. B is simply part of the designation for root mean square speed, and b is the averaging procedure.

When the average kinetic energy of thermal motion of molecules decreases by 4 times, their root mean square speed

1) will decrease by 4 times

2) will increase 4 times

3) will decrease by 2 times

4) will increase by 2 times

Solution.

The average kinetic energy of thermal motion of molecules is proportional to the square of the root mean square velocity:

Consequently, when the average kinetic energy of the thermal motion of molecules decreases by 4 times, their root mean square speed will decrease by 2 times.

Correct answer: 3.

Answer: 3

When the absolute temperature of a monatomic ideal gas increases by 2 times, the mean square speed of thermal motion of molecules

1) will decrease by a factor

2) will increase by times

3) will decrease by 2 times

4) will increase by 2 times

Solution.

The absolute temperature of an ideal monatomic gas is proportional to the square of the root mean square speed of thermal motion of the molecules. Really:

Consequently, when the absolute temperature of an ideal gas increases by 2 times, the mean square speed of thermal motion of molecules will increase by a factor.

Correct answer: 2.

Answer: 2

When the absolute temperature of an ideal gas decreases by 2 times, the mean square speed of thermal motion of molecules

1) will decrease by a factor

2) will increase by times

3) will decrease by 2 times

4) will increase by 2 times

Solution.

The absolute temperature of an ideal gas is proportional to the square of the root mean square speed of thermal motion of molecules. Really:

Consequently, when the absolute temperature of an ideal gas decreases by 2 times, the mean square speed of thermal motion of molecules will decrease by a factor.

Correct answer: 1.

Answer: 1

Alexey (St. Petersburg)

Good afternoon

Do not be confused, the average value of the square of the speed is not equal to the square of the average speed, but to the square of the root mean square speed. average speed for a gas molecule is generally zero.

Yuri Shoitov (Kursk) 11.10.2012 10:07

You are the one who is confusing and not the guest.

In all school physics the letter v without an arrow indicates the velocity module. If there is a line above this letter, then this indicates the average value of the velocity modulus, which is calculated from the Maxwell distribution, and it is equal to 8RT/pi*mu. The square root of the mean square velocity is 3RT/pi*mu. As you can see, there is no equality in your identity.

Alexey (St. Petersburg)

Good afternoon

I don’t even know what to say, it’s probably a question of notation. In Myakishev’s textbook, the mean square speed is denoted this way; Sivukhin uses the notation. How are you used to denoting this value?

Igor (Who needs it, knows) 01.02.2013 16:15

Why did you calculate the temperature of an ideal gas using the kinetic energy formula? After all, the root mean square speed is found by the formula: http://reshuege.ru/formula/d5/d5e3acf50adcde572c26975a0d743de1.png = Root of (3kT/m0)

Alexey (St. Petersburg)

Good afternoon

If you look closely, you will see that your definition of root mean square speed is the same as that used in the solution.

By definition, the square of the mean square velocity is equal to the mean square of the velocity, and it is through the latter that the gas temperature is determined.

When the average kinetic energy of thermal motion of molecules decreases by 2 times, the absolute temperature

1) will not change

2) will increase 4 times

3) will decrease by 2 times

4) will increase by 2 times

Solution.

The average kinetic energy of thermal motion of molecules of an ideal gas is directly proportional to the absolute temperature:

Consequently, when the average kinetic energy of thermal motion decreases by 2 times, the absolute temperature of the gas will also decrease by 2 times.

Correct answer: 3.

Answer: 3

As a result of heating neon, the temperature of this gas increased 4 times. The average kinetic energy of the thermal motion of its molecules in this case

1) increased 4 times

2) increased by 2 times

3) decreased by 4 times

4) has not changed

Thus, when neon is heated 4 times, the average kinetic energy of the thermal motion of its molecules increases 4 times.

Correct answer: 1.