Plan:

Introduction

• 1 Communication between temperature and energy
• 2 Determination of entropy
Notes

Introduction

Permanent Boltzmanna (k. or k. B) - a physical constant, determining the relationship between temperature and energy. Named in honor of the Austrian physics of Ludwig Boltzmann, who made a great contribution to statistical physics in which this constant plays a key role. Its experimental value in the SI system is equal

J / k.

The numbers in parentheses indicate the standard error in the latest values \u200b\u200bof the value of the value. The bolt holder can be obtained from the determination of absolute temperature and other physical constants. However, the calculation of the Boltzmann's constant with the help of basic principles is too difficult and impracticable at the current level of knowledge. In the natural system of plank units, the natural unit of temperature is set so that the boltzmann constant is equal to one.

Universal gas constant is defined as a work of a constant Boltzmann for the number of Avogadro, R. = k.N. A.. Gas constant is more convenient when the number of particles is set in moles.

1. Communication between temperature and energy

In a homogeneous ideal gas, located at absolute temperatures T. , Energy coming to each progressive degree of freedom is equal to, as follows from the distribution of Maxwell k.T. / 2. At room temperature (300 K), this energy is J, or 0.013 eV. In one-cattle ideal gas, each atom has three degrees of freedom, corresponding to three spatial axes, which means that every atom has energy in.

Knowing thermal energy, It is possible to calculate the root-mean-square speed of atoms, which is inversely proportional to the square nor of the atomic mass. The rms speed at room temperature varies from 1370 m / s for helium to 240 m / s for xenon. In the case of molecular gas, the situation is complicated, for example, the dioxide gas already has approximately five degrees of freedom.

2. Definition of entropy

The entropy of the thermodynamic system is defined as a natural logarithm from the number of various microstasses Z. corresponding to this macroscopic state (for example, a state with a given full energy).

S. = k.lN. Z..

Proportionality coefficient k. And there is a constant Boltzmann. This is an expression that determines the link between microscopic ( Z. ) and macroscopic states ( S. ), expresses the central idea of \u200b\u200bstatistical mechanics.

Notes

1. 1 2 3 http://physics.nist.gov/cuu/constants/Table / Caluscii.txt - physics.nist.gov/cuu/constants/table/ralscii.txt Fundamental Physical Constants - Complete Listing

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Permanent Boltzmanna ( K (\\ DisplayStyle K) or k b (\\ displaystyle k _ (\\ rm (b)))) - physical constant, determining the relationship between temperature and energy. Named in honor of the Austrian physics of Ludwig Boltzmann, who made a great contribution to statistical physics in which this constant plays a key role. Its value B. International System UN units according to the change in the definitions of the main units of SI (2018) exactly

k \u003d 1,380 649 × 10 - 23 (\\ displaystyle k \u003d 1 (,) 380 \\, 649 \\ TIMES 10 ^ (- 23)) J /.

Communication between temperature and energy

In a homogeneous ideal gas, located at absolute temperatures T (\\ DisplayStyle T), the energy coming to each progressive degree of freedom is equal to, as follows from the distribution of Maxwell, K T / 2 (\\ DisplayStyle KT / 2). At room temperature (300) this energy is 2, 07 × 10 - 21 (\\ DisplayStyle 2 (,) 07 \\ Times 10 ^ (- 21)) J, or 0.013 eV. In one-nuclear ideal gas, each atom has three degrees of freedom, corresponding to three spatial axes, which means that each atom has energy in 3 2 K T (\\ DisplayStyle (\\ FRAC (3) (2)) KT).

Knowing thermal energy, one can calculate the root-mean-square speed of atoms, which is inversely proportional to the square root of the atomic mass. The rms speed at room temperature varies from 1370 m / s for helium to 240 m / s for xenon. In the case of molecular gas, the situation is complicated, for example, the two-phase gas has 5 degrees of freedom - 3 translational and 2 rotational (at low temperatures, when the oscillations of atoms in the molecule are not excited and additional freedom degrees are added).

Determination of entropy

The entropy of the thermodynamic system is defined as a natural logarithm from the number of various microstasses Z (\\ displaystyle z)corresponding to this macroscopic state (for example, a state with a given full energy).

S \u003d k ln \u2061 z. (\\ displaystyle s \u003d k \\ ln z.)

Proportionality coefficient K (\\ DisplayStyle K) And there is a constant Boltzmann. This is an expression that determines the link between microscopic ( Z (\\ displaystyle z)) and macroscopic states ( S (\\ DisplayStyle S)), expresses the central idea of \u200b\u200bstatistical mechanics.

Physical meaning: Gas constanti am numerically equal to the work of expanding one mole of the perfect gas in the isobaric process with an increase in temperature by 1 to

In the GAS system, the gas constant is equal to:

Specific gas constant is:

In the formula, we used:

Universal gas constant (permanent Mendeleev)

Permanent Boltzmanna

Number of Avogadro

The Avogadro law - equal volumes of different gases at constant temperature and pressure contains the same number of molecules.

From the law, the Avogadro is displayed 2 of the investigations:

Corollary 1.: One mol of any gas under the same conditions occupies the same volume

In particular, under normal conditions (t \u003d 0 ° C (273K) and p \u003d 101.3 kPa), volume 1 praying gas is 22.4 liters. This volume is called the molar volume of the VM gas. Recalted this value to other temperatures and pressure can be using the Mendeleev-Klapairone equation

1) Charles Act:

2) Law Gay Loursak:

3) Parliament Mariotta:

Corollary 2.: The ratio of the masses of the same volumes of two gases is the value constant for these gases

This constant value is called the relative density of gases and is denoted by D. Since the molar volumes of all gases are the same (1st consequence of the Avogadro law), the ratio of molar masses of any pair of gases is also equal to this constant:

In the formula, we used:

Relative density of gas

Molar masses

Pressure

Molar volume

Universal gas constant

Absolute Temperature

The law of Boyl Mariotta - at a constant temperature and mass of the perfect gas, the product of its pressure and volume constantly.

This means that with an increase in pressure on gas, its volume is reduced, and vice versa. For constant amount of gas, the law of Boyle - Mariotta can also be interpreted as follows: at a constant temperature, the product of pressure on the volume is permanent. The law of Boyle - Mariott is carried out strictly for the ideal gas and is a consequence of the Clapairone's Mendeleev equation. For real gases, the law of Boyle - Mariotta is performed approximately. Almost all gases behave as ideal with not too high pressures and not too low temperatures.

To make it easier to understand Law of Boyl Marotta. Imagine that you comprehend an inflated balloon. Since the free space between air molecules is enough, you are without much difficulty, attaching some strength and having done a certain job, squeeze the ball by reducing the volume of gas inside it. This is one of the main differences in the liquid. In a ball with liquid water, for example, molecules are packed tight, as if the ball was filled with microscopic crushers. Therefore, water is not amenable to, in contrast to air, elastic compression.

There are also:

Charles Law:

Law Gay Louce:

In the law, we used:

Pressure in 1 vessel

Volume 1 vessel

2 vessel pressure

Volume 2 vessels

Law Gay Loursak - at constant pressure, the volume of constant gas mass is proportional to absolute temperature

Volume V of this mass of gas at constant gas pressure is directly proportional to temperature change

The Law of Gay-Loursak is valid only for ideal gases, real gases are subordinate to it at temperatures and pressures far from critical values. It is a special case of the Clayperon equation.

There are also:

Clapairone Mendeleeva equation:

Charles Law:

Law of Boyl Mariotta:

In the law, we used:

Volume in 1 vessel

Temperature in 1 vessel

Volume in 1 vessel

Temperature in 1 vessel

Primary volume of gas

Gas volume at temperature T

The thermal expansion coefficient of gases

The difference of initial and final temperatures

The law of Henry is a law on which, at a constant temperature, the solubility of gas in this fluid is directly proportional to the pressure of this gas above the solution. The law is suitable only for ideal solutions and low pressure.

The Henry Law describes the gas dissolution process in fluid. What is a liquid in which the gas is dissolved, we know on the example of carbonated drinks - non-alcoholic, low-alcohol, and on large holidays - champagne. In all these beverages, carbon dioxide was dissolved (the chemical formula CO2) - harmless gas used in the food industry due to its good solubility in water, and paradose after opening a bottle or can all these drinks for the reason that the dissolved gas begins to stand out from the liquid in The atmosphere, because after opening a sealed vessel, the pressure inside falls.

Actually, the law of Henry states a fairly simple fact: the higher the gas pressure above the surface of the fluid, the more difficult gas dissolved in it is released. And this is completely logical from the point of view of the molecular-kinetic theory, since the gas molecule to break free from the surface of the fluid, it is necessary to overcome the energy of collisions with gas molecules above the surface, and the higher the pressure and, as a result, the number of molecules in the cross-border area, It is more difficult to overcome this barrier to the dissolved molecule.

In the formula, we used:

Gas concentration in solution in shares praying

Coefficient Henry

Partial gas pressure over a solution

The law of radiation of Kirchhoff - the ratio of spontaneous and absorption capacity does not depend on the nature of the body, it is for all bodies of the same.

By definition, absolutely black body absorbs all the radiation falling on it, that is, for it (the absorption capacity of the body). Therefore, the function coincides with the emitting ability

In the formula, we used:

Empty body ability

The absorption capacity of the body

Kirchhoff function

Stefan-Boltzmann's law - the energy luminosity of absolutely black bodies is proportional to the fourth degree of absolute temperature.

It can be seen from the formula that with increasing temperature the luminosity of the body does not just increase - it increases to a much greater degree. Increase the temperature twice and luminosity will increase 16 times!

Heated bodies emit energy in the form of electromagnetic waves of various lengths. When we say that the body "rolled up hot" is that its temperature is high enough so that the thermal radiation occurs in the visible, the luminous part of the spectrum. At the atomic level, radiation becomes a consequence of the emission of photons with excited atoms.

To understand how this law is valid, imagine an atom, emitting light in the depths of the sun. The light is immediately absorbed by another atom, it is renewed again - and thus transmitted along the chain from the atom to the atom, so that the entire system is in a state energy equilibrium. In an equilibrium state, the light is strictly defined frequency is absorbed by one atom in one place simultaneously with the emission of the light of the same frequency by another atom elsewhere. As a result, the intensity of the light of each spectrum wavelength remains unchanged.

The temperature inside the sun drops as it deletes from its center. Therefore, as they move towards the surface, the spectrum of light radiation turns out to be appropriate more high temperaturesThan temperature environment. As a result, when re-radiation, according to the law of Stephen Boltzmannit will occur at lower energies and frequencies, but at the same time, due to the law of conservation of energy, will be abolished more photons. Thus, by the time they reach the surface, the spectral distribution will correspond to the temperature of the surface of the Sun (about 5,800 K), and not the temperature in the center of the Sun (about 15,000,000 k).

The energy that entered the surface of the Sun (or to the surface of any hot object) leaves it in the form of radiation. The law of Stefan-Boltzmann just tells us what is the emitted energy.

In the above wording the law of Stephen Boltzmann It applies only to an absolutely black body, absorbing everything that falls on its surface. Real physical bodies are absorbed only part of the radial energy, and the remaining part of them is reflected, but the pattern according to which the specific power of radiation from their surface is proportional to T in 4, as a rule, is also preserved in this case, but the Boltzmann constant in this case has to be replaced by another The coefficient that will reflect the properties of the real physical body. Such constants are usually determined by an experimental way.

In the formula, we used:

Energy luminosity of body

Permanent Stephen Boltzmanna

Absolute temperature

Charles Act - the pressure of this mass of the ideal gas at a constant volume is directly proportional to the absolute temperature.

To make it easier to understand charles law, imagine air inside aerial ball. At a constant temperature, the air in the ball will expand or compress, while the pressure produced by it molecules will not reach 101 325 of the pasteers and does not compare to atmospheric pressure. In other words, while on each blow of the air molecule from outside, directed inside the ball, there will be no similar blow to the air molecule, directed from the inside of the ball outside.

If you lower the air temperature in the ball (for example, putting it into a large refrigerator), the molecules inside the ball will move slowly, less vigorously driving from the inside about the ball wall. Outdoor air molecules will then put it stronger on the ball, squeezing it, as a result, the volume of gas inside the ball will decrease. This will occur until an increase in the gas density compensates for the temperature dropping temperature, and then the equilibrium will be established again.

There are also:

Clapairone Mendeleeva equation:

Law Gay Louce:

Law of Boyl Mariotta:

In the law, we used:

Pressure in 1 vessel

Temperature in 1 vessel

2 vessel pressure

Temperature in 2 vessel

The first law of thermodynamics is the change in the internal energy ΔU is not an isolated thermodynamic system equal to the difference between the amount of heat q, the transmitted system, and the work A of the external forces

Instead of work A, performed by external forces above the thermodynamic system, it is often more convenient to consider work a 'performed by the thermodynamic system over external bodies. Since these works are equal in the absolute value, but are opposed to the sign:

Then after such a conversion the first law of thermodynamics will look at:

The first law of thermodynamics - in a non-isolated thermodynamic system, the change in internal energy is equal to the difference between the resulting heat of the heat and the work A 'performed by this system

Speaking simple language the first law of thermodynamics Speaks about energy that cannot be created and disappeared into nowhere, it is transmitted from one system to another and turns from one form to another (mechanical in thermal).

An important consequence the first law of thermodynamics is that it is impossible to create a car (engine) that can perform useful work without energy consumption from the outside. Such a hypothetical machine was called the first kind of perpetual engine.

Bolzman Ludwig (1844-1906)- Great Austrian physicist, one of the founders of the molecular-kinetic theory. In the works of Boltzmann, the molecular-kinetic theory first appeared as a logically slim, consistent physical theory. Boltzmann gave a statistical interpretation of the Second Law of the Termodynamics. They are much done for the development and popularization of the Maxwell electromagnetic field theory. A wrestler by nature, Boltzmann passionately defended the need for molecular interpretation of thermal phenomena and accepted the basic burden of fighting scientists who denied the existence of molecules.

The relation of universal gas constant is included in equation (4.5.3) R. to Permanent Avogadro N. A. . This attitude is equally for all substances. It is called the Boltzmann's constant, in honor of L. Boltzmann, one of the founders of the molecular-kinetic theory.

Permanent Boltzmanna is equal to:

(4.5.4)

Equation (4.5.3), taking into account the Boltzmann constant, is written as follows:

(4.5.5)

The physical meaning of the constant Boltzmann

Historically, the temperature was first introduced as a thermodynamic value, and a unit of measurement was installed for it - degrees (see § 3.2). After establishing the temperature of the temperature with the average kinetic energy of the molecules, it became apparent that the temperature can be determined as the average kinetic energy of molecules and express it in Joules or Ergakh, that is, instead of the quantity T.enter value T *so that

The temperature defined in this way is associated with the temperature expressed in degrees, as follows:

Therefore, the Boltzmann constant can be considered as a value that binds the temperature expressed in energy units, with a temperature expressed in degrees.

The dependence of the gas pressure on the concentration of its molecules and temperature

Expressing E.from relation (4.5.5) and substituting in formula (4.4.10), we obtain an expression showing the dependence of the gas pressure from the concentration of molecules and temperature:

(4.5.6)

Formula (4.5.6) implies that with the same pressures and temperatures, the concentration of molecules in all gases is the same.

From here, the Avogadro law: in equal volumes of gases, at the same temperatures and pressures, contains the same number of molecules.

The average kinetic energy of the progressive movement of molecules is directly proportional to the absolute temperature. Proportionality coefficient- permanent Boltzmannak. \u003d 10 -23 j / k - need to remember.

§ 4.6. Distribution of Maxwell

In a large number of cases, knowledge of one average values \u200b\u200bof physical quantities is not enough. For example, the knowledge of the average growth of people does not allow planning the release of clothing of various sizes. It is necessary to know the approximate number of people whose growth lies at a certain interval. It is also important to know the number of molecules having speeds other than the average value. Maxwell first found how these numbers can be determined.

Probability of a random event

In §4.1, we have already mentioned that to describe the behavior of a large totality of Molecules J. Maxwell introduced the concept of probability.

As it was repeatedly emphasized, in principle it is impossible to trace the change in the speed (or impulse) of one molecule over a large time interval. It is also impossible to accurately determine the rates of all gas molecules at the moment. From macroscopic conditions in which gas is located (certain volume and temperature), do not flow with the need for certain values \u200b\u200bof molecules. The molecule speed can be considered as a random value, which in these macroscopic conditions can take different values, just as when throwing a playing dice can fall out any number of points from 1 to 6 (the number of bones is six). Predict which number of points will fall when a bone throwing is impossible. But the likelihood that falls, let's say, five points can be determined.

What is the probability of the occurrence of a random event? Let a very large number produced N.test (N. - number of bone casting). At the same time B. N." cases took place a favorable test of tests (i.e., the five loss). Then the likelihood of this event is equal to the ratio of the number of cases with a favorable outcome to the total number of tests, provided that this number is large:

(4.6.1)

For symmetric bone, the likelihood of any selected number of points from 1 to 6 is equal to.

We see that against the background of many random events, a certain quantitative pattern is detected, a number appears. This number is probability - allows you to calculate the average values. So, if you produce 300 bones, then the average number of false fallouts, as follows from formula (4.6.1), will be: 300 · \u003d 50, and absolutely indifferent, throwing 300 times the same bone or at the same time 300 identical bones .

There is no doubt that the behavior of gas molecules in the vessel is much more complicated by the motion of an abandoned playing bone. But here you can hope to detect certain quantitative patterns, allowing you to calculate the statistical averages, if only to put the task in the same way as in the theory of games, and not as in classical mechanics. It is necessary to abandon the unsolvable task of determining the exact value of the molecule rate at the moment and try to find the likelihood that the speed has a certain value.

Permanent Boltzmanna ( K (\\ DisplayStyle K) or k b (\\ displaystyle k _ (\\ rm (b)))) - physical constant, determining the relationship between temperature and energy. Named in honor of the Austrian physics of Ludwig Boltzmann, who made a great contribution to statistical physics in which this constant plays a key role. Its value in the international system of UN units according to the change in the definitions of the main units of SI (2018) is exactly equal

k \u003d 1,380 649 × 10 - 23 (\\ displaystyle k \u003d 1 (,) 380 \\, 649 \\ TIMES 10 ^ (- 23)) J /.

Communication between temperature and energy

In a homogeneous ideal gas, located at absolute temperatures T (\\ DisplayStyle T), the energy coming to each progressive degree of freedom is equal to, as follows from the distribution of Maxwell, K T / 2 (\\ DisplayStyle KT / 2). At room temperature (300) this energy is 2, 07 × 10 - 21 (\\ DisplayStyle 2 (,) 07 \\ Times 10 ^ (- 21)) J, or 0.013 eV. In one-nuclear ideal gas, each atom has three degrees of freedom, corresponding to three spatial axes, which means that each atom has energy in 3 2 K T (\\ DisplayStyle (\\ FRAC (3) (2)) KT).

Knowing thermal energy, one can calculate the root-mean-square speed of atoms, which is inversely proportional to the square root of the atomic mass. The rms speed at room temperature varies from 1370 m / s for helium to 240 m / s for xenon. In the case of molecular gas, the situation is complicated, for example, the two-phase gas has 5 degrees of freedom - 3 translational and 2 rotational (at low temperatures, when the oscillations of atoms in the molecule are not excited and additional freedom degrees are added).

Determination of entropy

The entropy of the thermodynamic system is defined as a natural logarithm from the number of various microstasses Z (\\ displaystyle z)corresponding to this macroscopic state (for example, a state with a given full energy).

S \u003d k ln \u2061 z. (\\ displaystyle s \u003d k \\ ln z.)

Proportionality coefficient K (\\ DisplayStyle K) And there is a constant Boltzmann. This is an expression that determines the link between microscopic ( Z (\\ displaystyle z)) and macroscopic states ( S (\\ DisplayStyle S)), expresses the central idea of \u200b\u200bstatistical mechanics.