The value of Boltzmann's constant. Boltzmann's constant plays a major role in static mechanics

Boltzmann constant (k (\displaystyle k) or k B (\displaystyle k_(\rm (B)))) - a physical constant that defines the relationship between temperature and energy. Named after the Austrian physicist Ludwig Boltzmann, who made major contributions to statistical physics, in which this constant plays a key role. Its value in the International System of Units SI according to changes in the definitions of basic SI units (2018) is exactly equal to

Relationship between temperature and energy

In a homogeneous ideal gas at absolute temperature T (\displaystyle T), the energy per each translational degree of freedom is equal, as follows from the Maxwell distribution, 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 a monatomic ideal gas, each atom has three degrees of freedom corresponding to three spatial axes, which means that each atom has an energy of 3 2 k T (\displaystyle (\frac (3)(2))kT).

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

Definition of entropy

The entropy of a thermodynamic system is defined as the natural logarithm of the number of different microstates Z (\displaystyle Z), corresponding to a given macroscopic state (for example, a state with a given total energy).

Proportionality factor k (\displaystyle k) and is Boltzmann's constant. This is an expression that defines the relationship between microscopic ( Z (\displaystyle Z)) and macroscopic states ( S (\displaystyle S)), expresses the central idea of ​​statistical mechanics.

Boltzmann constant (k (\displaystyle k) or k B (\displaystyle k_(\rm (B)))) - a physical constant that determines the relationship between temperature and energy. Named after the Austrian physicist Ludwig Boltzmann, who made major contributions to statistical physics, in which this constant plays a key role. Its experimental value in the International System of Units (SI) is:

The numbers in parentheses indicate the standard error in the last digits of the quantity value.

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Relationship between temperature and energy

In a homogeneous ideal gas at absolute temperature T (\displaystyle T), the energy per each translational degree of freedom is equal, as follows from the Maxwell distribution, 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 a monatomic ideal gas, each atom has three degrees of freedom corresponding to three spatial axes, which means that each atom has an energy of 3 2 k T (\displaystyle (\frac (3)(2))kT).

Knowing the thermal energy, we can calculate the root mean square velocity of the atoms, which is inversely proportional to the square root of the atomic mass. The root mean square velocity at room temperature varies from 1370 m/s for helium to 240 m/s for xenon. In the case of a molecular gas, the situation becomes more complicated, for example, a diatomic gas has five degrees of freedom (at low temperatures, when vibrations of atoms in the molecule are not excited).

Definition of entropy

The entropy of a thermodynamic system is defined as the natural logarithm of the number of different microstates Z (\displaystyle Z), corresponding to a given macroscopic state (for example, a state with a given total energy).

Proportionality factor k (\displaystyle k) and is Boltzmann's constant. This is an expression that defines the relationship between microscopic ( Z (\displaystyle Z)) and macroscopic states ( S (\displaystyle S)), expresses the central idea of ​​statistical mechanics.

Assumed value fixation

The XXIV General Conference on Weights and Measures, held on October 17-21, 2011, adopted a resolution in which, in particular, it was proposed that the future revision of the International System of Units should be carried out in such a way as to fix the value of the Boltzmann constant, after which it will be considered definite exactly. As a result, it will be executed exact equality k=1.380 6X⋅10 −23 J/K, where X stands for one or more significant figures, which will be determined further based on the most accurate CODATA recommendations. This alleged fixation is associated with the desire to redefine the unit of thermodynamic temperature kelvin, connecting its value with the value of Boltzmann's constant.

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Named after the Austrian physicist Ludwig Boltzmann, who made major contributions to statistical physics, in which this constant plays a key role. Its experimental value in the SI system is

The numbers in parentheses indicate the standard error in the last digits of the quantity value. In principle, Boltzmann's constant can be obtained from the definition of absolute temperature and other physical constants. However, calculating the Boltzmann constant using first principles is too complex and infeasible with the current state of knowledge. In the natural system of Planck units, the natural unit of temperature is given so that Boltzmann's constant is equal to unity.

Relationship between temperature and energy

In a homogeneous ideal gas at absolute temperature T, the energy per each translational degree of freedom is equal, as follows from the Maxwell distribution kT/ 2 . At room temperature (300 ) this energy is J, or 0.013 eV. In a monatomic ideal gas, each atom has three degrees of freedom corresponding to three spatial axes, which means that each atom has an energy of 3/2( kT) .

Knowing the thermal energy, we can calculate the root mean square velocity of the atoms, which is inversely proportional to the square root of the atomic mass. The root mean square velocity at room temperature varies from 1370 m/s for helium to 240 m/s for xenon. In the case of a molecular gas the situation becomes more complicated, for example a diatomic gas already has approximately five degrees of freedom.

Definition of entropy

The entropy of a thermodynamic system is defined as the natural logarithm of the number of different microstates Z, corresponding to a given macroscopic state (for example, a state with a given total energy).

Proportionality factor k and is Boltzmann's constant. This is an expression that defines the relationship between microscopic ( Z) and macroscopic states ( S), expresses the central idea of ​​statistical mechanics.

see also

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See what “Boltzmann constant” is in other dictionaries:

Physical constant k, equal to the ratio of the universal gas constant R to the Avogadro number NA: k = R/NA = 1.3807.10 23 J/K. Named after L. Boltzmann... Big Encyclopedic Dictionary

One of the fundamental physical constants; equal to the ratio of the gas constant R to the Avogadro constant NA, denoted by k; named after the Austrian physicist L. Boltzmann. The bp is included in a number of the most important relations of physics: in the equation... ... Physical encyclopedia

BOLZMANN CONSTANT- (k) universal physical. constant equal to the ratio of the universal gas (see) to the Avogadro constant NA: k = R/Na = (1.380658 ± 000012)∙10 23 J/K ... Big Polytechnic Encyclopedia

Physical constant k, equal to the ratio of the universal gas constant R to the Avogadro number NA: k = R/NA = 1.3807·10 23 J/K. Named after L. Boltzmann. * * * BOLZMANN’S CONSTANT BOLZMANN’S CONSTANT, physical constant k, equal to... ... encyclopedic Dictionary

Phys. constant k, equal to the ratio of the universal. gas constant R to the Avogadro number NA: k = R/NA = 1.3807 x 10 23 J/K. Named after L. Boltzmann... Natural science. encyclopedic Dictionary

One of the basic physical constants (See Physical constants), equal to the ratio of the universal gas constant R to the Avogadro number NA. (number of molecules in 1 mole or 1 kmol of a substance): k = R/NA. Named after L. Boltzmann. B. p.... ... Great Soviet Encyclopedia

Boltzmann constant ($k$ or $k\_(\backslash rm\; B)$) - a physical constant that defines the relationship between temperature and energy. Named after the Austrian physicist Ludwig Boltzmann, who made major contributions to statistical physics, in which this constant plays a key role. Its experimental value in the International System of Units (SI) is:

$k=1(,)380\backslash ,648\backslash ,52(79)\backslash times\; 10^(-23)$ J/.

The numbers in parentheses indicate the standard error in the last digits of the quantity value. In the natural system of Planck units, the natural unit of temperature is given so that Boltzmann's constant is equal to unity.

Relationship between temperature and energy

In a homogeneous ideal gas at absolute temperature $T$, the energy per each translational degree of freedom is equal, as follows from the Maxwell distribution, $kT/2$. At room temperature (300 ) this energy is $2(,)07\backslash times\; 10^(-21)$ J, or 0.013 eV. In a monatomic ideal gas, each atom has three degrees of freedom corresponding to three spatial axes, which means that each atom has an energy of $\backslash frac\; 3\; 2\; kT$.

Knowing the thermal energy, we can calculate the root mean square velocity of the atoms, which is inversely proportional to the square root of the atomic mass. The root mean square velocity at room temperature varies from 1370 m/s for helium to 240 m/s for xenon. In the case of a molecular gas, the situation becomes more complicated, for example, a diatomic gas has five degrees of freedom (at low temperatures, when vibrations of atoms in the molecule are not excited).

Definition of entropy

The entropy of a thermodynamic system is defined as the natural logarithm of the number of different microstates $Z$, corresponding to a given macroscopic state (for example, a state with a given total energy).

$S=k\backslash ln\; Z.$

Proportionality factor $k$ and is Boltzmann's constant. This is an expression that defines the relationship between microscopic ( $Z$) and macroscopic states ( $S$), expresses the central idea of ​​statistical mechanics.

Assumed value fixation

The XXIV General Conference on Weights and Measures, held on October 17-21, 2011, adopted a resolution in which, in particular, it was proposed that the future revision of the International System of Units should be carried out in such a way as to fix the value of the Boltzmann constant, after which it will be considered definite exactly. As a result, it will be executed exact equality k=1.380 6X 10 −23 J/K. This alleged fixation is associated with the desire to redefine the unit of thermodynamic temperature kelvin, connecting its value with the value of Boltzmann's constant.

see also

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An excerpt characterizing Boltzmann's Constant

- But what does this mean? – Natasha said thoughtfully.
- Oh, I don’t know how extraordinary all this is! - Sonya said, clutching her head.
A few minutes later, Prince Andrei called, and Natasha came in to see him; and Sonya, experiencing an emotion and tenderness she had rarely experienced, remained at the window, pondering the extraordinary nature of what had happened.
On this day there was an opportunity to send letters to the army, and the Countess wrote a letter to her son.
“Sonya,” said the Countess, raising her head from the letter as her niece walked past her. – Sonya, won’t you write to Nikolenka? - said the countess in a quiet, trembling voice, and in the look of her tired eyes, looking through glasses, Sonya read everything that the countess understood in these words. This look expressed pleading, fear of refusal, shame for having to ask, and readiness for irreconcilable hatred in case of refusal.
Sonya went up to the countess and, kneeling down, kissed her hand.
“I’ll write, maman,” she said.
Sonya was softened, excited and touched by everything that happened that day, especially by the mysterious performance of fortune-telling that she just saw. Now that she knew that on the occasion of the renewal of Natasha’s relationship with Prince Andrei, Nikolai could not marry Princess Marya, she joyfully felt the return of that mood of self-sacrifice in which she loved and was accustomed to living. And with tears in her eyes and with the joy of realizing a generous deed, she, interrupted several times by tears that clouded her velvety black eyes, wrote that touching letter, the receipt of which so amazed Nikolai.

At the guardhouse where Pierre was taken, the officer and soldiers who took him treated him with hostility, but at the same time with respect. One could still feel in their attitude towards him doubt about who he was (whether he was a very important person), and hostility due to their still fresh personal struggle with him.
But when, on the morning of another day, the shift came, Pierre felt that for the new guard - for the officers and soldiers - it no longer had the meaning that it had for those who took him. And indeed, in this big, fat man in a peasant’s caftan, the guards of the next day no longer saw that living man who so desperately fought with the marauder and with the escort soldiers and said a solemn phrase about saving the child, but saw only the seventeenth of those being held for some reason, by by order of the highest authorities, the captured Russians. If there was anything special about Pierre, it was only his timid, intently thoughtful appearance and the French language, in which, surprisingly for the French, he spoke well. Despite the fact that on the same day Pierre was connected with other suspected suspects, since the separate room he occupied was needed by an officer.
All the Russians kept with Pierre were people of the lowest rank. And all of them, recognizing Pierre as a master, shunned him, especially since he spoke French. Pierre heard with sadness the ridicule of himself.
The next evening, Pierre learned that all of these prisoners (and probably himself included) were to be tried for arson. On the third day, Pierre was taken with others to a house where a French general with a white mustache, two colonels and other Frenchmen with scarves on their hands were sitting. Pierre, along with others, was asked questions about who he was with the precision and certainty with which defendants are usually treated, supposedly exceeding human weaknesses. where he was? for what purpose? and so on.
These questions, leaving aside the essence of the life matter and excluding the possibility of revealing this essence, like all questions asked in courts, had the goal only of setting up the groove along which the judges wanted the defendant’s answers to flow and lead him to the desired goal, that is to the accusation. As soon as he began to say something that did not satisfy the purpose of the accusation, they took a groove, and the water could flow wherever it wanted. In addition, Pierre experienced the same thing that a defendant experiences in all courts: bewilderment as to why all these questions were asked of him. He felt that this trick of inserting a groove was used only out of condescension or, as it were, out of politeness. He knew that he was in the power of these people, that only power had brought him here, that only power gave them the right to demand answers to questions, that the only purpose of this meeting was to accuse him. And therefore, since there was power and there was a desire to accuse, there was no need for the trick of questions and trial. It was obvious that all answers had to lead to guilt. When asked what he was doing when they took him, Pierre answered with some tragedy that he was carrying a child to his parents, qu"il avait sauve des flammes [whom he saved from the flames]. - Why did he fight with the marauder? Pierre answered, that he was defending a woman, that protecting an insulted woman is the duty of every person, that... He was stopped: this did not go to the point. Why was he in the yard of the house on fire, where witnesses saw him? He answered that he was going to see what was happening in the building? Moscow. They stopped him again: they didn’t ask him where he was going, and why he was near the fire? They repeated the first question to him, to which he said he didn’t want to answer. Again he answered that he couldn’t say that. .