Boltzmann constant for air. The Boltzmann constant plays a major role in static mechanics
Among the fundamental constants is the Boltzmann constant k takes special place. Back in 1899, M. Planck proposed the following four numerical constants as fundamental for building a unified physics: the speed of light c, action quantum h, the gravitational constant G and the Boltzmann constant k. Among these constants, k occupies a special place. It does not define elementary physical processes and is not included in the basic principles of dynamics, but establishes a connection between microscopic dynamic phenomena and macroscopic characteristics of the state of particles. It is also included in the fundamental law of nature, which relates the entropy of the system S with the thermodynamic probability of its state W:
S=klnW (Boltzmann formula)
and determining the direction of physical processes in nature. Special attention It should be noted that the appearance of the Boltzmann constant in one or another formula of classical physics every time quite clearly indicates the statistical nature of the phenomenon described by it. Understanding the physical essence of the Boltzmann constant requires the opening of huge layers of physics - statistics and thermodynamics, the theory of evolution and cosmogony.
Research by L. Boltzmann
Beginning in 1866, the works of the Austrian theoretician L. Boltzmann were published one after another. In them, statistical theory receives such a solid justification that it turns into a true science of physical properties collectives of particles.
The distribution was obtained by Maxwell for the simplest case of a monatomic ideal gas. In 1868, Boltzmann shows that polyatomic gases in equilibrium will also be described by the Maxwell distribution.
Boltzmann develops in the works of Clausius the idea that gas molecules cannot be considered as separate material points. Polyatomic molecules also have rotation of the molecule as a whole and vibrations of its constituent atoms. He introduces the number of degrees of freedom of molecules as the number of "variables required to determine the position of all the constituent parts of the molecule in space and their position relative to each other" and shows that from the experimental data on the heat capacity of gases follows a uniform distribution of energy between different degrees of freedom. Each degree of freedom has the same energy
Boltzmann directly connected the characteristics of the microcosm with the characteristics of the macrocosm. Here is the key formula that establishes this ratio:
1/2 mv2 = kT
where m and v- respectively, the mass and average speed movement of gas molecules T is the gas temperature (on the absolute Kelvin scale), and k is the Boltzmann constant. This equation bridges the two worlds by linking atomic level properties (on the left side) with bulk properties (on the right side) that can be measured with human instruments, in this case thermometers. This connection is provided by the Boltzmann constant k, equal to 1.38 x 10-23 J/K.
Finishing the conversation about the Boltzmann constant, I would like to emphasize once again its fundamental importance in science. It contains huge layers of physics - atomistics and molecular-kinetic theory of the structure of matter, statistical theory and the essence of thermal processes. The study of the irreversibility of thermal processes revealed the nature of physical evolution, concentrated in the Boltzmann formula S=klnW. It should be emphasized that the position according to which a closed system will sooner or later come to a state of thermodynamic equilibrium is valid only for isolated systems and systems that are in stationary external conditions. In our Universe, processes are continuously taking place, the result of which is a change in its spatial properties. The non-stationarity of the Universe inevitably leads to the absence of statistical equilibrium in it.
Boltzmann's constant (k (\displaystyle k) or k B (\displaystyle k_(\rm (B)))) is 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 value in the International System of Units SI according to the change in the definitions of the basic SI units (2018) is exactly equal to
k = 1.380 649 × 10 − 23 (\displaystyle k=1(,)380\,649\times 10^(-23)) J / .Relationship between temperature and energy
In a homogeneous ideal gas at absolute temperature T (\displaystyle T), the energy per translational degree of freedom , is, as follows from the Maxwell distribution, kT / 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 energy in 3 2 k T (\displaystyle (\frac (3)(2))kT).
Knowing the thermal energy, one can calculate the rms atomic velocity, which is inversely proportional to square root 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 a 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).
S = k log Z . (\displaystyle S=k\ln Z.)Aspect ratio k (\displaystyle k) and is the Boltzmann 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.
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The Defining 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:
J / .The numbers in parentheses indicate the standard error in the last digits of the value. Boltzmann constant can be obtained from the definition absolute temperature and other physical constants. However, the calculation of the Boltzmann constant using basic principles is too complicated and impossible with the current level of knowledge. In Planck's natural system of units, the natural unit of temperature is given in such a way that the Boltzmann constant is equal to one.
Relationship between temperature and energy
In a homogeneous ideal gas at absolute temperature , the energy per translational degree of freedom is, as follows from the Maxwell distribution, . 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 energy in .
Knowing the thermal energy, one can calculate the root-mean-square atomic velocity, 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 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 corresponding to a given macroscopic state (for example, a state with a given total energy).
The coefficient of proportionality is the Boltzmann constant. This expression defining the relation between microscopic () and macroscopic states () expresses the central idea of statistical mechanics.
see also
Notes (edit)
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See what the "Boltzmann constant" is in other dictionaries:
- (denotation k), the ratio of the universal GAS constant to the AVOGADRO NUMBER, equal to 1.381.10 23 joules per degree Kelvin. It indicates the relationship between the kinetic energy of a gas particle (atom or molecule) and its absolute temperature. Scientific and technical encyclopedic dictionary
Boltzmann's constant- - [A.S. Goldberg. The English Russian Energy Dictionary. 2006] Topics energy in general EN Boltzmann constant … Technical Translator's Handbook
Boltzmann constant- Boltzmann Constant Boltzmann constant A physical constant that defines the relationship between temperature and energy. Named after the Austrian physicist Ludwig Boltzmann, who made a great contribution to statistical physics, in which this constant ... Explanatory English-Russian dictionary on nanotechnology. - M.
Boltzmann's constant- Bolcmano konstanta statusas T sritis fizika atitikmenys: engl. Boltzmann constant vok. Boltzmann Konstante, f; Boltzmannsche Konstante, f rus. Boltzmann's constant, f pranc. constante de Boltzmann, f … Fizikos terminų žodynas
The relation S k lnW between the entropy S and the thermodynamic probability W (k is Boltzmann's constant). The Boltzmann principle is based on the statistical interpretation of the second law of thermodynamics: natural processes tend to translate the thermodynamic ... ...
- (Maxwell Boltzmann distribution) equilibrium energy distribution of ideal gas particles (E) in an external force field (eg, in a gravitational field); is determined by the distribution function f e E/kT, where E is the sum of the kinetic and potential energies … Big Encyclopedic Dictionary
Not to be confused with the Boltzmann constant. Stefan Boltzmann's constant (also Stefan's constant), a physical constant that is a constant of proportionality in Stefan Boltzmann's law: total energy radiated per unit area ... Wikipedia
Constant value Unit 1.380 6504(24)×10−23 J K−1 8.617 343(15)×10−5 eV K−1 1.3807×10−16 erg K−1 Boltzmann constant (k or kb) a physical constant that defines the relationship between temperature and energy. Named after the Austrian ... ... Wikipedia
Statistically equilibrium distribution function in terms of momenta and coordinates of particles of an ideal gas, molecules to which obey the classical. mechanics, in an external potential field: Here is the Boltzmann constant (universal constant), absolute ... ... Encyclopedia of mathematics
Books
- Universe and physics without "dark energy" (discoveries, ideas, hypotheses). In 2 volumes. Volume 1, O. G. Smirnov. The books are devoted to the problems of physics and astronomy that have existed in science for decades and hundreds of years from G. Galileo, I. Newton, A. Einstein to the present day. The smallest particles of matter and planets, stars and ...
The numbers in parentheses indicate the standard error in the last digits of the value. In principle, the Boltzmann constant can be obtained from the definition of absolute temperature and other physical constants(for this you need to be able to calculate from first principles the temperature of the triple point of water). But the definition of the Boltzmann constant using the basic principles is too complicated and unrealistic for modern development knowledge in this area.
Boltzmann's constant is an unnecessary physical constant if the temperature is measured in energy units, which is very often done in physics. It is, in fact, a connection between a well-defined quantity - energy and a degree, the value of which has developed historically.
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, states with a given total energy).
Aspect ratio k and is the Boltzmann constant. This expression, which defines the relationship between microscopic (Z) and macroscopic (S) characteristics, expresses the main (central) idea of statistical mechanics.
