Boltzmann constant

Physical constant

Collection

zero Useful+1

zero

synonym Boltzmann constant (Boltzmann constant) Generally refers to Boltzmann constant

This entry is made by China Science and Technology Information Magazine Participate in editing and review Science Popularization China · Science Encyclopedia authentication.

Boltzmann constant（ k or k B ）It refers to the one related to temperature and energy Physical constant 。 Boltzmann He is an Austrian physicist who has made great contributions to the theory of statistical mechanics, and Boltzmann constant plays a very important role.

Thermodynamic unit Kelvin It is defined by Boltzmann constant.^[1]

Chinese name: Boltzmann constant
Foreign name: Boltzmann constant
Symbol: K or k B

Value: 1.380649 × 10^-23 J/K
Relevant reduced units: KT=0.025852 eV (when T=300K)
Discipline: Physics, Metrology^[1]

catalog

▪ Ideal gas temperature

brief introduction

Announce

edit

Boltzmann constant is a basic constant of thermodynamics, recorded as“ k ”, the value is: k =1.380649 × 10 -23 J/K， The Boltzmann constant can be derived as follows: Ideal gas constant R It's equal to Boltzmann's constant times Avogadro constant (i.e R = k · N A ）。

On November 16, 2018, the International Metrology Conference passed a resolution Kelvin It is defined as "corresponding Boltzmann constant is 1.380649 × 10 -23 J/K Thermodynamic temperature ”^[1] 。 The new definition will come into force on May 20, 2019^[1] 。

Physical meaning

Announce

edit

The physical meaning of Boltzmann constant is that the gas constant R is Boltzmann constant k times Avogadro constant N A 。

E k =(3/2) kT

Where E k Is the average translational kinetic energy of a single molecule, T by Thermodynamic temperature 。

Derivation process

Announce

edit

from Kinetic theory of gas From the point of view of, ideal gas is the simplest gas, and its microscopic model has three assumptions^[2] ：

1. The size of molecules is much smaller than the average distance between molecules. Molecules can be regarded as particles, and they comply with Newton's law of motion 。

2. Collisions between molecules or between molecules and vessel walls are completely elastic.

3. In addition to the instant of collision, the interaction force between molecules can be ignored, and the influence of gravity can also be ignored. So between two adjacent collisions, the molecule Uniform linear motion 。 In a collision, a single molecule affects the impulse ：

I=2m·vx

Vx is the velocity component in the x direction. The time of this collision is 2a/v x , so the number of collisions per unit time is v x ╱2a。

Therefore, the impulse of the molecule on the vessel wall in unit time is:

(2m·v x )(v x /2a)=m·v x ²/a.

And v x ²=v y ²=v z ²=(1/3) v ², so the pressure of all molecules in the container on the container wall per unit time

p=N×(1/3)m·v²/(a×b×c)= (1/3)N·m·v²/V，

Since molecular translational kinetic energy Ek=(1/2) m · v ²,

p=(1/3)N·m·v²/V=(2N/3V)E k 。 V is the volume. The formula is ideal gas Of pressure Formula.

and Ideal gas equation of state P=N/V × (R/N ') × T, where N is the molecular number and N' is Avogadro constant , R/N 'is defined as Boltzmann constant k, with P=NkT/V, namely: PV=nRT =nN'kT=NkT.

All the above v are the average velocity of particles, E k Is the average translational kinetic energy.

application

Announce

edit

Entropy function

Entropy can be defined as the logarithm of Boltzmann constant times the number of states of the system molecule:

S=k㏑Ω

This formula is the central concept of statistics. The greater the number of micro states corresponding to a macro state of the system, that is, the greater the degree of chaos, the greater the entropy of the state. Therefore, entropy is a physical quantity representing the disorder degree of system state.

Ideal gas constant

Ideal gas constant Equal to Boltzmann constant and Avogadro constant Product of:

R=kN

Ideal gas temperature

Ideal gas pressure The formula is p=(1/3) Nmv two /V=(2N/3V) Ek, V is the volume. and ideal gas Equation of state P=N/V * (R/N zero ）*T. Where N is the number of molecules and N 'is Avogadro constant , R/N 'is defined as Boltzmann constant k, so there is

P=（N/V)kT

So (1/3) Nmv two /V=（N/V)kT，（1/2)mv two =(3/2) kT, i.e

E k =(3/2)kT。

Considering that the motion of particles has three degrees of freedom (x, y, z), the kinetic energy of particles on a single degree of freedom is 1/3 of the total kinetic energy,

E kx =E ky =E kz =(1/2)kT，

You can see that:

① The temperature is completely determined by the average translational kinetic energy of gas molecules^[3] 。 In other words, the temperature measured at the macro level completely corresponds to the average translational kinetic energy of the molecular motion at the micro level, or the statistical expression of the average translational kinetic energy of a large number of molecules is the temperature (if only the translational motion of molecules is considered).

② If the temperature of the gas is known, the average square value of the translational velocity of the molecule at this temperature can be obtained in turn, and the square root of this average value is called Root mean square rate 。

Novice on the road

Growth task Getting Started with Editing Edit Rule Edit by myself

I have questions

Content query Online Service Official post bar Feedback

Complaints and suggestions

Report bad information Failed to appeal through entries Complaint of infringement information Blocking query and unblocking

Jinggong Network Anbei No. 1100000200001