Boltzmann Constant - Definition, Formula, Value, FAQs

The Boltzmann constant is a proportionality constant that is associated with the relative average kinetic energy of the particles present inside the gas with the gas’s thermodynamic temperature. It happens in the description of the gas constant and in Planck's ordinance of black-body radiation and formula of Boltzmann entropy and in the kelvin scale. It was the Austrian researcher Ludwig Boltzmann, who came up with this constant formula, and thus was given the name Boltzmann constant, consisting of dimensions similar to the entropy that is energy divided by the temperature.

The Boltzmann constant is one of the most well received seven defining constants which has applications in different mergers to describe the SI base units of the seven defining constants.

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History of the invention of the Boltzmann constant

The name Boltzmann constant is given the name after the Austrian researcher, Ludwig Boltzmann in the 19th century. Even though it was Ludwig first in the year 1877, who associated probability and entropy, in the black body radiation derivation initially in 19th century, however the association was not at all once indicated with a particular constant until Planck, invented the k and presented the most accurate value for it in the ordinance of the black body radiation derivation in the 19th century initially. Prior to the 19th century, calculations regarding the factors of Boltzmann were not put in writing applying the molecule per energy and the Boltzmann constant, instead applying a gas constant form, R and energy in macroscopy and quantities in macroscopy of the compound.

In the year 2017, the most precise calculations of the Boltzmann constant were acquired by gas thermometry which is acoustic, which represent the velocity of the volume of the monatomic gas in a chamber which is triaxial ellipsoid with applying resonances of acoustic and microwave. This time- consuming exertion was accepted with various experiments by many laboratories. It is one of the most well received cornerstones of the year 2019 SI base unit redefinition. Based upon the calculations, the CODATA endorsed 1.380 649 × 10^-23 J.K^-1 to be the concluding Boltzmann constant value to be applied for the international system of the units.
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Formula of Boltzmann constant/ Write kb formula.

On account of equation of ideal gas

PV=nRT

Where P stands for the pressure in the units of pascals

V stands for the volume in the units of meter cube

N stands for the number of moles of the gas present or given

R stands for the proportionality constant or the gas constant

T stands for the temperature in the unit of kelvin.

R=N/NA

Where NA represents Avogadro’s number and N is the number of molecules present

Numerical value of Avogadro’s number is 6.022×10²³ per mole molecules

The numerical value of R is 8.314 Joule/mole K.

Since the pressure, number of moles present and the volume are all quantities in macroscopy, but now we are considering the gas molecules which would be represented only in microscopic quantities.

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After rearranging the equation, we get

PV=N× K b× T

Where again P stands for pressure in the unit of pascals

V stands for the volume in the unit of meter cubes

N stands for the number of moles of gas present or given in consideration

And T stands for the temperature.

Since the values N×K b and n× R are equivalent

Equating both the sides of the equation we get

n× R= N× K b

K b = n/ N×R

Formula of Boltzmann constant: K b = 1 / Na ×R

Above equation gives the relationship between boltzmann constant and R.

Upon calculation of the above equation written, we get Boltzmann constant value

Kb = 1.3806452 × 10^-23 Joule per kelvin

SI units of Boltzmann constant is joule per kelvin

The equation written above concludes that the energy of the molecules of the gas is directly proportional to the absolute temperature.

Boltzmann constant in e V

Boltzmann constant is applied to represent the factor of Boltzmann, the idea of entropy in description of the idea of this constant as we are discussing the stochastic of the gas molecules upon the gas which is warmed.

Boltzmann constant in electron volt/boltzmann constant in ev

is equivalent to 0.000086173324 electron volts per kelvin.

The Boltzmann constant value in erg per kelvin

The Boltzmann constant value in K b in cgs units is given by 1.3806542×10^-16 erg per kelvin

Boltzmann constant applications

numerical methodology of both the quantum and classical branches of physics.

Boltzmann constant is interconnected link between microscopic and macroscopic branches of physics

For a classical system of temperature of equilibrium denoted by E, the average energy per degree of freedom is k ×E/ 2

The total thermal energy of the gas molecules present is given by 3× D ×E/2 = m×z²/2

Where z² stands for the average of the squared speed of the molecules of the gas present, and E stands for the absolute temperature in the unit of kelvin.

Thermodynamics of Clausius

Boltzmann proved that the numerical quantity is equivalent to the 2/3^rd of the Clausius entropy of thermodynamics of a molecule of ideal gas.

Boltzmann called the gamma as the permutability measure.

Constant of Planck.

Dividing the constant of Planck p by the 4.8 ×10^-34

K b = p/ 4.8×10^-11 = 6.62610^-11

We get the K b value as 1.38041×10^-23

We came to know that the irregularities of the entropy or the particles which directly interconnected to the molecule temperature inside the gas, which means higher the temperature the more will be the entropy.

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