What is Boltzmann constant

The Boltzmann constant (kB or k), named after its discoverer, Ludwig Boltzmann, is a physical constant that relates the average relative kinetic energy of particles in a gas with the temperature of the gas.


We can find it in the definitions of the kelvin ( which is the base unit of temperature) and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula. The kelvin is defined by fixing the numerical value of the Boltzmann constant k to 1.380 649×10−23 J⋅K−1. _________________

The Boltzmann constant

Boltzmann constant

is a physical constant relates the relative kinetic energy of particles in a gas with the temperature of the gas.
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Application

Used in Planks Constant

Describes density of electromagnetic radiation emitted by a black body thermal equilibrium at a temperature T.
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Gas Constant / Avogadro Number

Simple terms Boltzmann constant is Gas Constant devided by Avogadro Number. It's value is 1.38064852 × 10^-23 m² kg s^-2 K^{-1
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The mole (symbol: mol) is the unit of measurement for amount of substance. It is defined as exactly 6.02214076×10²³ constitutive particles, which may be atoms, molecules, ions, or electrons.

1 mole = 6.02214076×10²³  particles. = N/N_A where N = Number of molecules. and N_{A =} Avogadro Number.

The gas constant is also known as the molar, universal, or ideal gas constant, denoted by the symbol R or R and is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole, i.e. the pressure–volume product, rather than energy per temperature increment per particle.



gas constant =  energy per temperature increment per mole. mole = 6.02214076×10²³ particles.

boltzman constant =  energy per temperature increment per particles.



Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.



How we reach at Boltzmann constant

gas constant if divided by Avogadro number we will get the Boltzmann constant....


Boltzmann constant


so

Boltzman constant is GasConstant / Avogadro Number.



N_A x n = N


NA = Avogadro number
n = moles
N = Number of molecules




In Ideal Gas Law
PV = constant.
and it depends on

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