Boltzmann Constant

In thermodynamics, Boltzmann constant is the physical constant relating average kinetic energy of the gas particles and temperature of the gas represented by k or kB. The value of Boltzmann constant is measured using J/K or m2Kgs-2K-1. Which is mostly observed in Boltzmann’s entropy formula and Planck’s law of Black body radiation.

Value Of Boltzmann Constant

The values of Boltzmann constant is got by dividing gas constant R by Avogadro’s number NA. The value of k is

Boltzmann constant kB= 1.3806452 × 10-23J/K

Value Of k

The value of Boltzmann constant in eV is 8.6173303 × 10-5 eV/K

The value of Boltzmann constant can be expressed in various units. The table given below comprised of the value of k along with different units.

Value Of k

Units

1.3806452 × 10-23

m2.Kg.s-2.K-1

8.6173303 × 10-5

eV.K-1

1.38064852 × 10-16

erg.K-1

2.0836612(12)×1010

Hz.K-1

3.2976230(30)×10-24

cal.K-1

0.69503476(63)

cm-1.K-1

−228.5991678(40)

dB.WK-1.Hz-1

4.10

pN.nm

0.0083144621(75)

kJ.mol-1K-1

1.0

Atomic unit (u)

What is Boltzmann Constant?

The Boltzmann constant is introduced by Max Plank and named after Ludwig Boltzmann. It is a physical constant obtained by taking the ratio of two constants namely gas constant and Avogadro number.

Boltzmann constant Formula

The behaviour of the gases made to understand a step closer by Planck and Boltzmann by introducing constants. The value of Boltzmann constant is mathematically expressed as-

\(k=\frac{R}{N_{A}}\)

Where,

  • K is Boltzmann’s constant.
  • NA is Avogadro number.
  • R is the gas constant.

Applications

The Boltzmann Constant is used in diverse disciplines of physics. Some of them are listed below-

  • In classical statistical mechanics, Boltzmann Constant is used to express the equipartition of energy of an atom.
  • It is used to express Boltzmann factor.
  • It plays a major role in the statistical definition of entropy.
  • In semiconductor physics, it is used to express thermal voltage.

Hope you have understood what is Boltzmann constant. the value of Boltzmann constant or value of k or value of kb in different units along with the Boltzmann Constant formula and Application in physics.

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Practise This Question

A particle moves along a semicircle of radius 10 m in 5 seconds. The average velocity of the particle is 

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