Derive the value for boltzman's constant
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Explanation:
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=RNA
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 expressing the equipartition of the 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.
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Answer:
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.[3] It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula. The Boltzmann constant has the dimension energy divided by temperature, the same as entropy.
As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven "defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly 1.380649×10−23 J/K.[4][5]
This definition allows the temperature unit (in SI system: the kelvin) to be redefined in terms of mechanical units of time, length and mass (in SI respectively the second, the metre and the kilogram). Before 2019, the value of Boltzmann constant was a measured quantity. Measurements of the Boltzmann constant depended on the definition of the kelvin in terms of the triple point of water. The measured values were used to determine the quantity that is used in the 2019 definition, to make the definition's value for the kelvin identical to the old value to within the limits of experimental accuracy at the time of the definition.