Boltzmann constant

The Boltzmann constant is an extremely important proportionality factor. It appears in Planck’s law of black-body radiation as well as Boltzmann’s entropy formula. It is also used to determine the kelvin temperature and the gas constant. The Boltzmann constant is defined as the proportionality constant that illustrates the relationship between a gas’s thermodynamic temperature and its average relative kinetic energy. The Boltzmann constant has the same unit as entropy, which is energy divided by temperature.

What is the Boltzmann constant?

The Boltzmann constant (k) is a basic physical constant that appears in practically every statistical formulation of both classical and quantum physics. The constant is named after Ludwig Boltzmann, an Austrian scientist who made significant contributions to the establishment and development of statistical mechanics, a field of theoretical physics. The Boltzmann constant, which has dimensions of energy per degree of temperature, has a specified value of 1.380649 × 10−23 joule per kelvin (K), or 1.380649 × 10−16 erg per kelvin. The molar gas constant R is defined as the product of Avogadro’s number and the Boltzmann constant. 

Boltzmann Constant in Ideal Gas Equation

Amadeo Avogadro (1776–1856) observed that one mole of any gas has the same number of molecules at normal pressure and temperature. N = 6.02 × 10 23 molecules/mole is the value known as Avogadro’s number. The ideal gas law is stated in terms of Avogadro’s number as PV = NkT, where k, known as the Boltzmann’s constant, has the value 1.38 × 10 23 J/K. At standard temperature and pressure (STP), one mole of any gas occupies a standard volume of 22.4 litres.

The kinetic theory of gases describes a gas as a collection of molecules in continuous motion that collide elastically according to Newtonian law.

The pressure on the wall (P) may be calculated using Newtonian mechanics and the average kinetic energy of the gas molecules:

P=23(NV)(12m0vavg2)

After the results, it is concluded that, The pressure is proportional to the number of molecules per unit volume (N/V) and the average linear kinetic energy of the molecules.  The correlation between temperature and average linear kinetic energy can be established using this formula and the ideal gas law:

32kT=12m0vavg2

Where k is again Boltzmann’s constant; hence, the average kinetic energy of gas molecules is exactly proportional to the gas’s temperature in degrees Kelvin.

Temperature is a direct measure of an ideal gas’s average molecular kinetic energy.

Formula

Planck and Boltzmann brought the behaviour of gases one step closer to understanding by establishing constants. The Boltzmann constant’s value can be stated mathematically as-

K=RNA

Where,

Boltzmann’s constant is denoted by K.

NA stands for Avogadro’s number.

R denotes the gas constant.

The Dimensional Formula for the Boltzmann Constant is given by:

[M1 L2 T-2 K-1]

Boltzmann Constant Applications

There is no possible to identify the state of each individual molecule in a huge ensemble of things, such as the billions of trillions of heated molecules powering a piston in a steam engine (the dominating technology of Boltzmann’s age), because they move at various speeds and have varying energies. The Boltzmann Constant is employed in many areas of material science. Some of them are as follows:

• The Boltzmann Constant is used in classical physical mechanics to represent the proportionality of a molecule’s energy.
• This constant is used to transmit Boltzmann factors.
• It is essential in the definition of entropy.
• In semiconductor material research, the Boltzmann Constant is employed to convey heated voltage.

Boltzmann’s Constant Value

The value of Boltzmann’s constant is 1.3807 x 10-23 joules per kelvin (JK-1)

The most exact measurements of the Boltzmann constant were made in 2017 using acoustic gas thermometry, which estimates the speed of sound of a monatomic gas in a triaxial ellipsoid container using microwave and acoustic resonances. This decade-long effort was carried out by several laboratories using varied approaches, and it is one of the components of the 2019 SI base unit redefinition.

The Boltzmann constant is defined as energy per unit of temperature.

Based on these findings, CODATA suggested 1.380649 x 1023 JK1 as the final fixed value of the Boltzmann constant for the International System of Units.

The true definition of k is a fraction of the measure of energy (i.e., heat) that is connected to the irregular heated movements of the particles that comprise a material.

Boltzmann Constant in electronvolts

Divide the gas steady R by Avogadro’s number NA to get the Boltzmann constant. The Boltzmann constant k or kB is estimated to be 1.3806452 x 1023 J/K.

The Boltzmann constant in eV is 8.6173303 x 10-5 eV/K.

Conclusion 

The Boltzmann constant is defined as the proportionality constant that illustrates the relationship between a gas’s thermodynamic temperature and its average relative kinetic energy. The Boltzmann constant has the same unit as entropy, which is energy divided by temperature. The Boltzmann constant, which has dimensions of energy per degree of temperature, has a specified value of 1. The Boltzmann Constant is used in classical physical mechanics to represent the proportionality of a molecule’s energy. The Boltzmann constant is defined as energy per unit of temperature.