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Value of Boltzmann Constant

Last updated date: 17th Apr 2024
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Boltzmann Constant

The Boltzmann constant (kB or k) is the proportionality factor that relates the typical relative dynamic energy of particles in a gas with the thermodynamic temperature of the gas. It happens in the meanings of the kelvin and the gas steady and Planck's law of dark body radiation and Boltzmann's entropy recipe. The Boltzmann constant has measurements of energy separated by temperature, equivalent to entropy. It is named after the Austrian researcher Ludwig Boltzmann.

For instance, air particles at a room temperature of 25 degrees Celsius (300 kelvins, or 77 degrees Fahrenheit) are going at a normal speed of around 500 meters each second (1,100 mph). Be that as it may, some are moving at 223 m/s, some at 717 m/s, etc, and they are for the most part moving in various ways. Every individual property can't be known.

Applications of Boltzmann Constant (k)

The Boltzmann Constant is utilized in assorted orders of material science. Some of them are recorded beneath:

  • In traditional factual mechanics, Boltzmann Constant is accustomed to communicating the equipartition of the energy of a molecule. 

  • It is utilized to communicate Boltzmann factors. 

  • It assumes a significant part in the factual meaning of entropy. 

  • In semiconductor material science, it is utilized to communicate warm voltage.

Value of Boltzmann Constant

Having estimations of energy per level of temperature, the Boltzmann constant has an assessment of 1.380649 × 10⁻²³ joule per kelvin (K) or 1.380649 × 10⁻¹⁶ erg per kelvin.

The actual meaning of k is that it gives a proportion of the measure of energy (i.e., heat) relating to the irregular warm movements of the particles making up a substance. 

For a traditional framework at balance at temperature T, the normal energy per level of opportunity is kT/2. In the most straightforward illustration of a gas comprising of N noninteracting iotas, every molecule has three translational levels of opportunity (it can move in the x-, y-, or z-bearings), thus the complete nuclear power of the gas is 3NkT/2.

Boltzmann Constant Units

The conduct of the gases made comprehension a bit nearer by Planck and Boltzmann by presenting constants. The estimation of Boltzmann constant is numerically communicated as- 

K = RNA 


K is Boltzmann's constant. 

NA is Avogadro number. 

R is the gas constant.

Boltzmann Constant in eV

The estimation of Boltzmann constant in eV is 8.6173303 × 10⁻⁵ eV/K 

The estimation of the Boltzmann constant can be communicated in different units. The table given beneath involves the estimation of k alongside various units. 

Estimation 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

Value of Boltzmann Constant K

The estimations of the Boltzmann constant is obtained by separating gas steady R by Avogadro's number NA. The estimation of k or kB is 

Boltzmann constant k or kB = 1.3806452 × 10⁻²³ J/K. 

The estimation of the Boltzmann constant can be communicated in different units. The table given beneath included the estimation of k alongside various units. 

Estimation 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)

Boltzmann Factors and the Thermal Voltage

The likelihood of a framework in balance at a specific temperature to obtain a specific state with explicit energy is given by the comparing Boltzmann factor. At the point when we guess a warm framework at temperature T and attempt to compute the likelihood of possessing a state I with energy E. 

​To characterize the connection between the electrostatic potential and the progression of electric flow in a semiconductor across a P-N intersection. We need to utilize the Shockley diode condition. This condition relies upon a trademark voltage known as the warm voltage. This voltage is signified by the image VT. The reliance of the warm voltage on supreme temperature takes utilization of the Boltzmann constant. 

The estimation of the warm voltage at the standard temperature of 298.15K is roughly 25.69mV. The warm voltage gives the proportion of impacts on the spatial dispersion of particles or electrons because of a breaking point at a fixed voltage.

FAQs on Value of Boltzmann Constant

1. What is the Boltzmann Constant Used for?

Ans. The Boltzmann constant (kB) relates temperature to energy. It is a fundamental device in thermodynamics, the investigation of warmth and its relationship to different sorts of energy. It's named for Austrian physicist Ludwig Boltzmann (1844–1906), one of the pioneers of quantifiable mechanics. 

Quantifiable mechanics create old-style Newtonian mechanics to depict how the social occasion leads to huge collections of articles that emerge from the infinitesimal properties of each thing.

2. How is the Boltzmann Constant Estimated?

Ans. Acoustic thermometry gives the most exact estimation of the Boltzmann constant. It utilizes the way that the speed of sound in a gas is straightforwardly reliant on the temperature of the gas. Dielectric steady gas thermometry (DCGT) is additionally a main technique that quantifies the reaction of gas to change in an electric field. 

This is finished by estimating the dielectric constant. The dielectric constant relies upon the temperature and in this manner, the Boltzmann constant can be estimated. Some elective techniques like Johnson Noise Thermometry are likewise used to quantify the estimation of the Boltzmann constant. This technique gives esteem right to the vulnerability of 5 sections in 1,000,000.

3. What is K Boltzmann's Formula?

Ans. In the new SI framework, the estimation of the Boltzmann constant k is characterized as precisely k= 1.380 649.10⁻²³ J/K or k= 8.617 333 262.10⁻⁵ eV/K 

The Boltzmann constant relates the normal active energy for every level of opportunity of an actual framework in balance to its temperature. For instance, the Boltzmann constant relates the normal dynamic energy of particles in a gas with the temperature of the gas.

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