[Physics Class Notes] on Value of Boltzmann Constant Pdf for Exam

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. 

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 

Where, 

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.