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
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.
FAQs on Value of Boltzmann Constant
1. What is the Boltzmann constant and what is its exact value?
The Boltzmann constant, denoted as kB or k, is a fundamental physical constant that relates the average kinetic energy of particles in a system with the system's thermodynamic temperature. As per the 2019 redefinition of SI base units, the value of the Boltzmann constant is now fixed at exactly 1.380649 × 10-23 J·K-1 (joules per kelvin).
2. What is the primary importance of the Boltzmann constant in Physics?
The primary importance of the Boltzmann constant is its role as a bridge between the microscopic and macroscopic worlds. It directly connects the properties of individual atoms and molecules (like kinetic energy) to the large-scale properties of matter that we can observe and measure (like temperature and pressure). This makes it a cornerstone of statistical mechanics and thermodynamics.
3. How is the value of the Boltzmann constant expressed in different common units?
The value of the Boltzmann constant can be expressed in various units depending on the physical context. The most common values are:
- In SI units (joules per kelvin): kB = 1.380649 × 10-23 J/K
- In electronvolts per kelvin (often used in semiconductor physics): kB ≈ 8.617333 × 10-5 eV/K
- In CGS units (ergs per kelvin): kB = 1.380649 × 10-16 erg/K
4. How does the Boltzmann constant (kB) relate to the Universal Gas Constant (R)?
The Boltzmann constant (kB) and the Universal Gas Constant (R) describe the same physical relationship but at different scales. The Universal Gas Constant relates energy to temperature for a mole of a substance, while the Boltzmann constant does so for a single particle. The direct relationship is given by the formula R = NA · kB, where NA is Avogadro's number.
5. What is the dimensional formula for the Boltzmann constant?
The dimensional formula for the Boltzmann constant (kB) is derived from its relationship with energy and temperature (Energy ∝ kB × Temperature). Since the dimension of energy is [ML2T-2] and the dimension of thermodynamic temperature is [K], the dimensional formula for kB is [Energy]/[Temperature]. Therefore, the dimensional formula is [ML2T-2K-1].
6. How is the Boltzmann constant used in the ideal gas equation?
The ideal gas equation has a microscopic form that uses the Boltzmann constant. While the common form is PV = nRT (where n is moles), the more fundamental version is PV = NkBT. In this equation, 'N' represents the total number of individual molecules. This form is powerful because it directly connects macroscopic properties like pressure (P) and volume (V) to the actual count of microscopic particles.
7. Why is the Boltzmann constant a more fundamental constant than the universal gas constant?
The Boltzmann constant is considered more fundamental because it deals with properties on a per-particle level, which is the most basic constituent of matter. The universal gas constant (R), in contrast, is a molar quantity, meaning it depends on the human-defined concept of a 'mole' (via Avogadro's number). Since R = NA · kB, the universal gas constant is essentially the Boltzmann constant scaled up for practical chemical calculations.
