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Updated on 10th June, 2023 , 5 min read
The Boltzmann Constant is a fundamental physical constant that plays a critical role in statistical mechanics and thermodynamics. It is denoted by the symbol k and has a value of approximately 1.38 x 10^-23 J/K. In this article, we will discuss the value of Boltzmann Constant in detail and understand its significance in various scientific applications.
Boltzmann Constant is a proportionality constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. The constant is named after the Austrian physicist Ludwig Boltzmann, who first introduced the concept of entropy in statistical mechanics.
The Boltzmann Constant has several definitions, but the most commonly used definition is based on the ideal gas law. It can be defined as the ratio of the gas constant R to the Avogadro's number N. The mathematical representation of Boltzmann Constant is given as:
k = R/N
The SI unit of Boltzmann Constant is J/K (joules per Kelvin).
The Boltzmann constant, named after Ludwig Boltzmann, was established by Max Planck. It is a physical constant obtained by dividing two other constants, the Avogadro number and the gas constant. The purpose of introducing the Boltzmann constant was to make the behavior of gases more comprehensible.
The Boltzmann constant is represented mathematically as-
K = R/NA
Where,
The value of Boltzmann constant is critical in various fields of science, including statistical mechanics, thermodynamics, and quantum mechanics. Some of the significant applications of Boltzmann Constant are:
The Boltzmann constant, denoted as k, has a value of 1.3807 x 10^-23 joules per kelvin (JK^-1). In 2017, the most precise measurements of the constant were obtained using acoustic gas thermometry, which estimates the speed of sound of a monatomic gas in a triaxial ellipsoid container through microwave and acoustic resonances. This work, carried out by various laboratories using different methodologies, spanned a decade and played a significant role in the 2019 redefinition of SI base units.
The Boltzmann constant is a measure of energy per unit of temperature, expressed as JK^-1. Based on the data obtained from the acoustic gas thermometry measurements, the final fixed value of the Boltzmann constant for the International System of Units proposed by CODATA is 1.380649 x 10^-23 JK^-1.
Fundamentally, the Boltzmann constant is a fraction of the measure of energy, specifically heat, related to the random motions of the particles comprising a substance.
The Boltzmann constant is calculated by dividing the gas steady R by Avogadro's number NA. Boltzmann constant k or kB = 1.3806452 x 1023 J/K is the estimate of k or kB.
In eV, the Boltzmann constant is 8.6173303 x 10-5 eV/K.
The Boltzmann constant can be represented in a variety of different units. The value of k, as well as other units, are listed in the table below.
Value Of k |
Units |
1.3806452 × 10-23 |
m-2.Kg.s-2.K-1 |
8.6173303 × 10-5 |
eV.K-1 |
0.0083144621(75) |
kJ.mol-1K-1 |
1.38064852 × 10-16 |
erg.K-1 |
2.0836612(12) × 1010 |
Hz.K-1 |
3.2976230(30) × 10-24 |
calK-1 |
0.69503476(63) |
cm-1K-1 |
−228.5991678(40) |
dBWK-1Hz-1 |
4.10 |
pN.nm |
1.0 |
Atomic unit (u) |
The Boltzmann constant serves as a link between the microscopic energy E and the macroscopic temperature scale.
T = E/k
Setting k to unity, which results in temperature and energy numbers of the same kind, is a common practice in physics. Temperature is essentially measured in units of energy in this situation.
Unit |
Value of Boltzmann Constant |
J/K |
1.380649 x 10^-23 |
eV/K |
8.617333262 x 10^-5 |
cal/K |
3.297773 x 10^-24 |
erg/K |
1.380649 x 10^-16 |
The Boltzmann constant, denoted by the symbol k, has significant applications in various fields of science. Here are some of the key applications of the Boltzmann constant:
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