Value of Boltzmann Constant Overview
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.
What is Boltzmann Constant?
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).
Keywords: Value of Boltzmann Constant, Boltzmann Constant, Physical Constants
Units of Boltzmann Constant
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,
- Boltzmann's constant is K.
- Avogadro's number is NA.
- The gas constant is R.
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Significance of Boltzmann Constant
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:
- Boltzmann Constant plays a crucial role in determining the distribution of particles in a gas. It helps in understanding the behavior of gases at different temperatures and pressures.
- The constant is used in the calculation of thermodynamic quantities such as entropy, enthalpy, and free energy.
- Boltzmann Constant is also used in the study of quantum mechanics, where it is used to define the energy of a single particle at absolute zero.
Value of Boltzmann Constant
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.
Boltzmann Constant in eV
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.
Common values of Boltzmann Constant in Different Units
|
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 |
Values of Boltzmann Constant: Application
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:
- Statistical Mechanics: One of the primary applications of the Boltzmann Constant is in statistical mechanics. It is used to calculate the average kinetic energy of particles in a gas at a given temperature. The constant plays a crucial role in determining the distribution of particles in a gas, which is essential for understanding the behavior of gases at different temperatures and pressures.
- Thermodynamics: The Boltzmann Constant is used extensively in the field of thermodynamics. It helps to calculate thermodynamic quantities such as entropy, enthalpy, and free energy. The constant is also used in the calculation of the heat capacity of substances, which is critical for understanding heat transfer and energy conversion processes.
- Quantum Mechanics:The Boltzmann Constant is also used in the study of quantum mechanics. It is used to define the energy of a single particle at absolute zero, which is known as the zero-point energy. The constant also plays a crucial role in calculating the partition function, which is used to describe the distribution of particles in a system in quantum mechanics.
- Astrophysics:The Boltzmann Constant is also essential in astrophysics. It is used to calculate the temperature of stars and galaxies, which is crucial for understanding the evolution and behavior of celestial bodies. The constant is also used to calculate the radiation emitted by stars, which is critical for studying the composition and structure of the universe.
- Electrical Engineering: The Boltzmann Constant is used in electrical engineering to calculate the noise level in electronic devices. The constant helps to determine the minimum detectable signal in electronic devices, which is essential for designing sensitive electronic circuits.
Value of Boltzmann Constant: Things to Remember
- The connection between absolute temperature and the kinetic energy contained in each molecule of an ideal gas is defined by Boltzmann's constant, often known as the Boltzmann constant, and symbolized by k or kB.
- The constant is named after Ludwig Boltzmann, an Austrian scientist who made significant contributions to the creation and foundation of statistical mechanics, a branch of theoretical physics, in the nineteenth century.
- Temperature and energy are related by the Boltzmann constant (kB).
- The Boltzmann Constant is used to describe the equipartition of an atom's energy in classical statistical mechanics. It's a symbol for the Boltzmann factor. It has a significant impact on the statistical definition of entropy.
- It is used to express thermal voltage in semiconductor physics.
- The Boltzmann constant establishes a relationship between wavelength and temperature (dividing hc/k by a wavelength yields a temperature), with one micrometer equaling 14387.777 K, as well as a relationship between voltage and temperature (multiplying the voltage by k in units of eV/K yields a temperature), with one volt equaling 11604.518 K. The numerical value of hc in eVm is the ratio of these two temperatures, 14387.777 K /11604.518 K = 1.239842 K.