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The Boltzmann constant, denoted by k or kB, is a basic physical constant that relates the average kinetic energy and temperature of the gas particles.
- In the SI system, the value of the Boltzmann constant is 1.380649 x 10-23 joule per kelvin (JK-1).
- In the CGS system, the value of the Boltzmann constant is 1.380649 x 10-16 erg per kelvin.
- It has dimensions of energy per degree of temperature.
- The molar gas constant, R, is defined as the product of the Boltzmann constant (kB) and Avogadro's number.
- Temperature and energy are also related through the Boltzmann constant.
- It is an essential tool in thermodynamics and named after Ludwig Boltzmann (1844–1906), an Austrian scientist.
In this article, we will have a look at the value of the Boltzmann constant, its units, and its applications.
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Key Terms: Boltzmann constant, Avogadro's number, Quantum physics, Molar Gas, Kelvin, Thermodynamics, Kinetic energy, Gas molecule
Value of k (Boltzmann Constant)
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The value of the Boltzmann constant is given by
| Value of Boltzmann Constant (k or kB) = 1.3807 x 10-23 joules per kelvin (JK-1) |
This value is obtained by taking the ratio of the gas constant (R) to Avogadro’s constant (NA).
Value of Boltzmann Constant in eV
The value of the Boltzmann constant is electron-volt (eV) is given by
| Value of Boltzmann Constant in eV = 8.6173303 x 10-5 eV/K |
The Boltzmann constant can be represented in a variety of different units. The value of k along with different units are listed in the table below.
| Value Of k | Units |
|---|---|
| 1.3806452 × 10-23 | Kg m-2 s-2 K-1 |
| 8.6173303 × 10-5 | eV K-1 |
| 1.38064852 × 10-16 | erg K-1 |
| 0.0083144621(75) | kJ.mol-1K-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.
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What is the Boltzmann Constant?
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The Boltzmann constant (k or kB) is a fundamental physical constant that relates the average kinetic energy of the particles in an ideal gas to their absolute temperature., symbolized by k or kB.
- This constant is equal to the ratio of the gas constant to Avogadro’s constant.
- It was introduced by Max Plank and named after the Austrian scientist Ludwig Boltzmann (1844-1906).
Boltzmann Constant
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Applications of Boltzmann Constant
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There is no way to determine the state of each individual molecule in a large ensemble of objects, such as the billions of trillions of hot molecules propelling a piston in a steam engine (the dominant technology of Boltzmann's era) as they are moving at different velocities with a range of different energies. Boltzmann Constant is used in several branches of material science. Some of them are as listed below:
- In classical factual mechanics, the Boltzmann Constant is used to express the proportionality of a molecule's energy.
- Boltzmann factors are communicated using this constant.
- It plays an important role in the definition of entropy.
- Boltzmann Constant is used for transmitting warm voltage in semiconductor material research.
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Units of Boltzmann Constant
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Max Plank established the Boltzmann constant, which was named after Ludwig Boltzmann. It's a physical constant that's calculated by dividing two constants, the gas constant, and the Avogadro number.
Planck and Boltzmann introduced constants to bring the behavior of gases closer to our understanding. 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.
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.
Previous Year Questions
Sample Questions
Ques. In the relation, p =α/β e(-αz/kbθ) where p is the pressure, z is the distance, θ is the temperature, then the value of β is? (5 marks)
Ans. The dimension of P = [M1L-1T-2]
z = [L1]
Kb = [M1L2T-2K-1]
θ = [K1]
e-αz/kbθ is dimensionless
α = θKb/z = [M1L2T-2K-1][K1]/[L1] = [M1L1T-2K0]
Since p = α/β or β = α/p
So, we get the dimension of β as [M1L1T-2K0]/[M1L-1T-2]= [M0L2T0K0].
Ques. Find the relation between The Ideal Gas Constant and Boltzmann's Constant. (5 marks)
Ans. We will discover the value of R by developing the ideal gas equation and analyzing experimental findings for a range of gases. R may be represented in a variety of energy units, which is useful. Values that are frequently beneficial include
R = 8.314 Pa.m3K−1mol−1
= 8.314 J K−1 mol−1
= 0.08314 L bar K−1 mol−1
= 1.987 cal K−1 mol−1
= 0.08205 L atm K−1mol−1
The gas constant must also be given per molecule rather than per mole. We may divide any of the figures above by N to get R on a per-molecule basis because there is Avogadro's number of molecules per mole. This constant, however, is known by a different name: Boltzmann's constant, which is commonly denoted by the sign k.
k = R/N =1.381×10−23 J K−1 molecule−1
This indicates that the ideal gas equation may alternatively be written as PV = nRT = nNkT. We have N = nN since the number of molecules in the sample, N, is N= nN.
PV = NkT
Ques. What is the dimension of the Boltzmann constant? (1 mark)
Ans. The Boltzmann constant is dimensionally represented as [M1L2T-2K-1].
Ques. What is the purpose of the Boltzmann Constant? (3 Marks)
Ans. Temperature and energy are related by the Boltzmann constant (kB). It is a crucial tool in thermodynamics & the study of heat.
The Boltzmann Constant represents the distribution of energy in an atom. It's a representation of the Boltzmann factor. It has a significant influence on entropy's statistical definition. In semiconductor physics, it is used to represent thermal voltage.
Ques. What is the Boltzmann constant and what does it mean? (1 mark)
Ans. The Boltzmann constant connects temperature and energy (kB).
Ques. What is the method for calculating the Boltzmann Constant? (3 Marks)
Ans. The value of k is taken using the Clausius–Mossotti relation, to yield Boltzmann's constant at a certain temperature
The Boltzmann constant is best estimated using acoustic thermometry. It makes use of the fact that the speed of sound in a gas is directly proportional to the temperature of the gas. Dielectric steady gas thermometry (DCGT) is another important technique for determining how a gas reacts to changes in an electric field.
The final step is to calculate the dielectric constant. The dielectric constant is affected by temperature, therefore the Boltzmann constant may be calculated this way. Some optional approaches, such as Johnson Noise Thermometry, are also employed to quantify the Boltzmann constant estimation.
Ques. What is the value of the Boltzmann constant? (1 mark)
Ans. kB= 1.3806452 x 10-23J/K is the Boltzmann constant.
Ques. What is the value of the Boltzmann constant in eV? (1 mark)
Ans. The Boltzmann constant is 8.6173303 x 10-5 eV/K in eV.
Ques. What is the significance of the Boltzmann distribution? (2 Marks)
Ans. The Boltzmann distribution predicts the likelihood of a system being in a given state as a function of its energy, whereas the Maxwell-Boltzmann distributions predict particle speeds or energies in perfect gases.
The Boltzmann constant connects the usual active energy of an actual framework in equilibrium with its temperature at every degree of opportunity. The Boltzmann constant, for example, is a relationship between the normal dynamic energy of particles in a gas and the temperature of the gas.
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