Dimensional Formula of Boltzmann Constant (original) (raw)
Last Updated : 23 Jul, 2025
**Dimensional Formula of the Boltzmann constant is [M 1 L 2 T -2 K -1 ]. As we know, a dimensional formula is a way of representing a physical quantity in terms of its dimensions.
Boltzmann constant is a physical constant of great significance in physics, especially when discussing the Kinetic Theory of gases. Now let's learn about the Boltzmann constant and its dimensional formula.
Table of Content
- What is Boltzmann Constant?
- What is Dimensional Formula of Boltzmann Constant?
- Importance of Dimensional Formula
- Boltzmann Constant Dimensions: FAQs
What is Boltzmann Constant?
Boltzmann Constant is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. It is named after the Austrian physicist Ludwig Boltzmann, who made significant contributions to the field of statistical mechanics.
In simple terms, Boltzmann Constant can be defined as the ratio of the other two constants, these constants being the gas constant and the Avogadro Number.
**Read More about **Stephen-Boltzmann Law
Boltzmann Constant Formula
Boltzmann constant (k) is defined as the ratio of gas constant (R) to Avogadro's number (NA) and mathematically can be written as:
k = R/NA
Where,
- **k is the Boltzmann constant.
- **R is the gas constant, which is the product of the Boltzmann constant and Avogadro's number.
- **N A is Avogadro's number, the number of atoms, ions, or molecules in one mole of a substance. [NA = 6.022×1023mol−1]
Unit Of Boltzmann Constant
The unit of the Boltzmann constant (k) depends on the units used for other thermodynamic quantities in the formula. The most common unit for the Boltzmann constant is joules per kelvin (J/K).
Other than J/K, eV/K, and m2Kg.s-2/K are also other units of Boltzmann Constant.
**Note: Value of Boltzmann constant is **8.6173303 × 10 -5 **eV/K or 1.380649 × 10 -12 J/K.
What is Dimensional Formula of Boltzmann Constant?
**Dimensional Formula of Boltzmann constant is [M 1 L 2 T -2 K -1 ]
Derivation of Dimensional Formula of Boltzmann constant
We derive a dimensional formula of Boltzmann constant. For this we already need to know the dimensions of Avogadro number and gas constant
As, Boltzmann Constant = Gas Constant(R)/Avogadro Number(NA)
Thus, Dimensional formula of k = dimensional formula of (R/NA) . . . (1)
Now we calculate the dimensional formula of each quantity individually
Dimensional formula of R= [M1L2T-2K-1] From(PV=nRT)
Dimensional formula of NA= [M0L0T0] (It is 1/mol)
Putting all the above three-dimensional formulas in Equation (1) we get
Dimensional Formula of k = [M1L2T-2K-1] / [M0L0N0]
⇒ Dimensional Formula of k = [M1L2K-1T-2]
**Hence, the dimensional formula of Charge is [ML 2 T -2 K -1 ]
Importance of Dimensional Formula
There are various advantages of representing a physical quantity through its dimensional formula:
- Dimensional Formula can be used to check the consistency of a dimensional equation.
- It can be used to derive the relation between physical quantities in physical phenomena.
Like in Equation **v = u + at
- Dimensional Formula can be used to change units from one system to another conveniently.
- It can be used to find the dimension of constants in a given relation.
Conclusion
The Boltzmann constant (k or kB) relates the average kinetic energy of particles in a gas with the temperature of the gas. The Boltzmann constant has the dimensional formula of [ML 2 T -2 K -1 ] or [ML 2 T -2 θ -1 ] and its unit is J/K (Joules per Kelvin).
**Read More,