Dimensional Formula of Boltzmann Constant

Dimensional Formula of the Boltzmann constant is [M¹L²T^-2K^-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.

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 (N_A) and mathematically can be written as:

k = R/N_A

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. [N_A = 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^-12J/K.

What is Dimensional Formula of Boltzmann Constant?

Dimensional Formula of Boltzmann constant is [M¹L²T^-2K^-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(N_A)

Thus, Dimensional formula of k = dimensional formula of (R/N_A) . . . (1)

Now we calculate the dimensional formula of each quantity individually

Dimensional formula of R= [M¹L²T^-2K^-1] From(PV=nRT)

Dimensional formula of N_A= [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 [ML²T^-2K^-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 k_B) relates the average kinetic energy of particles in a gas with the temperature of the gas. The Boltzmann constant has the dimensional formula of [ML²T^-2K^-1] or [ML²T^-2θ^-1] and its unit is J/K (Joules per Kelvin).

Read More,

• Dimensional Formulas in Units and Measurements
• Stefan Boltzmann Law
• Maxwell-Boltzmann Distribution
• Heat Transfer Formulas

Boltzmann Constant Dimensions: FAQs

1. What is Dimensional Formula?

Dimensional Formula is a representation of any quantity in terms of 7 fundamental quantities.

2. How is Boltzmann Constant Represented?

Boltzmann constant is represented as k.

3. What is value of Boltzmann Constant?

The value of Boltzmann Constant (k) is 8.6173303 × 10^-5 eV/K.

4. What is the SI Unit of Boltzmann Constant?

We can derive the SI units of Boltzmann constant from its dimensional formula. The dimensional formula of constant is Joule/Kelvin

5. What is Boltzmann Constant?

Boltzmann constant is a physical constant of great significance used when dealing with kinetic nature of gases.