Degree of Freedom, Learn its Definition, Types, Laws, & Uses

The term degree of freedom might sound complex, but it’s actually a simple concept used in physics, chemistry, and even statistics. It tells us how many independent ways something can move or change. For example, a moving object in space can go forward, backward, up, or down mechanical parts in physics, or analysing data in statistics, understanding degrees of freedom helps you solve problems more clearly. In this article, we’ll break down step by step, explain the types, share formulas, and show how it’s used in real life.

What is Degree of Freedom?

The Degree of Freedom simply means the number of interdependent ways a system or object can move, change, or behave. In even simpler words, it tells you many choices something has to move or vary without being restricted.

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For example: If you place a ball on the floor, it can roll forward, backward, left, right, and even jump up or down. That gives it three degrees of freedom, one for each direction.

Molecules can move and behave in different ways they can shift position, spin, or even stretch and compress. Each of these movements adds a different type of degree of freedom.Let’s look at the main ones below.

Translational Degree of Freedom

This type of degree is possessed by a gas molecule by absorbing the kinetic energy of translational motion. A gas molecule possesses kinetic energy of translational motion due to its linear motion. This type of parameter is possessed by monoatomic, diatomic and triatomic gases.

Rotational Degree of Freedom

This type of degree is possessed by a molecule by absorbing the kinetic energy of rotational motion. If the gas molecule is treated as a point mass (monoatomic gas molecule), then its moment of inertia is equal to zero. Hence, such a gas molecule cannot possess kinetic energy of rotational motion. Therefore, monoatomic gases do not have this physical parameter. However, for a diatomic gas molecule moment of inertia may not be equal to zero. Therefore, such a gas molecule can possess kinetic energy of rotational motion. Diatomic gases have a rotational degree.

Vibrational Degree of Freedom

This type of degree is possessed by a molecule by absorbing the kinetic energy of its vibrational motion. A gas molecule possesses kinetic energy of vibrational motion when it vibrates about its mean position. The vibrational motion gets excited only at very high temperatures (above 5000 K).

Laws of Degree of Freedom

Degrees of freedom don’t just describe motion, they follow some important scientific rules that help us understand how systems behave in physics, chemistry, and thermodynamics. Let’s look at the most important ones:

1. Law of Equipartition of Energy

This law says that each degree of freedom gets an equal share of energy exactly ½ kT of kinetic energy per molecule, where:

• Kkk is boltzmann’s constant
• TTT is the absolute temperature (in Kelvin)

Example: A monoatomic gas (like helium) has 3 translational degrees, so its energy is:

E=\frac{3}{2} k T

Gibbs Phase Rule 

This rule helps determine the number of degrees of freedom (F) in a system with C components and P phases:

F=C-P+2

Example: For water in equilibrium (liquid + vapor),

Components(C) = 1

Phases (P) = 2

F=1-2+2=1

This means we can change only one condition (like temperature or pressure) independently.

C. Constraints in Mechanics

Constraints reduce the degree of freedom. For example, a box sliding on a table can’t move up or down in only 2 directions. So instead of 3, it has just 2 translational DoF.

Uses of Degree of Freedom

Using the equipartition theorem helps us in determining the values of various thermodynamic variables. In physics, this parameter completely describes the molecule’s state.

So, this was all about this parameter. We are hopeful that you understood all the concepts of this topic without any difficulty. For similar Chemistry topics, go to the Google play store and download the Testbook App. It is a great app that provides all the necessary study resources, which include sample papers, mock tests, revision notes, previous year question papers, and much more. So, do not waste any more time and download the Testbook app now!

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