EQUIPARTITION OF ENERGY

• In a three-dimensional space, an atom can move around easily, but it needs energy to do so. This energy comes from the force that moves basic particles.
• When an atom or molecule moves in different ways, such as translationally, vibrationally, or rotationally, it gets different amounts of energy. This is called equipartition energy or the equipartition theory.
• But first, we need to understand what "degree of freedom" (d.o.f.) means in order to understand what "equipartition of energy" means.

Degree of Freedom

• Think about an atom that is in empty space. Giving details about where it is in three dimensions, let's say it's the x, y, and z coordinate lines.
• Any of the directions can be used to move this atom around easily.
• The way an atom moves from one place to another is called its translational motion. In this way, an atom in empty space would be able to move in three different ways, giving it three degrees of freedom.
• The number of degrees of freedom for a monatomic (single atom) would be 3.
• But molecules with two atoms, like O2, can move in two more ways besides just translating.
• These molecules are linked to each other, which makes it easy for them to spin around their center of mass. This means that a molecule with two atoms can move in a total of five different directions.
• But if we say that a diatomic molecule is a non-rigid rotator, we mean that it can also move around in space.
• By vibrating in this way, it can move in more than five different ways.
• This is what an atom or molecule is based on when it comes to the ways or options for motion it can have.This is the idea of the degree of freedom on which the equilibrium of energy is based.
• The degree of freedom of an atom or molecule is the number of ways it can move from one place to another.

Equipartition of energy

• It's important to know what "equipartition" means before you can understand the idea.
  Equi means "equal," and split means "to divide."
• When put together, equipartition means that something is split or spread out evenly.
• This means that the energy is spread out evenly among particles or atoms moving in different directions.
• It has been said that a particle can move in three main ways: translationally, rotationally, and vibrationally. These moving atoms and molecules have the same amount of energy going in each direction.
• As a general rule, the law says that molecules in thermal balance have the same average energy for all of their separate motion degrees.

Kinetic energy of a monatomic molecule

• K stands for Boltzmann's constant.
• For a molecule with only one atom, there is only translational motion, and each motion has 1/2 KT of energy.
• To find this, divide the total energy by the number of degrees of freedom.
• These numbers are k for the oscillator's force constant and y for the vibrational point. There are both kinetic and potential modes at play here.

Significance of equipartition of energy

• Equipartition of energy is used in a very useful way with ideal gas.
• The equipartition theory will help us find the formulas for ideal gas and internal energy.
• Having a good grasp on Brownian motion can be helpful.
• It's also possible to use this rule to study the space world. With this rule and the virial theorem, it's easy to figure out what the average temperature of stars far away is.
• It is also used to look at how the stars are forming right now.

Limitations of equipartition of energy

• The law of equipartition only works for ergodic systems that are in thermal equilibrium. This means that when quantum effects are added, the law of equipartition of energy doesn't work anymore.
• At temperatures above 1000K, quantum effects control the vibrating energies of atoms and molecules more than the other two energy distributions.
• A new theory of dynamical systems, on the other hand, gets around this problem.

IMAGE SOURCE (THUMBNAIL)