Statistical Mechanics: Definition, Applications, Mechanics

In this lesson, the focus will be on statistical mechanics and their related terms such as thermodynamics, thermodynamic equilibrium, and quantum mechanics. These terms are related to statistical mechanics. In physics, generally, two types of mechanics have been explained one is classical mechanics and another one is quantum mechanics. Classical mechanics described the motion of macroscopic objects like the orbital motion of satellites around the Earth. And quantum mechanics described the physical properties of nature at the scale of atoms and subatomic particles.

Keywords: Statistical mechanics, Thermodynamics, Thermodynamic equilibrium, Quantum mechanics, Classical mechanics, Microscopic entities.

Also check: Potential Energy

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Introduction

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Energies of the state of the system we can use those energies to calculate the probabilities with equations like the Boltzmann probability distribution.

{E_i} → {P_i}

These brackets mean if I know the set of all energies, I can calculate the complete set of all these probabilities. Boltzmann probability distribution helps us to do that.

 {E_i} → {P_i} → Entropy of the system S

 {E_i}→ {P_i} → Energies of the system E

Once we get the probabilities we can calculate the entropy of the system and all the energies of that system. These collections of techniques are called statistical mechanics. Statistical mechanics move from microstate to macrostates. In the above equation, a microstate is {E_i} and microstate is entropy S and Energies E.

Further, these entropy (S) of the system and energies (E) will help to calculate enthalpy, pressures, free energies, and other thermodynamic properties, these are all relations called thermodynamics.

In statistical mechanics, conversion of microstate into macrostate and relationships to those properties will tell us how to predict the other properties of the system using thermodynamics.

On the other side, they predict the molecule of the energy of the system is quantum mechanics

Predict the molecule of energy→ {E_i} → {P_i}

So let’s see about quantum mechanics and see how to predict the {E_i}

Also check:

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Quantum mechanics

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Quantum mechanics of light- Light is a wave, it behaves like a wave. It diffracts in different ways in a different medium. Light contains particles. It is not a pure wave. Individual particles of light are photons. The following equation has described the energy of photons.

E= hÏ =hc/λ

h- Planks constant= 6.67×10^-34 Joules times second

c- Speed of light - 3×10⁸

E- Energy of an individual particle

λ- Wavelength of light

The energy of one individual particle of light, one photon of light is E= hÏ =hc/λ

Ex- If the wavelength of red light is 671 nm, then what is the energy of photons of light with this wavelength?

Ans: λ- Wavelength of light- 671nm- 671×10^-9 m

E= hÏ =hc/λ= (6.67×10^-34×3×10⁸)/ 671×10^-9

E= 2.98×10-¹⁹ Js

This is the energy of a single photon of red light whose wavelength is 671nm.

Here we can say light is quantized, we can break the photons but we cannot split out the photons into smaller pieces. It calls it quantum mechanics because it describes how things are quantized.

Also check:

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Statistical thermodynamics

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Thermodynamic system – An assembly of subatomic entities (atoms, molecules, photons, electrons, etc) in a very large number of ever-changing quantum states, each entity has a probability of being in a particular state.

A probability function describes each entity that will be in a particular state

Assembly (system) – A large collection of identical particles

Basic postulate- All possible microstates of an isolated assembly are equally probable. In each energy state, a microstate is specified by the number of particles. A macrostate is specified by the number of particles in each of the energy levels of the system.

In each state, state 1 has two particles and state 2 has two particles i.e. four particles. In other figures, there are also two particles in each state but in different ways of arrangement, the four particles are 1,2,3,4. There are six different possible ways of arrangement. So we call the same macrostate because four particles are in all six states but different microstates because the arrangement is different in every state.

Purpose and objective of statistical thermodynamics

• Predict the properties of an assembly (system)
• Because of large numbers analysis must be done statistically
• Molecules interact via collisions
• Statistical thermodynamics provides a means of averaging

Also check:

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Thermodynamic equilibrium

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This concept is related to statistical thermodynamics. The word equilibrium defines a state of balance. There are no unbalanced potentials within the system of equilibrium. An equilibrium state has no changes when it is isolated from its surrounding. The system is called thermodynamic equilibrium if the value of properties is the same at all points in the system.

Nonequilibrium thermodynamics is the opposite of thermodynamic equilibrium. The irreversible process is in non-thermodynamic equilibrium. For example, is the transport of heat by internal motions within a material is driven by imbalances in the temperature.

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Points to remember

• A connection between macroscopic properties of the materials coming in thermodynamic equilibrium is provided by Statistical Mechanics. 
• Statistical mechanics includes dynamics and statistical equilibrium.
• Statistical mechanics is useful in the fundamental study of the physical system with numerous degrees of freedom
• Quantum mechanics provides a description of the physical properties of nature at the scales of the atom and subatomic particles.

Also check: