PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD → Statistical mechanics and thermodynamics ↓


Classical thermodynamics


Classical thermodynamics is a branch of physics that deals with the macroscopic behaviour of energy, heat and work within physical systems. It is based on predictable macroscopic outcomes rather than the microscopic behaviour of individual particles, unlike statistical mechanics. Let us explore this topic in detail.

Fundamental concepts

Classical thermodynamics revolves around certain fundamental principles and laws. These are observed in systems that are large enough that quantum and statistical fluctuations can be ignored.

System and environment

In thermodynamics, a system is the part of the universe we are interested in studying, while everything outside this system is considered the surroundings. For example, if you are studying the thermodynamics of the gas inside a balloon, the gas is your system, and the balloon and everything else is the surroundings.

The systems may be further classified into the following categories:

  • Open systems - can exchange both matter and energy with the surrounding environment.
  • Closed systems - can exchange only energy, not matter, with the surroundings.
  • Isolated systems - cannot exchange matter or energy with the surrounding environment.

State functions

The description of the system is given by certain properties called state functions. These include pressure (P), volume (V), temperature (T) and internal energy (U). State functions depend only on the state of the system, not on how the state was reached.

U = f(P, V, T)

Procedures

Thermodynamic processes describe changes from one state to another. They can be classified depending on how the state functions change:

  • Isothermal process - occurs at constant temperature.
  • Adiabatic process – occurs without heat exchange.
  • Isobaric process - occurs at constant pressure.
  • Isovolumic process - occurs at constant volume.

First law of thermodynamics

The first law of thermodynamics, also called the law of conservation of energy, states that energy cannot be created or destroyed. The total energy change in a closed system is the sum of the heat added to the system and the work done on it.

ΔU = Q - W

Here:

  • ΔU is the change in internal energy.
  • Q is the heat added to the system.
  • W is the work done by the system.

Imagine a steam engine where heat is supplied to the steam in a closed cylinder. The steam expands and does work by moving the piston. The change in energy of the system can be calculated using the first law.

Second law of thermodynamics

The second law introduces the concept of entropy, which is a measure of disorder or randomness in a system. It states that in an isolated system, the total entropy can never decrease over time, indicating that processes tend toward thermodynamic equilibrium with maximum disorder.

This law can be observed in operations such as adding milk to coffee, where the cream will continue to spread until it is evenly distributed.

higher order High Entropy

The concept that entropy will increase makes it impossible to convert heat completely into work. For example, in a heat engine, not all the heat absorbed is converted into useful work; some is always rejected as waste.

Third law of thermodynamics

The third law states that as the temperature of a closed system approaches absolute zero, its entropy approaches a constant minimum. This implies that it is impossible to reach absolute zero temperature through any finite series of processes.

In practical terms, this law means that no matter how efficient a refrigerator or heat pump is designed, it is impossible to completely remove energy from the system as it approaches absolute zero.

Applications of classical thermodynamics

Classical thermodynamics is widely applicable to a variety of fields, including:

  • Aerospace - Designing engines and systems that can tolerate varying temperatures and pressures.
  • Mechanical Engineering – for efficient energy conversion in engines and systems.
  • Chemistry - Understanding reaction energies and equilibrium states.
  • Environmental Science - in Climate Modelling and Sustainability Studies.

Understanding through examples

Steam engine

One of the most classic examples of thermodynamics is the steam engine. In a steam engine, water is heated in a boiler to create steam. This steam pushes against a piston or turbine blades to do mechanical work, which is an example of how heat can be converted into work.

Piston Steam

Refrigeration cycle

Refrigerators work based on thermodynamic cycles. By compressing the refrigerant, heat is absorbed from the interior of the refrigerator and expelled, keeping the inside cool. This entire process involves understanding and using enthalpy and entropy changes in thermodynamic cycles.

Classical thermodynamics may seem abstract due to its statistical nature and reliance on macroscopic properties. However, its principles are useful in the design and operation of countless everyday applications and systems. Its focus on the flow and conversion of energy rather than the specifics of atomic behavior provides a comprehensive understanding of the physical world.


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Classical thermodynamics

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