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 ↓


Laws of Thermodynamics


The laws of thermodynamics are fundamental principles that describe how energy is transferred and transformed in physical systems. These laws form the foundation of classical thermodynamics and extend into the realm of statistical mechanics, which provides deeper insights into the microscopic behavior of systems. Understanding these laws is important for many fields, such as physics, engineering, chemistry, and even biology, because they apply universally to all forms of matter and energy.

Introduction to thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and energy. The subject focuses primarily on how energy is transferred between systems and how this transfer affects the properties of matter. The laws of thermodynamics provide a quantitative description of these processes and establish the limits within which energy transformations can occur.

Zeroth law of thermodynamics

The zeroth law of thermodynamics is fundamentally about temperature and thermal equilibrium. Simply put, if two systems are in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. This law allows us to use thermometers effectively, as it implies that a single temperature reading accurately represents the thermal conditions of a system.

Example of zeroth rule

Imagine three cups of water: cup A, cup B, and cup C. If cup A is at the same temperature as cup B, and cup B is at the same temperature as cup C, then according to the zeroth law, cup A must be at the same temperature as cup C.

A B C

First law of thermodynamics

The first law is essentially the law of conservation of energy. It states that energy cannot be created or destroyed in an isolated system. Instead, the change in the internal energy of a system is equal to the heat added minus the work done by the system.

    ΔU = Q - W

Where:

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

Example of the first law

Consider the steam engine, which works by converting heat energy into mechanical energy. When heat is applied, it increases the internal energy of water, causing it to turn into steam. As the steam expands, it does work by pushing a piston.

Steam

Second law of thermodynamics

The second law introduces the concept of entropy, which is a measure of disorder in a system. It states that in any energy exchange, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state, which is commonly referred to as an increase in entropy. In more practical terms, energy will spontaneously tend to spread out from being localized if it is not prevented from doing so.

Entropy can be thought of as the arrow of time because it only increases or stays the same; it never decreases. This law is why other kinds of perpetual motion machines are impossible.

    ΔS ≥ 0

Example of the second law

Consider a piece of ice placed in a cup of hot water. Over time, the piece of ice will melt, and the temperature of the water will drop until both reach the same temperature. The water has dispersed its thermal energy with the ice, increasing the overall entropy of the system.

Water

Third law of thermodynamics

The third law of thermodynamics states that as the temperature of an ideal crystal approaches absolute zero, its entropy approaches zero. This principle means that reaching absolute zero is impossible because it would require an infinite number of steps or an infinite amount of energy.

    lim (T→0) S = 0

Example of the third law

In practice, it is impossible to reach a temperature of absolute zero. Even systems cooled close to absolute zero exhibit some entropy due to the inherent quantum mechanical nature of particles, which prevents a state of complete stability.

Relevance in statistical mechanics

While classical thermodynamics provides these macroscopic laws, statistical mechanics provides a molecular perspective by linking them to the properties of individual particles within a system. For example, statistical mechanics describes entropy in terms of the number of microscopic configurations that correspond to the macroscopic state of a system.

Conclusion

The laws of thermodynamics are universal truths that apply across various fields of science and engineering. They set limits and help us understand the flow of energy that is fundamental to all natural processes. By studying these laws, we gain insight into how the universe operates on both macroscopic and microscopic scales, revealing a continuity of orderly processes marked by the inexorable motion of entropy.


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Laws of Thermodynamics

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