Laws and Cycles
Master the four laws, ideal gas law (PV = nRT), heat transfer modes, and the Carnot efficiency formula.
Thermodynamics
The four laws of thermodynamics, entropy, heat engines, and statistical mechanics — the physics of energy conversion and disorder.
Overview
Thermodynamics describes how energy is stored, transferred, and converted between heat and work. It governs everything from steam engines and refrigerators to the metabolic efficiency of cells and the ultimate fate of the universe. Classical thermodynamics uses macroscopic variables (temperature, pressure, volume, entropy), while statistical mechanics derives these from atomic-level probabilities.
The Four Laws
Zeroth Law — Temperature
If systems A and B are each in thermal equilibrium with C, then A and B are in equilibrium with each other. This law defines temperature as an equivalence relation and justifies the use of thermometers.
First Law — Energy Conservation
Energy cannot be created or destroyed: ΔU = Q − W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done by the system. The first law is energy accounting for thermodynamic processes.
Second Law — Entropy
The entropy of an isolated system never decreases spontaneously. Heat flows spontaneously from hot to cold, not vice versa. The second law sets the direction of time and limits the efficiency of all heat engines. Clausius stated it as: dS ≥ δQ/T, with equality for reversible processes.
Third Law — Absolute Zero
As temperature approaches absolute zero (0 K), the entropy of a perfect crystal approaches zero. This makes it impossible to reach absolute zero in a finite number of steps.
Entropy and the Arrow of Time
Entropy S = k_B ln Ω, where Ω is the number of microstates compatible with a macrostate and k_B is Boltzmann's constant. The second law follows from probability: high-entropy states have overwhelmingly more microstates than low-entropy ones, so systems naturally evolve toward them.
Heat Engines and the Carnot Cycle
The Carnot cycle is the theoretically most efficient heat engine: two isothermal and two adiabatic steps. Its efficiency η_Carnot = 1 − T_C/T_H depends only on the temperatures of the hot (T_H) and cold (T_C) reservoirs, not on the working fluid. Real engines (Otto, Diesel, Rankine) are always less efficient due to friction, heat loss, and irreversibility.
Statistical Mechanics
Statistical mechanics bridges the microscopic (atoms) and macroscopic (thermodynamic variables). The Boltzmann distribution P(E) ∝ e^(−E/k_BT) gives the probability of a state with energy E at temperature T. From this, all thermodynamic quantities follow: the partition function Z encodes everything about a system in equilibrium.
Learning Pathways
Entropy and Free Energy
Study entropy changes in irreversible processes, Gibbs and Helmholtz free energy, phase transitions, and chemical potential.
Statistical Mechanics
Boltzmann distribution, partition functions, quantum statistics (Bose-Einstein and Fermi-Dirac), and phase transitions.
Key Articles
Second Law of Thermodynamics
A deep treatment of entropy, irreversibility, and the arrow of time.
Read →Maxwell's Demon
The thought experiment that links information theory to thermodynamics.
Read →Specific Heat of Solids
Einstein and Debye models: quantum effects on heat capacity.
Read →Brownian Motion
Einstein's 1905 paper connecting thermal fluctuations to atomic reality.
Read →The Langevin Equation
Stochastic dynamics: modelling particles in a thermal bath.
Read →Boltzmann Brains
A thought experiment on entropy, cosmology, and the far future of the universe.
Read →Frequently Asked Questions
What is entropy and why does it increase?
Entropy counts microstates. High-entropy states are more probable, so isolated systems naturally evolve toward them — the second law follows from statistics, not new physics.
What is the Carnot efficiency?
η = 1 − T_cold/T_hot. It is the maximum possible efficiency for any heat engine between two temperature reservoirs. Real engines are always less efficient.
What is the zeroth law?
If A is in equilibrium with C, and B is in equilibrium with C, then A and B are in equilibrium. This defines temperature as a transitive property.
What is the difference between heat and temperature?
Temperature is average energy per degree of freedom (intensive). Heat is the transfer of thermal energy due to a temperature difference (energy in transit).