Introduction
Thermodynamics studies energy in the form of heat and work, and why some energy transformations happen spontaneously while their reverse never does — a question mechanics alone cannot answer. Kinetic theory then explains these macroscopic (bulk) laws in terms of the microscopic (molecular) motion underneath, connecting this chapter back to mechanics and forward to statistical physics.
1. Perfect and real gases; the van der Waals equation
The ideal (perfect) gas law, PV = nRT, models gas molecules as point particles with no volume and no intermolecular forces, colliding elastically. It works well at low pressure and high temperature, where molecules are far apart. Real gases deviate from this at high pressure or low temperature, because molecules do occupy volume and do attract each other (especially just before condensation). The van der Waals equation, (P + a n²/V²)(V − nb) = nRT, corrects for both effects: the term a n²/V² accounts for intermolecular attraction (which reduces the pressure a gas actually exerts compared to the ideal prediction), and b accounts for the finite volume occupied by the molecules themselves (reducing the volume available for them to move in).
2. Laws of thermodynamics, internal energy, temperature, entropy
- Zeroth law: if two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other — this is what makes temperature measurement with a thermometer meaningful.
- First law: ΔU = Q − W (change in internal energy equals heat added minus work done by the system). This is energy conservation applied to thermal systems: energy is never created or destroyed, only converted between heat, work, and internal energy.
- Second law: heat does not spontaneously flow from a colder to a hotter body, and the total entropy of an isolated system never decreases. This law introduces a direction to time in physics — many processes conserve energy in both directions but are only observed in one direction (a broken cup does not spontaneously reassemble, even though doing so would not violate energy conservation).
- Third law: the entropy of a perfect crystal approaches zero as temperature approaches absolute zero.
Internal energy (U) is the total kinetic and potential energy of a system’s molecules. Temperature is a measure of the average kinetic energy of molecular motion. Entropy (S) is a measure of the number of microscopic arrangements (microstates) consistent with a system’s macroscopic state — informally, a measure of disorder or of the energy no longer available to do useful work. The second law’s statement that entropy never decreases explains why heat engines can never be 100% efficient: some energy is always “spread out” into a less useful form.
3. Thermal properties of simple systems
This covers how temperature affects specific physical quantities: specific heat capacity (energy needed to raise a unit mass by one degree), latent heat (energy absorbed or released during a phase change, such as ice melting, at constant temperature), and thermal expansion (most materials expand when heated, because increased molecular kinetic energy increases average intermolecular spacing). These properties must be understood physically, not just as formulas — for instance, water’s unusual density maximum at 4°C, arising from hydrogen-bond geometry, is why ice floats and lakes freeze from the top down.
4. Kinetic theory, the Maxwell distribution, and Brownian motion
Kinetic theory derives the ideal gas law from Newtonian mechanics applied to a large number of randomly moving molecules colliding elastically with each other and the container walls — pressure arises from the rate and force of these collisions, and temperature corresponds to the average molecular kinetic energy, ⟨KE⟩ = (3/2)kT.
Not all molecules in a gas move at the same speed; the Maxwell–Boltzmann speed distribution gives the probability of finding a molecule with a particular speed at a given temperature — a skewed curve that broadens and shifts to higher speeds as temperature rises.
Brownian motion — the observed random jittering of pollen grains (or other small particles) suspended in a fluid — was explained by Einstein (1905) as the visible result of constant, random bombardment by the fluid’s invisible molecules. This was historically crucial evidence for the real, physical existence of atoms and molecules, at a time when their existence was still debated.
5. Transport phenomena
Transport phenomena describe how a system relaxes toward equilibrium by moving a quantity from a region where it is more concentrated to where it is less concentrated: diffusion transports matter (down a concentration gradient), thermal conduction transports heat (down a temperature gradient), and viscosity transports momentum (between fluid layers moving at different speeds). All three are described mathematically by very similar equations, because at the molecular level they all arise from molecules carrying a property (mass, energy, or momentum) as they move and collide.
6. Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac statistics
At the microscopic level, statistical mechanics asks how particles are distributed among available energy states. Maxwell–Boltzmann statistics apply to distinguishable, classical particles (ordinary gas molecules) with no restriction on how many can occupy the same state. Quantum mechanics reveals that identical particles are fundamentally indistinguishable, and this splits into two cases depending on particle type (a distinction developed further in Modern and Quantum Physics):
- Bose–Einstein statistics apply to bosons (particles with integer spin, such as photons), which can occupy the same quantum state without limit — this underlies phenomena like laser light (many photons in the same state) and Bose–Einstein condensates.
- Fermi–Dirac statistics apply to fermions (particles with half-integer spin, such as electrons), which obey the Pauli exclusion principle — no two identical fermions can occupy the same quantum state. This is why electrons in an atom or a solid fill up successive energy levels rather than all collapsing into the lowest one, a fact essential to both atomic structure and the electrical behaviour of solids (Solid State Physics).
Key Takeaways
- The ideal gas law is a limiting case; the van der Waals equation corrects for real molecular volume and intermolecular attraction.
- The four laws of thermodynamics govern energy conservation (first law), the directionality of spontaneous processes via entropy (second law), and the equilibrium/zero-temperature limits (zeroth and third laws).
- Kinetic theory derives macroscopic gas behaviour from molecular motion; Brownian motion provided direct experimental evidence for the reality of molecules.
- Diffusion, conduction and viscosity are all transport phenomena moving mass, energy or momentum down a gradient toward equilibrium.
- Classical (Maxwell–Boltzmann) statistics assume distinguishable particles with no occupation limit; quantum statistics split into Bose–Einstein (bosons, no limit) and Fermi–Dirac (fermions, Pauli exclusion) — a distinction that underlies both quantum optics and the electronic structure of matter.