Deep Physics: Thermodynamics for Talented High Schoolers
Real thermodynamics, taught from the kinetic theory of gases up through entropy and the second law. For talented high schoolers.
Online for homeschool families anywhere · or in-person in Princeton, NJ
A World Through the Lens of Thermodynamics
Some of the deepest puzzles in physics live in the everyday: in heat, in time, in the direction nature runs.
Stir cream into coffee. The cream spreads. Wait forever. The cream never reassembles itself, even though every molecular collision could in principle run in reverse.
Two objects in contact, of any size, made of any materials. They settle to one common temperature. A single number, agreed on by both.
No machine, however cleverly built, converts heat fully into work. The bound is set not by engineering but by a theorem.
Heat ice from below zero. The temperature climbs to zero degrees Celsius and stops. Pour in more energy. The ice melts, but the temperature does not move until the last crystal is gone.
Thermodynamics is the theory that makes sense of all of this. With two laws and a single new quantity, entropy, it predicts what is and is not possible for any system that exchanges energy with its surroundings.
You will:
- Derive the ideal gas law from the motion of molecules.
- Use the first law to track energy through any process, cyclic or otherwise.
- Compute the entropy change of a process and predict from it, alone, whether the process can happen.
- Prove that no heat engine can beat a Carnot engine, working from the second law.
What You Will Actually Understand
1. Temperature, Heat, and the Zeroth Law
The starting point: what these words actually mean in physics. Thermal equilibrium, the zeroth law, and the operational definition of temperature. The distinction between heat and internal energy. Specific heat, latent heat, and calorimetry as the first quantitative tools of the theory.
2. The First Law and Energy Conservation
Energy conservation, extended to include heat. Internal energy as a state function. Work done by and on a system. The first law as accounting: energy in, energy out, and what stays. Isothermal, adiabatic, isobaric, and isochoric processes traced on a pressure–volume diagram.
3. Kinetic Theory of Gases and Transport Phenomena
Where pressure and temperature come from, microscopically. Molecules in motion, momentum transfer to walls, and the derivation of the ideal gas law from Newtonian mechanics. The Maxwell distribution of speeds. The equipartition theorem and why temperature is a measure of average kinetic energy per degree of freedom. Mean free path. Transport phenomena: diffusion, thermal conductivity, and gas viscosity, all rooted in the same molecular picture.
4. Entropy and the Second Law
Reversible and irreversible processes. Entropy as a state function defined by reversible heat flow over temperature. The second law as a one-way constraint on the universe. Boltzmann’s statistical interpretation: entropy as a count of microstates compatible with a given macrostate, S = k ln W.
5. Heat Engines and the Carnot Cycle
The hard limit on every engine ever built. Heat engines, refrigerators, and heat pumps as cycles on a P–V diagram. The Carnot cycle and the proof that no engine operating between two reservoirs can be more efficient than a reversible (Carnot) engine operating between the same two. Why this limit follows from the second law alone, independent of any technology.
6. Phase Transitions, Real Gases, and Thermodynamic Potentials
Why ice melts at zero degrees and water boils at one hundred. Phase diagrams and the Clausius–Clapeyron relation. Latent heat in transitions. Real gases past the ideal-gas regime: the Van der Waals equation and the critical point where the gas–liquid distinction vanishes. Free energies (Helmholtz and Gibbs) as the right quantities to minimize when temperature or pressure is held fixed. The thermodynamic foundation for chemistry, materials, and biology.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and certificates apply to every Lyceum course. They live on the Physics Lyceum: High School overview.
To enroll, schedule a call. We confirm fit, prerequisites, and the right semester.
Part of the SoTS Physics Lyceum
Thermodynamics is one of six classical core courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ. Students earning the Mastery in Classical and Modern Physics complete the six classical core courses plus any two of the four modern electives.
Classical core: Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Geometric optics.
Modern electives: Special Relativity. Quantum mechanics. Nuclear and particle physics. Astronomy and cosmology.
The Lyceum is built on the Deep Physics methodology.