Deep Physics: Thermodynamics for Talented High Schoolers, Princeton
Real thermodynamics, taught from the kinetic theory of gases up through entropy and the second law. For talented high schoolers.
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.
This course teaches you what physicists actually know about it. From first principles.
You will:
- Derive the ideal gas law from the motion of molecules, with no formula handed to you.
- 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.
By the end, you will think about heat, temperature, and entropy the way a physicist thinks about them.
What You Will Actually Understand
By the end of the course, you will understand six core ideas of thermodynamics.
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
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.
4. Entropy and the Second Law
The deepest idea in classical physics. 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. The statistical view: entropy as a count of microstates compatible with a given macrostate.
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 temperatures can do better. Why this limit follows from the second law alone, independent of any technology.
6. Phase Transitions 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. 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. The destination, a working understanding of thermodynamics from temperature through entropy and the second law, stays the same.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and transcripts 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 eight semester-long physics courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ.
Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Optics and atomic structure. Special Relativity. Quantum mechanics.
The Lyceum is built on the Deep Physics methodology.