Thermodynamics + statistical mechanics¶

What you will develop¶

Track energy, entropy and free energy; derive equilibrium tendencies; connect microscopic states to macroscopic limits and transport.

Before you begin¶

Recorded prerequisites:

Study and practice¶

Progress by the work you can do, not by a fixed calendar.

Practice sequence 7¶

Spine: OpenStax University Physics Vol. 2

Reading: Ch. 1-2 temperature/heat and kinetic theory

Know: Distinguish temperature, internal energy and heat; connect microscopic motion to pressure and transport scales.

Reconstruct: Derive ideal-gas kinetic pressure scaling and equipartition-style energy relation.

Do: Estimate gas/thermal sensor response and mean molecular speed across operating temperatures.

Defend: Why is temperature not 'amount of heat'?

Gate: Pass: microscopic and macroscopic accounts agree dimensionally and numerically.

Source: source

Practice sequence 8¶

Spine: OpenStax University Physics Vol. 2

Reading: Ch. 3 First Law of Thermodynamics

Know: Write control-volume energy balances; distinguish work modes and state vs path variables.

Reconstruct: Derive first-law forms for closed systems and steady-flow device intuition.

Do: Energy-budget a closed habitat subsystem or thermal battery during a charge/discharge cycle.

Defend: What information is lost if you only track energy and ignore entropy?

Gate: Pass: complete energy balance with sign conventions and explicit boundary.

Source: source

Practice sequence 9¶

Spine: OpenStax University Physics Vol. 2 + David Tong

Reading: Ch. 4 Second Law; Tong Statistical Physics Ch. 1 ensembles/entropy

Know: Understand entropy as state-count/information-compatible quantity and second-law constraint.

Reconstruct: Derive multiplicity/entropy relation intuition and Carnot efficiency bound.

Do: Compare two heat-engine/refrigeration designs and show why one advertised efficiency is impossible.

Defend: Is entropy production a bookkeeping artifact or a physical limitation?

Gate: Pass: identify irreversible step and quantify an efficiency/exergy ceiling.

Source: source

Practice sequence 10¶

Spine: David Tong, Statistical Physics

Reading: Ch. 1-2 canonical ensemble, partition function, classical gases

Know: Use partition functions to obtain equilibrium averages and connect micro/macro descriptions.

Reconstruct: Derive canonical probability and simple two-state partition function; recover ideal-gas/equipartition results.

Do: Model a two-level sensor/material population vs temperature and compute heat capacity/occupancy.

Defend: Why does the partition function act like a generator of thermodynamic information?

Gate: Pass: derive one observable from Z and explain assumptions.

Source: source

Practice sequence 11¶

Spine: David Tong Statistical Physics + Kinetic Theory

Reading: Tong Ch. 4-5 thermodynamics/phase transitions; Kinetic Theory Ch. 1 transport

Know: Reason about free energies, phase stability, diffusion/viscosity/thermal conduction and heat rejection.

Reconstruct: Derive equilibrium from free-energy minimization and diffusion timescale L²/D.

Do: Heat-rejection design for fusion/spacecraft/data-center toy system; calculate radiator/transport scaling.

Defend: Why do many futuristic systems become heat-rejection problems before energy-supply problems?

Gate: Module defense: mass/energy/entropy/transport budget for a frontier system with one hard thermodynamic bound.

Source: source

Exit gate¶

Closed-book: 120 min: first-law balances, entropy/Carnot, free-energy equilibrium, partition-function and transport scaling.

Novel problem: Given a futuristic power/thermal system, derive a hard efficiency or heat-rejection bound.

Artifact: Energy/entropy/radiator/transport budget with parameter sweep.

Defend: Defend system boundary, reversible limit, entropy production and dominant transport bottleneck.

Pass criterion: Pass if claimed performance respects first/second law and heat/mass transport.

Transfer problems¶

Try these before consulting solutions or asking for the complete answer.

First law: Energy-budget a closed thermal store including charging loss and heat leak.
Entropy: Compare two processes with identical energy balance but different entropy production.
Carnot: Find the maximum possible efficiency for a heat engine and show how radiator temperature changes system mass.
Partition function: Compute occupancy and heat capacity for a two-state system.
Free energy: Determine which of two phases/reactions is favored from free-energy data.
Transport: Estimate diffusion time across 1 mm, 1 cm and 1 m; explain why scaling matters.
Heat transfer: Compare conduction/convection/radiation for a high-temperature spacecraft component.
Kinetic theory: Estimate mean free path change with pressure and explain continuum breakdown.
Phase transition: Sketch a Landau-like free-energy landscape before/after a transition.
Heat rejection: Show why a high-power compact system can be limited by radiator area rather than fuel energy.