Physics / core
Heat, work, and thermodynamic structure
Build equilibrium thermodynamics from state variables and the first two laws, then apply potentials and stability criteria to real processes.
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Module 01 core
Heat, work, and thermodynamic structure
Build equilibrium thermodynamics from state variables and the first two laws, then apply potentials and stability criteria to real processes.
- 01
Equilibrium states and thermodynamic coordinates
Choose independent state variables, distinguish intensive and extensive properties, and identify the constraints behind thermal equilibrium.
23 min - 02
Quasistatic work and path dependence
Calculate pressure-volume work with a work-on convention and distinguish equilibrium paths from reversible processes.
24 min - 03
The first law and heat capacities
Use heat-in and work-on energy accounting, distinguish constant-volume and constant-pressure heating, and derive the ideal-gas capacity difference.
24 min - 04
Carnot cycles and absolute temperature
Derive a reversible two-reservoir benchmark, relate heat ratios to kelvin temperatures, and distinguish engine efficiency from refrigerator performance.
25 min - 05
Clausius inequality and entropy production
Define entropy through reversible heat and audit irreversibility by including both a system and the reservoirs that exchange heat with it.
26 min - 06
The fundamental thermodynamic identity
Read temperature, pressure, and chemical potential as derivatives of one equilibrium energy function while keeping heat and work path dependent.
26 min - 07
Free energies and natural variables
Use Legendre transforms to match equilibrium potentials to imposed constraints and derive useful-work bounds without confusing a minimum principle with a coordinate derivative.
26 min - 08
Maxwell relations and measurable responses
Derive cross-response identities from a smooth potential and translate entropy derivatives into expansion, compression, and heat-capacity measurements.
27 min - 09
Phase coexistence and the Clapeyron equation
Derive the slope of a coexistence curve from equal chemical potentials, track latent-heat and volume signs, and separate exact coexistence relations from vapor approximations.
26 min - 10
Thermodynamic convexity and stability
Connect entropy maxima and energy curvature to measured response signs while respecting ensemble constraints, coupled variations, and phase separation.
28 min