Entropy and Equilibria Course

Lesson 1 • Reversible and Irreversible Processes

Distinguishes reversible from irreversible processes using idealized examples. Prepares students for entropy analysis in later chapters.

Lesson 2 • Energy Forms and the First Law

Covers internal energy, heat, and work as energy transfer modes. Applies the first law to calculate energy changes in closed systems.

Lesson 3 • State Variables and Properties

Introduces intensive and extensive properties and state functions. Connects property definitions to measurable physical quantities.

Lesson 4 • Systems, Boundaries, and Surroundings

Defines open, closed, and isolated systems and their boundaries. Establishes the vocabulary needed for all subsequent thermodynamic analysis.

Lesson 1 • Third Law and Absolute Entropy

States the third law and defines absolute entropy referenced to zero kelvin. Enables use of standard molar entropy tables in reaction calculations.

Lesson 2 • The Second Law of Thermodynamics

Presents the second law through Kelvin-Planck and Clausius statements. Establishes entropy as the central quantity governing process direction.

Lesson 3 • Entropy of Phase Transitions

Calculates entropy changes for melting, vaporization, and sublimation. Introduces Trouton's rule as a practical estimation tool.

Lesson 4 • Entropy as a State Function

Derives entropy from the Clausius inequality and proves its state-function character. Connects the mathematical definition to physical intuition.

Lesson 1 • Configurational and Thermal Entropy

Separates entropy contributions from positional disorder and thermal motion. Applies the distinction to solids, liquids, and gases.

Lesson 2 • Entropy of Mixing

Calculates entropy of mixing for ideal gases and ideal solutions. Explains why spontaneous mixing occurs without energy input.

Lesson 3 • Microstates and Macrostates

Defines microstates and macrostates and their relationship to thermodynamic probability. Grounds statistical mechanics in observable thermodynamic behavior.

Lesson 4 • Information Theory and Entropy

Introduces Shannon entropy and its formal analogy to thermodynamic entropy. Broadens students' conceptual toolkit for interpreting disorder.

Lesson 1 • Combining Entropy and Enthalpy

Introduces the Gibbs and Helmholtz criteria by combining first and second law results. Establishes the thermodynamic driving force concept.

Lesson 2 • Maxwell Relations and Thermodynamic Identities

Derives Maxwell relations from the four thermodynamic potentials. Uses them to relate unmeasurable quantities to measurable ones.

Lesson 3 • Helmholtz Free Energy

Defines A = U - TS and identifies its role in constant-volume processes. Contrasts Helmholtz and Gibbs functions for different constraints.

Lesson 4 • Gibbs Free Energy in Depth

Derives G = H - TS and explores its temperature and pressure dependence. Connects G to maximum non-expansion work.

Lesson 1 • Equilibrium Constant Expressions

Derives K from standard Gibbs energy and writes expressions for gases and solutions. Distinguishes Kp, Kc, and Ka for different system types.

Lesson 2 • Temperature Dependence of K

Applies the van't Hoff equation to predict K at different temperatures. Connects enthalpy of reaction to the direction of K change.

Lesson 3 • Chemical Potential and Activity

Defines chemical potential as the partial molar Gibbs energy and introduces activity. Links chemical potential to composition for ideal and non-ideal systems.

Lesson 4 • Reaction Gibbs Energy and Equilibrium

Derives the reaction Gibbs energy and the condition for equilibrium. Connects the minimum in G to the equilibrium composition.

Lesson 1 • Binary Phase Diagrams

Introduces liquid-vapor and solid-liquid phase diagrams for two-component systems. Applies the lever rule to determine phase compositions and amounts.

Lesson 2 • Clausius-Clapeyron Equation

Derives and applies the Clausius-Clapeyron equation to vapor pressure curves. Calculates enthalpy of vaporization from vapor pressure data.

Lesson 3 • Gibbs Phase Rule

Derives F = C - P + 2 and applies it to single- and multi-component systems. Enables determination of degrees of freedom in any phase system.

Lesson 4 • Conditions for Phase Equilibrium

Derives equality of chemical potential across phases as the equilibrium criterion. Connects phase stability to the minimum Gibbs energy principle.

Lesson 1 • Chemical Potential in Solutions

Expresses chemical potential of solvent and solute in terms of activity. Connects solution composition to thermodynamic driving forces.

Lesson 2 • Colligative Properties

Derives boiling point elevation, freezing point depression, and osmotic pressure. Applies colligative property equations to determine molar masses.

Lesson 3 • Ideal and Non-Ideal Solutions

Defines Raoult's and Henry's laws and their ranges of validity. Distinguishes ideal from non-ideal solution behavior using activity coefficients.

Lesson 4 • Solubility and Partition Equilibria

Applies chemical potential equality to solid-liquid and liquid-liquid equilibria. Predicts solubility trends and partition coefficients from thermodynamic data.

Lesson 1 • Dissipative Structures and Far-from-Equilibrium Systems

Introduces Prigogine's dissipative structures and self-organization far from equilibrium. Connects entropy production to pattern formation in open systems.

Lesson 2 • Coupled Reactions and Biochemical Equilibria

Analyzes thermodynamically unfavorable reactions driven by coupling to favorable ones. Applies free energy coupling to metabolic and industrial processes.

Lesson 3 • Electrochemical Equilibria

Connects cell potential to Gibbs energy and derives the Nernst equation. Calculates equilibrium constants from standard electrode potentials.

Lesson 4 • Onsager Relations and Linear Irreversible Thermodynamics

Presents Onsager reciprocal relations for coupled irreversible fluxes. Applies linear irreversible thermodynamics to diffusion, heat flow, and thermoelectric effects.

Lesson 5 • Simultaneous Equilibria

Solves systems with multiple coupled equilibria using algebraic and numerical methods. Applies to acid-base, complexation, and precipitation equilibria.