A First Course in the Mathematical Foundations of Thermodynamics (Undergraduate Texts in Mathematics)

I Classical Thermodynamicsl.- 1. Homogeneous Fluid Bodies.- 2. The First Law; Energy.- 3. The Second Law; Entropy.- 4. A General Efficiency Estimate.- II Systems with Perfect Accessibility.- 1. Definition and Example.- 2. Actions.- III A Modern Treatment of the First Law.- 1. Thermodynamical Systems (1) and the First Law.- 2. Products of Systems and Preservation of the First Law.- 3. The First Law and Joule's Relation.- IV A Modern Treatment of the Second Law.- 1. Introduction.- 2. Hotness Levels and Temperature Scales.- 3. The Accumulation Function for an Ideal Gas.- 4. Thermodynamical Systems (2) and the Second Law.- 5. Products of Systems and Preservation of the Second Law.- 6. The Second Law and the Accumulation Inequality.- 7. Estimates for Heat Absorbed and Heat Emitted.- V Energy and Entropy for Thermodynamical Systems.- 1. Introduction.- 2. Actions with the Clausius Property.- 3. Actions with the Conservation Property.- 4. Actions with the Dissipation Property.- VI Isothermal Processes of Homogeneous Filaments.- 1. Introduction.- 2. Elastic Filaments.- 3. Viscous Filaments.- 4. Elastic-Perfectly Plastic Filaments.- 5. Phase Transitions in Elastic and Viscous Filaments.- VII Homogeneous Bodies with Viscosity.- 1. Bodies with Viscosity as Thermodynamical Systems.- 2. Consequences of the First Law.- 3. Consequences of the Second Law.- Comments and Suggestions for Further Reading.- Problems.