Advanced thermodynamics engineering

Importance, Significance and Limitations -- Limitations of Thermodynamics -- Mathematical Background -- Explicit and Implicit Functions and Total Differentiation -- Exact (Perfect) and Inexact (Imperfect) Differentials -- Conversion from Inexact to Exact Form -- Relevance to Thermodynamics -- Homogeneous Functions -- Taylor Series -- LaGrange Multipliers -- Composite Function -- Stokes and Gauss Theorems -- Overview of Microscopic Thermodynamics -- Matter -- Intermolecular Forces and Potential Energy -- Internal Energy, Temperature, Collision Number and Mean Free Path -- Pressure -- Gas, Liquid, and Solid -- Work -- Heat -- Chemical Potential -- Boiling/Phase Equilibrium -- Entropy -- Properties in Mixtures -- Partial Molal Property -- Air Composition -- Proof of the Euler Equation -- Brief Overview of Vector Calculus -- First Law of Thermodynamics -- Zeroth Law -- First Law for a Closed System -- First Law for an Open System -- Integral and Differential Forms of Conservation Equations -- Mass Conservation -- Energy Conservation -- Conservation Relations for a Deformable Control Volume -- Second law and Entropy -- Thermal and Mechanical Energy Reservoirs -- Statements of the Second Law -- Informal Statements -- Consequences of the Second Law -- Reversible and Irreversible Processes -- Cyclical Integral for a Reversible Heat Engine -- Clausius Theorem -- Clausius Inequality -- External and Internal Reversibility -- Entropy -- Relation between ds, [delta]q and T during an Irreversible Process