Thermodynamics 2

This module supplements and formalizes the thermodynamic concepts introduced in the Thermodynamics 1 course unit, exploring several aspects in greater depth: thermodynamic potentials defined using Legendre transformations, the thermodynamics of open systems, phase transitions in pure substances, and irreversible processes, with forays into the microscopic level to provide an overview of the physical foundations of the theory.

• Use differential forms and their properties in the context of thermodynamics.
• Perform the energy balance and entropy balance for a composite thermodynamic system.
• Predict the macroscopic properties of simple physical models (e.g., ideal gas, real gases, harmonic solid).
• Apply methods for solving ordinary differential equations to thermodynamic problems (e.g., pressure in a compressible fluid).
• Perform an energy and entropy balance for an open system
• Incorporate a diffusion equation in simple cases.
• Establish the connection between the macroscopic and microscopic descriptions of a system

• EU Thermodynamics 1:
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• Concepts of Newtonian Dynamics
  • Conservative forces
  • Kinetic and Potential Energy
  • Harmonic oscillators
• Math
  
  
  • Derivatives, Integrals, Limit Expansions 
  • Differential Forms

Terminal Control

• Thermodynamics at Equilibrium
  • Review: Thermodynamic systems. State variables and functions: equations of state, intensities, extensivities, additivity. The concepts of equilibrium and local equilibrium. Thermodynamic transformations: quasi-static vs. reversible. Work and heat and their elementary expressions. Internal energy.
  • Axiomatic Presentation: First Law: Statement and Consequences, Connection to Calorimetry. Dulong and Petit’s Law. Second Law: Statement and Consequences. Fundamental Equation and Equations of State. Thermal Equilibrium. Third Law.
  • Thermodynamic potentials: the Helmholtz potential (free energy) and the Gibbs potential (free enthalpy), and their applications. Enthalpy. Introduction to Legendre transformations. Review of phase diagrams. The Clausius-Clapeyron equation and its applications.
  • Thermodynamics of Open Systems: Formulation of the first and second laws for open systems. Chemical potential. Application to chemical reactions
  • Phase transitions: concavity and convexity of thermodynamic potentials. Response functions. Applications. Phase transitions: first-order transitions and continuous transitions.
  • Transport phenomena: Thermodynamic forces. Local energy and entropy balance. Diffusion equation. Coupling of irreversible phenomena: application to thermoelectric effects.
• Microscopic Findings
  • Internal Energy: Conservation and Equidistribution of Energy
  • Pressure and Temperature: Elements of Kinetic Theory of Gases
  • Entropy: Microscopic Interpretation, Microstates, and Macrostate