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This lecture covers the concept of thermodynamic potentials, including the fundamental relations such as Gibbs relation and Euler relation. It explains the analogy between mechanics and thermodynamics, the definition of thermodynamic potentials, and their physical dimensions. The lecture also discusses Legendre transformations, the concept of energy free, enthalpy, and Gibbs free energy, as well as the equilibrium of coupled subsystems. The instructor provides insights into the mathematical transformations involved and the significance of these potentials in practical physical situations.