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This lecture covers the choice of state variables and state functions in thermodynamics, including the selection of elastic and calorimetric coefficients, the impact of different system conditions, and the importance of counting all state variables in open systems. It also delves into mathematical concepts such as homogeneous functions and the Euler theorem, emphasizing the significance of energy exchange and the Gibbs equation in open systems. The discussion extends to the entire Gibbs equation, the Gibbs-Duhem equation, and the third law of thermodynamics, highlighting the behavior of entropy at absolute zero temperature.