Thermodynamic Functions and Equilibria: Mathematical Tools

This lecture covers thermodynamic functions and their mathematical tools, focusing on the relationships between state variables. The instructor introduces the concept of extensive and intensive variables, emphasizing their roles in thermodynamics. The discussion includes the derivation of partial derivatives and their cyclic relationships, which are crucial for understanding thermodynamic systems. The instructor explains how to express one variable in terms of others, using examples from ideal gases. The lecture also delves into Gibbs, Euler, and Gibbs-Duhem relations, highlighting their significance in thermodynamic analysis. The instructor illustrates how these relations can be applied to real systems, demonstrating the importance of understanding state functions and their interdependencies. The lecture concludes with a summary of key concepts and their applications in thermodynamics, providing a solid foundation for further study in the field.