This lecture provides a detailed explanation of vapor-liquid equilibrium (VLE) and introduces pinch analysis. It begins with the fundamental principles of thermodynamics, including the first and second laws, and the importance of energy conversion. The instructor discusses systems modeling, emphasizing the significance of stream properties and thermodynamic relationships. The lecture covers the calculation of pure component properties in ideal conditions and the complexities of mixture properties. A key focus is on vapor-liquid equilibria, which are crucial for various chemical and environmental processes. The thermodynamic definition of equilibrium is explored, along with the mathematical expressions governing VLE. The lecture also delves into heat integration and pinch analysis, highlighting their roles in optimizing energy use in processes. The importance of life cycle assessment and uncertainty analysis is mentioned, providing a comprehensive overview of the methodologies used in systems modeling for renewable energy processes.