What theoretical foundations form the bedrock of chemical engineering principles? Analyze the fundamental theories and concepts that underpin the design and operation of chemical processes and systems. Explore the principles of thermodynamics, kinetics, and transport phenomena, elucidating their role in understanding and optimizing chemical reactions, phase equilibria, and mass and energy transfer processes. Investigate the application of mathematical modeling and simulation techniques in predicting the behavior of complex chemical systems and designing efficient industrial processes. Delve into the principles of reactor design, separation processes, and process control, examining how these concepts enable the development of sustainable and cost$-$effective chemical processes. Additionally, discuss the interdisciplinary nature of chemical engineering, highlighting its integration with chemistry, physics, biology, and materials science to address contemporary challenges in areas such as renewable energy, environmental sustainability, and advanced materials synthesis.