How does the application of thermodynamics principles contribute to the design and optimization of chemical processes in the field of chemical engineering? Specifically, how do concepts such as energy conservation, entropy, and equilibrium play crucial roles in determining the feasibility, efficiency, and sustainability of various chemical reactions and unit operations? Moreover, how do engineers utilize mathematical models and computational tools to analyze thermodynamic properties, predict phase behavior, and optimize process parameters? Additionally, what are the implications of thermodynamic considerations on industrial$-$scale production, product quality, and environmental impact? Exploring these intersections between theory and practice elucidates the fundamental underpinnings of chemical engineering processes.