"How does the process of distillation exploit the differences in boiling points of components in a mixture to separate them effectively? Discuss the key principles involved, including vapor$-$liquid equilibrium, Raoult's Law, and the concept of azeotropes. Provide examples of industrial applications where distillation plays a crucial role in separating various chemicals. Analyze how factors such as temperature, pressure, and the composition of the mixture influence the efficiency of the distillation process."