In this chapter, we cover fundamental principles of thermodynamics as they apply to energy transfer and entropy, with a focus on understanding the First and Second Laws of Thermodynamics and their implications. We describe how energy is transferred as heat and work, how entropy quantifies disorder, and how these concepts govern the direction of natural processes. Through the example of carbon dioxide mixing and separation, we examine entropy changes during gas expansion and mixing, derive mathematical relationships for entropy and minimum work, and gain insight into the challenges of gas separation in practical applications. Our goal is to understand how thermodynamic principles set the limits on energy efficiency and guide the feasibility of processes like carbon capture.