Developing intuition for entropy and Carnot limits beyond textbooks

[ScottLH]

I'm a mechanical engineering student struggling to conceptually bridge the gap between the theoretical laws of thermodynamics and their practical application in our heat transfer and power cycles course. I can solve the textbook problems, but I don't feel I truly understand the physical intuition behind concepts like entropy or the Carnot efficiency limit. For engineers who have moved beyond rote memorization, what analogies or real-world examples helped you develop a deeper, more intuitive grasp of these fundamental principles? How do you approach a complex, open-ended problem involving multiple systems, and what mental models do you use to keep track of energy and entropy changes without getting lost in the equations?