Open Book Versus Closed Book

With rare exception, most of my exams have been open everything (textbook, notes, anything the students want to bring with them). Recently, in Thermodynamics, I have had one exam closed everything - these have included questions on mathematical manipulations involving thermodynamic variables and relations between them. For example, students will have to prove that the ideal gas heat capacity at constant pressure is not a function of pressure or that the Joule thompson coefficient for an ideal gas is zero (and so on). What I do is prepare a set of questions (with detailed answers) and provide that to the students to study, for about a week. I then select questions from that list for the exam. Thus, students have had an opportunity to study the questions (and answers) and I expect that they would do well.

I am wondering if this is the best way to teach students about how to manipulate thermodynamic variables. Are many simply memorizing the steps? (Rather difficult I'd say, I am very strict about the grading - I want to see close to perfection for a good grade since the students have had a week to study the questions and answers). Do they remember the manipulations long after the exams?