How to study for the final

I've had a couple of folks inquire as to the best way to study for the final. Here are my thoughts on that.

It is very easy to feel like there are a tremendous number of equations, processes, and special cases to deal with, particularly in the last few chapters on engines that we covered this week and last. You should not try to memorize each and every case. Instead, you should try to understand what are the systematic approaches you take to solve these problems so that you can tackle any problem!

So what should you know? How should you approach a problem?

(1) Sketch out complete diagrams. Make flow diagrams, labeling streams in complete detail, if it is an open system. Make PV diagrams, labeling all points and processes, including work and heat flows and their signs. Making complete diagrams should tell you immediately what is known and what is unknown. Moreover, this process helps you translate the textual description of the problem into a clearer more organized format that will be easier to work from.

(2) Apply the fundamental equations. We wrote these out for you on a handout so you could see what these are. Each and every problem you have tackled can essentially be worked out starting from these equations. The book spends a lot of time deriving special case formulas based on these, but it is much more productive for you to understand how to get from the fundamental equations to the final answer without having to flip through the book looking for the specific case formula (which can often cause you to make errors during exams if you are time crunched and don't read the text surrounding the equations). On the exam, our main intent for having open book is so that you have access to reference data like heat capacities, equation of state parameters, etc. You should not have to flip through the book to find equations for each problem.

(3) Use variables as much as possible, and plug in numbers at the very end. This helps prevent numerical and units mistakes.

(4) Do consistency checks. Do the units work out? Are the numbers physically reasonable?

In studying for the final, I would recommend you go back to all of the homework problem statements. Look at the problems, without looking at the solutions, and ask yourself: "Can I solve this right now from the fundamental equations, without looking up a bunch of formulas in the book or reading the text?" If you can do that, you are good to go. If you can't, I would try to sketch an outline for the solution to that problem again starting from fundamentals.

A good way to test yourself would be to pick one of the application-oriented problems from the book in the later chapters we've been studying, and see how far you can get through it without having to rely on text in the book.

Prof. Chmelka and I will both be around next week if you would like to see us. You can come in if our office doors are open; otherwise, feel free to shoot us an email to find a good time to meet.

MSS