CH 431/What (not) to do

From WolfWikis

The CH 431 comprises an introduction to Thermodynamics. This course has been a common part of the chemistry curriculum for many years and the content has only varied slightly. It is generally considered a difficult course and it often functions as a bit of a lithmus test for a chemistry students.

Its difficulty

1. Why is this course difficult?
   1. Firstly, because it is not based so much on memorization as on understanding of concepts and developing the skill to combine and apply them.
   2. Secondly, the course depends on your math skills.
2. Don't I need to memorize anything?

   Sure, there are things to memorize but that is only part of the job. You do need to 'know your stuff', but just knowing is not enough, you also need to be able to work with it.

Acquiring skill

Skills are acquired through practice. That is why problem sessions and exercises (at the end of a chapter) are important.

Make sure your try and solve problems yourself before checking an answer of asking the TA. Use the problem sessions and the TA well. The more active your role, the better. Some people get together to do problems. That is fine, but make sure you do more than copy the result from someone else. Think of the gym: if someone else lifts the weight, your muscles do not grow...

Do not make the mistake to think that you are supposed to memorize how a problem goes. Olympic athletes do not memorize their weights or treadmills either. They do use them to train and build muscle, stamina and skill. The problems encoutered in a test or -even more so- in real life will undoubtedly be different ones than the ones used for training. What is the same is your brain and what it is able to do!

That also means that you could very well go and find other problems in other books and see what you can do with them. That may well add to your mental muscle. The only problem might be that a different course or book might put different emphasis on different topics. The truth is that there thermo is a very rich subject of which any teacher (or author) must necessarily pick a selection of topics and sadly de-emphasise others.

Math skills

There are only a few topics of math used in Thermodynamics that are perhaps unfamiliar to you and they can be taught as the course progresses.

Multivariate functions

Most of your math was done in x'es and y's. A function was usually written as f(x) = (a + x)² or so.

In this course a function can very well be called ΔG^o_excess and it can be a function of a number of variables, e.g. P,T and x. Mathematically it does not matter whether I call something 'x' or 'Wolfpack', but if I rewrite the function f(x) = (a + x)² as ΔG^o_excess = (Duke + Wolfpack)² this may lead to some reading problems, particularly once you are asked to take the derivative versus Duke at Wolfpack constant. The problem is mostly one of letting your eyes get accustomed to the unfamiliar symbols. If necessary, rewrite the expression in more familiar x and y format. Mathematically you can always substitute!

A good exercise: take a calculus problem that you can easily to in x and y and redo it in G's and P's.

Calculus

The main math problem is that there is a lot of functions of more than one variable and calculus is applied to it. Thus: You really need your calculus. Has it been a while? Has it sunk away? It is a prerequisite! That means it is entirely your job to refresh your memory. Your lecturer is not able to spend his time on redoing a math class you have already had other than surreptitiously. If necessary, take out those math books and practice.

Some common do's and don'ts

Integration limits

Integals always have two limits a bottom and a top one. (You integrate from bottom to top. A lot of mistakes are made with that.

In general an integral like ∫dS can have three types of answers:

1. S + c
2. S_top - S_bottom
3. ΔS (=S_top - S_bottom)

The first case is the indefinite case, where the two limits are not specified. Note that in the last case the d symbol becomes a Δ symbol. The latter is always a finite quantity the former is its infinitesimal cousin (dS obtained by letting ΔS dwindle to nothingness).

For more complicated integrals like ∫1/T.dT, always first write the primitive function (the logarithm in this case) in square brackets: [lnT] together with whatever the two integration limits are and then substitute and subtract: [lnT]^top -[lnT]_bottom.

Logarithms

A very common mistake in thermodynamics is to confuse ln(a)-ln(b) with ln(a-b). It is actually ln[a/b]!

There is a lot of logarithms in this course. Make sure your do not fall in this trap.

Limits

We will not use a lot of limits, but there is a few important ones. First of all of course, all of calculus is one big application of limits and you should be aware of that. For example, see the difference between ΔS and dS above: one is the limit of the other: if we let ΔS go to zero we get dS. To go back we take another limit: lim Σ dS, aka an integral over dS. Nothing about this should surprise you. (If is does: revisit your calculus book!!)

There is also a number of expressions known as limiting laws. These are expressions that only become valid in case a certain limit is taken. A good example is Henry's law. This law says that the vapor pressure P of a solute is proportional to its mole fraction x, but this is only (approximately) true at low enough mole fractions. Mathematically we could write:

lim [P/x] for x->0 = K_H where K_H is a constant for sufficiently small concentrations.

Lectures and lecture notes

1. Prepare for lecture.
   1. Make sure to review what has been done in the previous one. (Good opportunity to find a good question to ask)
   2. Read ahead in book and wiki. Even if you do not understand, it may well fall in place when you hear the lecture.
2. Go to lecture unless compelled to stay away by virusses or other emergencies.
   1. Be as active in lecture as you can: try to come up with a decent question occasionally.
   2. Try to answer questions the lecturer poses, either silently or even loudly (not all at once please). Don't be ashamed to have it wrong: often that is even better than having it right, because it allows to get it right (and also your lecturer to expain it better).
   3. Make notes. Use shorthand or skribble, whatever, but make sure you revisit your notes in time so that what was left unwritten is still in memory.
3. Process the lecture
   1. After lecture, preferably the same day, revisit your notes, compare with those of others, with the book and or with the wiki, whatever works best for you. Twenty minutes after lecture is optimal (but not always possible of course), because human memory has a number of different time scales, a very brief one, a medium one and a long one. There are things in medium memory you want transfered into permanent storage.

Do not let it all slip to one big cram the last few days before exam. The material cannot be learned in such a small amount of time, because skill can only be acquired gradually

Take homes

Consider a take home an adventurous challenge: here is the jungle, your are tarzan, go find the treasure. Some students find the questions daunting, because they do not realize the power of their own brains. Give your brain some credit. It can do more than you think!

Are you stuck? Try using an index and a key word and read something. Maybe you missed something. Isn't there something analogous or similar? Seek and ye shall find.

Exams

What to do and what not

Reading questions

The way questions are worded is typically such that it gives you the necessary information to solve the problem. Maybe the information is hidden a bit and it is your task to dig it out. Read well!'. Read more than once!!! If the problem gives you hints, it is usually worth your while to consider how that information could be used. For example if a formula is mentioned or given, try to fill in some numbers and see what you can get from it. It may not give you the complete answer, but it might take you halfway or inspire you to find the whole answer.

If a formula is not given, see if the text does not give you a clue what formula might be useful. Check if you have the appropriate bit and pieces to put in the formula and get something else out. If not you may be barking up the wrong tree.

Symbols and reading formula's

Make sure you know what every symbol in a formula stands for. Note that some symbols can be used for more than one concept. The symbol A for example could stand for a surface area, but also for the Helmholtz free energy. Make sure you take the right one. The question will often tell you. Notice also that nothing is easier than making typo's in formulas. If a given formula does not seem to make sense, please do ask whomever is proctoring.

'Crawl into the formula', if you can. For example the formula contains the derivative (∂P/∂T) |_V. Imagine what it does. How would you keep that volume V the same? How would you change that temperature T? How would you measure what it does to the pressure P? The symbol stands for a whole experiment in a nutshell!

What are the limitations of the formula?

Many formulas are only valid in specific cases. For example many expression are valid only for an ideal gas. If the gas is not ideal the formula is different. If you have a solid yet another expression may hold. Some laws are only valid in a limited range or in a limiting case in the mathematical sense of the word limit. It is your job to know this about a formula, otherwise you end up using the wrong one in the wrong case. (As said above: you do have to memorize some things).

Don't be spooked

If the first question looks daunting, do not be spooked! First find another question you find easier to answer. Often your brain will continue to process the daunting one in the background. You may find that once you read it again, it proves a paper tiger. It is often good practice to just read through all the questions before picking up a pen.

The eve of the exam

Make sure you set a decent deadline for when to stop studying.

Many students make the mistake to study heavily the evening before the exam, often deep into the night or even through the night... This is a well-known recipe for disaster. To do a test properly, you need to be alert, awake and in top mental shape. A foggy, sleepy or drugged brain is not going to get you through the exam with flying colors. On the contrary: many students have ended up with unnecessarily low grades this way. Set a deadline: e.g. no more caffeine after 4 pm, no more cramming after 8 pm, then relax and go to bed early. Think of training for a sport event. There is no point in training yourself to death the last evening. You should train the whole semester, regularly. Whether you have done that or not: the last evening is not going to make the difference, other than making you fail unnecessarily.