1: Measurement, energy, and the quantites of state

This introduction is taken from my first introduction of the content to students in CHEM 411 at Tusculum University in Fall 2019 - the first to study from this material. I still am trying to build this material with these principles in mind.

You have had enough courses that ask you to remember a ton of facts and terms. And you will still need to make sure you know old and new terms for this course, and you will need to be certain you are using those terms precisely, but there’s no good means to test you on the terms themselves as a means to make them meaningful.

You’ve also had enough experience being given equations that are rules and having to use those equations (frequently without much context) to solve simple one- or two-step problems. Those skills are important to build, and I will check skills on equation sets from time to time here, especially when those equations involve calculus. But they don’t need to be our primary business either.

The development of physical chemistry, especially chemical thermodynamics, is a necessarily theoretical discipline. Energy is a constructed physical quantity we use to make our language understandable across disciplines - it doesn’t have the tangibility of force or the broad common meaning of temperature. We can take some of that language and directly apply it to behavior we do see - but even then, much of that is the behavior of gases, which are atoms and molecules spread out over wide distances from one another. We have to make some effort to describe that behavior meaningfully. That effort to describe that behavior demands the use of our imaginations, and demands development of a new language, and demands mathematical descriptions to fit that language - and all must fit together to make a coherent whole.

Our primary business in chemical thermodynamics is the development of a good theory of the transfer of energy through physical and chemical change. My writing in this text, and the problems I assign for you to solve, will all be in support of developing this theory in a meaningful way, in a way that allows you both to understand the richness of the fundamental ideas of energy and to describe energy transfer in practical contexts.

There will be both English-language concepts and mathematical concepts that we will use precisely. I can’t emphasize enough how important it is to not be careless with how you use the mathematics you’ll be developing in this course - tricks you’ve employed in the past are much less likely to work, and points where you’ve taken mathematical shortcuts in the past are much more likely to lead to dead ends now.

But our process in this course is going to be very intentional as well. I will do my best to not assume that you automatically understand some of the core math concepts, particularly calculus concepts. For many - perhaps most - of you, this is the first serious physical science problem solving you will ever do that involves calculus. My development of methods for this kind of problem solving will be patient and total.

I joke that I’m interested in making good theoreticians in this course. But you’ve had a host of good experience in lab sciences where your work is very practical. I want you to master the symbolic and conceptual logic necessary to develop physical ideas using the most powerful scientific tools: pencil, paper, and your mind.