2: State functions, process functions, and the first law

Energy is not created or destroyed; it is merely transformed from one form to another. 

When you take a course that’s called physical chemistry, you’ve heard that statement a ton of times over the course of your life, in a ton of contexts. You may even recognize that a lot of those contexts are quite imprecise, and they don’t tell you a whole lot. 

Physical chemistry, however, is a discipline that requires precision. We don’t want to use the language that describes energy imprecisely. How we classify the types of energy we will use to describe the physical systems we study is critical work, and we want to take that work seriously.

You’re already familiar with two very specific kinds of energy; we know the phrases kinetic energy and potential energy very well. We instinctively associate kinetic energy with the motion of objects; it’s worth it to think about what kinds of motion go into the specific behavior of gas molecules. That motion doesn’t merely include moving back and forth in more-or-less straight line trajectories - the motion we call translation - but it involves the tumbling of molecules beyond the monoatomic, rotation, and also the wiggling and twisting of the bonds within those molecules - vibration. The fact that monoatomic gas particles can’t undergo rotation and vibration the way that polyatomic gases can turns out to have massive implications in other energy changes. We’ll deal with those later. 

Gas molecules also have potential energy. Again, this could be the simple attraction or repulsion between particles. But this could also be the energy stored within bonds of a molecule, as that molecule starts to pull apart and finds itself pulled back together again. For both kinetic and potential energy, it’s not useful to apply a single equation like ½mv² or ½kx² to the state of an atom or a molecule - we have to study the whole range of the behavior of the molecule to get its energy state. 

And, you might imagine very quickly, that’s complex to do for a single molecule. We really don’t want to do this, molecule by molecule, for an entire container full of literally of billions of billions of molecules.

The power of how we construct the discipline of thermodynamics is found in how we build up quantities that take the properties of individual atoms and molecules and utilize them as descriptions of the much larger whole. Our first definition is of a quantity that takes all of the individual atoms and molecules and adds up all of the kinetic energies and potential energies - all of the translation, rotation, vibration, electric repulsion and attraction, and elastic stretching and compressing. That summed total energy for a specific system is what we will declare that system’s internal energy. 

What can we do to a system to change its internal energy - to add energy to the molecules in the system in all different ways? There are a host of suggestions that we can make, but we will find as we study the possibilities that they can be summarized in one of two ways - as state functions, or as process functions.