Thermodynamics in Song

Over at the World’s Fair, they’ve posted a song about love and thermodynamics.  This made me wonder, are there more thermo songs out there?  A quick search turned up just one (scroll down to the Flanders and Swan section).  If anyone who reads this knows of more, please post them in the comments section.

Some Questions

Here are some questions that a student who has been studying thermodynamics should be able to answer:

1. How would you explain the difference between phase equilibrium and a phase transition to a student in general chemistry? Better yet, if you were a student in physical chemistry, who had just worked through some activities on vapor pressure and single component phase diagrams, how would you explain the difference to another student in the class?
2. Why don’t equilibrium constants have units?

A Unifying Theme

It has been quite a while since I’ve posted anything, and I apologize to all the tens of readers I have out there. I admit, I’ve been somewhat lazy, but I’ve tried to make sure that everything else I have to do got done. I guess this blog is lower priority.

We have been hitting a variety of topics in class, from chemical equilibrium to phase equilibrium, and a few places in between. What do they all have to do with one another? Quite simply, ΔG. And the good news is, that won’t go away for a while!

Spontaneity and… CHEMICAL POTENTIAL!

So, now you know what the title of this blog really is! We’ve developed an array of different quantities that tell us if a process will occur irreversibly (i.e., the final state can’t get back to the initial state following the same pathway). I don’t really like it, but this is the definition of spontaneous. I’d much rather just leave it irreversible, but I’m fighting history here.

The three quantities we have are ΔS _total, ΔG (the change in the Gibbs free energy), and ΔA (the change in the Helmholz free energy).

Good questions?

We are now officially in spring break mode.  Great job in class yesterday by the way.  If you think of questions for me, be sure to email them or post them here before we resume classes.  I have a couple of questions for you to start thinking about:

1. What is entropy?
2. What is temperature?

Some form of the first question will appear on the exam after break.  Some form of the second will show up on the third exam.

Entropy

The Energy of the World is constant.
The Entropy of the World tends towards a maximum.
-Ruldolf Clausius, 1865

Here’s a question for you. Is it possible to build an engine that just runs on the thermal energy of the surroundings? You’ve learned that temperature is related to thermal energy, and so it seems reasonable to think that if the temperature isn’t 0 K it should be possible to utilize that energy. Right? Couldn’t this solve many of our energy related problems? Inexpensive energy for developing nations, cars that run of the warm air around them (therefore no CO₂ emissions) … Sounds wonderful. In other words, why not simply convert heat directly into work?

I’d like to pull a quote from one of my favorite texts on Thermodynamics, “The Second Law: An Introduction to Classical and Statistical Thermodynamics” by Henry Bent (Oxford, 1965):

As it turns out, this (getting energy from the surroundings) is rather like asking a cold man to warm himself on the energy of an icicle. Nothing in the First Law prohibits the transaction icicle colder – man warmer; nonetheless, it is well known that energy transfers of this kind never occur.

I added the parenthetical (sorry Dr. Bent…). I think the last part is the most important:

“nonetheless, it is well known that energy transfers of this kind never occur”

The First Law only governs what happens to energy. It’s a boring law. It only says that the total energy change in any process is zero. Wow, energy is conserved. Whoop-de-do. The First Law says nothing about what will or won’t happen. This is where the Second Law becomes important.

Heat Capacities and Enthalpy

Molar heat capacities, as you well know, are related to the amount of energy needed to raise the temperature of one mole of a substance by a Kelvin. You also know that heat is a path function, so that heat transfer under constant volume conditions is different than it is under constant pressure conditions. Therefore, we end up with two heat capacities:

and

Using these relationships, it is possible to determine many quantities. You’ve seen several examples of their use already in general chemistry, where you did coffee cup (constant pressure) calorimetry to determine the change in enthalpy of several different reactions. This week, we’ll try some constant volume calorimetry to determine the calorie content of gummy bears (aka the great gummy bear burn off!).

Putting it all together

At this point, you know how to determine ΔU, ΔH, q, and w for almost any process. Yesterday in class, I put a problem up on the board, that showed the following cycle on a P-V diagram (aka an indicator diagram):

I asked you to set up the necessary calculations to determine ΔU, ΔH, q, and w for each step and the entire cycle, assuming a monatomic ideal gas.

Enthalpy and PV

Sorry for a late post – grading took over my life for a little while, but now I’m back. We’ve been studying the first law, and have developed some basic ideas about work, heat, energy and the first law. All of this can be summarized in two equations

We already know how to determine the work done for several processes, and today we’ll learn how to determine q. To think about the second equation, we looked at several models involving a gas phase reaction under the following conditions:

The First Law

A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.

Albert Einstein

Now that, folks, is quite an endorsement. We are on our way now, and there’s no turning back. The beauty of thermodynamics – the mathematics, the chemical insights, the physics – is a large part of what made me want to be a physical chemist in the first place. Spectroscopy and lasers of course, are what really iced it for me.

None of that has anything to do with the first law of thermodynamics, which states that the total energy of the universe is constant: