# Physical Chemistry – Overview of Thermodynamics

Song: the Laws of Thermodynamics by Flanders and Swann:

The challenge of teaching thermodynamics to physical chemistry life science students is to have them understand the relationships between the macroscopic properties involving heat, work, energy and entropy. After dispelling the myth that energy is stored in chemical bonds; after introducing the concept of temperature, and contrasting it to heat capacity; and after doing some introductory examples, I give an overview of the Laws of thermodynamics. The purpose is to encapsulate the ideas in simple terms in an effort to dispel angst.

http://en.wikipedia.org/wiki/Classical_thermodynamics

In one example I use bond energies to calculate the energy per mole of sucrose and TNT (the explosive trinitrotoluene). Most students expect that TNT has more energy, but it turns out the two have about the same. So why is TNT an explosive (actually a detonation)? TNT burns rapidly and involves a huge volume change. It is the rate of reaction (chemical kinetics) and the rapid volume change that causes the explosive damage. Then I can move to the thermodynamics overview.

In fact these ideas are readily accepted by the students but that is not the issue. The issue is to translate these into useful mathematical representations so they can be applied to their particular area of interest. Since basically all the equations of thermodynamics can be concisely can be placed on a page, the problem is those equations take some time to appreciate.

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From Chapter 6 of Laidler, Meiser and Sanctuary, Physical Chemistry.

I do NOT show students this at first. (click to enlarge)

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“Thermodynamics”, I say, “is a macroscopic theory that gives no numbers. All it gives is the relationship between quantities we can measure under different conditions. The numbers come from comparison with experimental data.”

Of course this is the problem: too many conditions. I refrain from talking about reversible and irreversible at this stage and contrast two common cases:

- Bench top experiment at constant temperature and pressure: a reaction occurs in a lab on a table. Hence the temperature is room temperature and the pressure is the atmospheric pressure.
- Bomb calorimetric experiment at constant temperature and volume: a reaction occurs in an apparatus that has constant volume because the volume is fixed. Since the apparatus is immersed in a heat bath, the temperature is constant.

I think this makes sense to them: I show pictures and animations.

Now I say that thermo is concise and is summarized in four laws:

- The Zeroth Law of thermodynamics: thermal equilibrium.
- The First Law of thermodynamics: conservation of energy
- The Second Law of thermodynamics: heat won’t flow uphill
- The Third Law of thermodynamics: at absolute zero of temperature, the entropy of a perfect crystal is zero.

**The Zeroth Law of thermodynamics:**

When two bodies are in thermal contact their temperature is the same and no heat flows between them.

Objects in thermal equilibrium have the same temperature

Well that is easy.

**The First Law is conservation of energy,**

Now I mention the system, which is the engine in this case, and the surroundings, a hot heat source and the cold outdoors. Heat flows into the engine from the hot reservoir (we pay for that heat), and the engine produces some work and the rest is ejected into the cold reservoir.

This introduces the sign of energy. When energy goes into the engine it is positive and when it comes out the signs are negative, so the energy balance is

*q _{h} = q_{c} +w*

The First Law concept is also easy to grasp.

**The Second Law says heat won’t flow uphill**

Heat flows from a hotter to a colder

Whereas the First Law is about energy, the Second Law is about entropy. Entropy is a measure of the randomness of a system. It is a substance as tangible as energy.

Examples of entropy of substances

**The Third Law says that at zero K a perfectly ordered crystal has entropy of zero.**

When we measure the energy of a substance, we take the difference between the start and finish of a process. This means there is no absolute energy. In contrast entropy does have an absolute value. If a substance is cooled to absolute zero of temperature, (-273 C) then there is no motion and so a crystal has only one state. That is, if the position of one atom in the crystal is known, then the position of all the others is known. A system with one state only has zero entropy.

The Second and Third Laws involve entropy, and are more challenging conceptually than the Zeroth and First Laws.

I state that this overview encapsulates what we will study for two months.

I usually teach a two-semester 6 credit course in P. Chem. I & II each summer after retiring from full time teaching. I tried to condense my notes into a text “Essentials of Physical Chemistry” (CRC Press, 2012) by selecting key topics but not sparing the math details. My class contains several Majors including a lot of Biochemistry and Forensic Science Majors. My pet peeve is that I have to teach multi-variant calculus and differential equations as I go because the American Chemical Society has allowed degradation of requirements in basic university mathematics. On top of that recent ACS requirements only insist on one semester of Physical Chemistry, although most major university programs have sensibly retained two semesters in their internal degree requirements. The cause of this degradation of standards is the inclusion of Biochemistry and Inorganic Chemistry as required in upper level courses. I have included the triple-point of Iodine as used in fingerprint analysis and Michaelis-Menten enzyme kinetics for Biochemistry majors along with emphasis on Powell’s five-equivalent d-orbitals in ferrocene bonding for a contact with Inorganic bonding. Emphasis is also on the application of the Particle-on-a-Ring energy levels to the (4n+2) rule for aromaticity in Organic Chemistry. I make use of mnemonic chants such as HUGA, HUGA, etc. for the basic Thermodynamic equations including the Maxwell relationships for partial derivatives. The point of this message is that even when you try very hard to include a maximum of connections to other sub disciplines in Chemistry the over riding limitation is the background in mathematics of typical students! At the present time I have to teach substantial portions of multi-variant calculus, differential equations and basic vector analysis as well and was told by a Chemistry Department Chairman that is the way it should be! I do this by requiring memorization of (Cp-Cv) (Ideal Gas and General Case), the A->B->C kinetic scheme and the Michaelis-Menten Km derivation for the case of a Competitive Inhibitor as well as the basic treatment. Memorization may not be the best form of education but homework using specific examples are intended to reinforce the derivations. Personally I took undergraduate courses where equations appeared without derivation and homework consisted of “plug-and-chug” solutions. I always yearned to know where the equations came from and now I always try to provide the whole derivation as for Poiselle’s Law of laminar flow applied to blood viscosity. I was told by the Chair of Forensic Science to say “blood” and “bullet” as often as possible in lecture and the Pre-Med. students need to hear “aorta” and “heart” as well, so the viscosity of blood provides a justification of the derivation of Poiselle’s Law. The point I am trying to reinforce here is that even with carefully selected applications the TIME FOR LECTURE MATERIAL IS REDUCED BY HAVING TO TEACH NECESSARY MATHEMATICS! My conclusion is that the B.S. in Chemistry is now spread too thin trying to expose students to every sub discipline at the expense of basic education in background Mathematics. Maybe this is partially the fault of Mathematic courses being too abstract, although I believe that most “Engineering Math” courses try to make connections to applications. On one hand maybe the whole country only needs about 100 good Ph.D. Chemists per year from the U.S. system so let the cream rise to the top through sheer ability? No, our society is now more dependent on technology than ever so we do need to think through how to provide thorough basic education based on a solid foundation in Mathematics, but at an applied level!

Don Shillady

Emeritus Professor of Chemistry

Virginia Commonwealth University

Thanks for your comments and I agree that the math preparation of many students is inadequate. When I teach honours courses, then I do what you do and teach the math as I go, but not when I teach p. chem. to life science students. In that case the only new thing I introduce is the partial derivative. Then I tell them they do not have to integrate or differentiate anything harder than lnx (1/x) and xn.

I guess I have to disagree with memorization of any p. chem. I try to discourage this as much as possible.

It is nevertheless a challenge to teach these courses which are required and usually unpopular. I get average course evaluations, and to me this is really above average when all those popular and rote course are included.

This is a nice BLOG, maybe I can help stimulate further interest in a subject of interest to both of us. You are free to suppress my comments if you wish but I want to comment on the concept of memorizing Physical Chemistry topics. This summer I coined a new term/word: “Learnalize” = Learn + internalize + memorize. We should remember that Chemistry majors are usually fresh from a year (hopefully) of Organic Chemistry and Biochemistry students have had to learnalize things like the Krebs Cycle. With demonstrated skill in memorizing massive amounts of non-mathematical information why not harness this developed talent to mathematical treatments? The way to make this process more than rote memorization is to assign homework and give test questions requiring a sequence of mathematical steps. This develops math skills if clean examples are chosen where no approximations are needed. Examples are the derivation of “a” and “b” parameter formulas from the Critical Point of a Van der Waals Gas, (Cp-Cv) expressions, A->B->C kinetics, the energy levels of a Particle-on-a-Ring etc.; wherever there is a clean calculus/algebraic sequence of operations. Then reinforce this with numerical examples. I was converted to this approach as an undergraduate by my friend Prof. Jim Harrison (now at Mich. State Univ.) when we were classmates using a “plug-and-chug” textbook by Maron and Prutton (2nd. Ed.). For a problem in liquid diffusion all we had to do was plug some constants into a formula, but Jim decided to show a First-Principles derivation of Fick’s Law first and then solve the problem when it came time to put our homework on the board in class. My reaction was “Wow, that is where Fick’s Law comes from!”. Since that time I have told my class what I wanted them to learn and then tested them on those derivations and I construct my tests so that thinking-problem solvers have half the questions and memory-dumpers have the other half of the questions so that both approaches are tested. I claim that many teachers do not get the full response from their students by being afraid of “using too much math”. I have found that students can learnalize quite complex math derivations and use them in applications if you just tell them they are required to learnalize that material. I have had students give the full derivation of Poiselle’s Law of laminar flow, the A->B->C kinetic equations and even the full derivation of the Planck Black-Body radiation equation and of course I give extra credit on the tests when they do these heroic treatments in a test situation. One Senior student adamantly spoke out against the full derivation of the A->B->C kinetics saying that he would likely never see that in a real-life situation but I was sitting behind him in a seminar the next afternoon when a graduate student presented a time-developing NMR sequence and he used the NMR peak heights to find the rate constants for a case of three species. Another example is to use an egg carton as a “beaker” to demonstrate the application of Sterling’s Approximation for the Entropy of Mixing for binary liquids. I use red and white poker chips which fit nicely into the egg positions and you can demonstrate distinguishability/indistinguishability by numbering the chips on one side and then turn them over to show the entropy is zero for a perfectly ordered system. The students can calculate Stirling’s Approximation on their calculators for low numbers using a one dozen crate/beaker but most calculators give overflow for more than about N=69 so the use of a “one-dozen beaker” is about right for using a calculator. The entropy of binary mixing can easily be required as a derivation and to show the entropy is a maximum for a 1/2 amount of both species. The point I am laboring over here is that Physical Chemistry teachers should recognize that students who pass Organic Chemistry and Biochemistry should have no difficulty learnalizing math derivations which are clean applications of calculus/algebra and in my opinion we are letting them get off too easy so that they are handicapped for further applications in their future careers. I offer my “Rate My Professor” record as proof that P. Chem. with full Math derivations can be FUN if the teacher includes some full derivations. Perhaps these comments will stir up some further discussion?

Don Shillady

Emeritus Professor of Chemistry

Virginia Commonwealth University