What is temperature?

Temperature is NOT the average kinetic energy.

When I taught thermodynamics to second year undergraduates one of the preconceived notions that was hard to dislodge from students was that temperature IS a measure of the average kinetic energy of the atoms or molecules in a system.

First, I will give the merits of this view and then explain why it is problematic.

A profound and important insight from Maxwell's kinetic theory of ideal gases was that the average kinetic energy of the atoms/molecules in the gas is related to the absolute temperature defined by Kelvin. This result was important because it provided a microscopic basis for Joule's discovery of the mechanical equivalence of heat.

The result does not just hold for an ideal gas. Classical statistical mechanics can be used to show that for any system of interacting particles, the average kinetic energy of each particle is 3/2 kT. The proof proceeds in the same manner as the equipartition theorem. In the partition function, the integral over momentum factorises and can be evaluated exactly as it is Gaussian integral.

However, this simple relationship between temperature and kinetic energy does not hold for quantum systems. Consider the case of a harmonic oscillator, with frequency omega. By the virial theorem, the average kinetic energy is equal to the average potential energy. Thus, the average kinetic energy is half of the internal energy U(T), which is a universal function f(T/omega). Thus, if we compare two oscillators with different frequencies, at the same temperature, they will have different kinetic energies.

This problem is not just some quantum exotica that is only relevant at extremely low temperatures. Most solids are "quantum" at room temperature because they have a Debye temperature in the range of 200-1000 K.

Temperature is a macroscopic variable, not a microscopic one. It should be defined in terms of the zeroth law of thermodynamics.

Temperature is a state variable associated with a system in thermal equilibrium. It tells us whether that system will be in thermal equilibrium with another system. Consider two separated systems with temperatures T1 and T2. If they are brought into thermal contact, their states will not change if and only if T1=T2.

A thermometer is a system with a single state variable. The value of that variable is an empirical temperature.

Aside. This view of temperature was used by Planck in his book, Treatise on Thermodynamics, first published in 1905.

I am thankful to my undergraduate mentor, Hans Buchdahl for teaching me that thermodynamics is conceptually coherent and beautiful. 

This discussion illustrates that temperature is an emergent property. It is a property of a macroscopic system that the parts of the system do not have. The temperature is independent of the microscopic composition of the system or its history. This universality is a characteristic of many emergent properties.

In another post, I hope to explain what the absolute temperature, first introduced by Kelvin, is.

Maxwell's demon and the history of the second law of thermodynamics

I recently reread Warmth Disperses and Time Passes: The History of Heat by Hans Christian von Baeyer

As a popular book, it provides a beautiful and enthralling account of the discovery of the first and second laws of thermodynamics. The book is a great companion to teaching and learning thermodynamics and statistical mechanics. The narrative is unified by the puzzle of Maxwell's demon.

Aside: The book was first published in 1998 with the title Maxwell's Demon. My guess is that the publisher changed the title because most people have probably not heard of the demon, unlike Schrodinger's cat.

Baeyer captures both the wonder of the subject and the fascinating story of how the science of thermodynamics developed. He describes quirky personalities and illustrates how science proceeds with a mixture of brilliant insights, clever experiments, false leads, and forgotten discoveries. It is easy and compelling reading.

I appreciated that there is a lack of hype, in contrast to too many popular science books.

The book is enhanced by showing that the story is not over. Many reports of the demise of the demon have been premature. The penultimate chapter discusses Zurek's definition of entropy in terms of algorithmic randomness. The last chapter considers molecular motors, such as kinesin, which can be viewed as ratchets driven by thermal noise.

Physical insights

The first and second laws tell us something about the fundamental nature of the universe. Although they are macroscopic and may have some (debatable) microscopic justification,  they can be viewed as fundamental.

Central to the development of the first law was the notion of the mechanical equivalent of heat.

There are three rather different ways to formulate the second law: a Carnot cycle represents an engine of optimal efficiency, heat never passes from a cold to a hot body, and the arrow of time. It is profound that these formulations are equivalent and not something that was anticipated. We should marvel at this.

Entropy can be viewed as the absence of information. Consequently, the second law can be viewed as statistical.

Things I want to understand

A good book stimulates us to want to engage more with its subject. Some things I want to understand are the entropy of the initial state of the universe, Boltzmann's H theorem, Feynman's ratchet, Shannon's information theory, molecular motors, Zurek's definition of entropy, and Gerald Holton's book, Thematic origins of scientific thought.

A recent tutorial is A Friendly Guide to Exorcising Maxwell’s Demon, by A. de Oliveira Junior, Jonatan Bohr Brask, and Rafael Chaves

Beautiful things missed

As a popular book, I think the length and scope of topics are right. Nevertheless, in a longer book, here are some things I would enjoy reading about: the zeroth and third laws, the contributions of Gibbs, the ergodic hypothesis, Brownian motion and evidence for atoms, the role of thermodynamics (and statistical mechanics) in the development of quantum theory (blackbody radiation, Einstein solid, identical particle statistics, and the Sackur-Tetrode equation) and perhaps phase transitions.

Two quibbles

von Baeyer has a somewhat reductionist perspective that the true nature of thermodynamics was revealed by the microscopic descriptions of Maxwell and Boltzmann.

I will write separate posts on why I am not comfortable with the following two statements.

Temperature IS the average kinetic energy of molecules.

Entropy was mysterious until Boltzmann's definition S=k ln W. 

Ising model basics

The Ising model is a paradigm in both statistical mechanics and condensed matter physics. Today for most theorists it is so familiar that some of its historical and conceptual significance is lost.
Previously, I posted about what students can learn from computer simulations of the Ising model.

If you had to talk about the Ising model to an experimental chemist what would you say?
[Last week I had to do this].

The Ising model is the simplest effective model Hamiltonian that can describe a thermodynamic system that undergoes a first-order phase transition and has a phase diagram containing a critical point.

On each site i of a lattice one defines a spin sigma_i= +1 or -1, representing spin up or spin down.

The Hamiltonian H is

J_ij describes the interaction between spins on sites i and j. In the simplest version the interactions are only between nearest neighbours, and have the same value J.
h is the external magnetic field.

If J is positive, the ground state at h=0 is a ferromagnet.
If J is negative, the ground state at h=0 is an anti-ferromagnet for a bipartite lattice.

[Caution: just like for the Heisenberg model, some authors define the Hamiltonian with the opposite sign of J].

For h=0 there is a critical point at a finite temperature Tc, for lattices of dimension two and higher.

The spins sigma_i= +/- 1 defined at each lattice site i, were originally to represent the atomic magnetic moments in a ferromagnetic material. However, the sigma's can represent any two states of the site i. For example, the ``spin'' or pseudo-spin can represent the presence or absence of an atom or molecule in a ``lattice gas'', atom A or atom B in a binary alloy (mixture), or the low-spin and high-spin states in a spin-crossover material.

The mean-field theory of the Ising model is mathematically equivalent to the thermodynamic theory of binary mixtures with an entropy of an ideal mixture.
There is a nice discussion of such mixtures in Section 5.4 [and the associated problems] of Introduction to Thermal Physics by Schroeder.
[Here are the slides for a lecture I have given based on that text].
Chapter 15 of the text by Dill and Bromberg is also helpful as it has more detail.
Neither text makes an explicit connection to the Ising model. Following this paper on alloys, one has

This is shown in Section 8.1.2 of James Sethna's text, Statistical MechanicsEntropy, Order Parameters and Complexity.

When interactions beyond nearest-neighbours are included in the Ising model or when the lattice is frustrated (e.g. fcc or triangular) a richer phase diagram is possible. Examples include the ANNNI model and some models for spin-state ice considered by Jace Cruddas and Ben Powell.

What can students learn from an Ising model simulation?

Computer simulations can provide significant insight into different physical phenomena. Two decades ago the best one could do in a class or seminar was show screen shots of simulations and try and explain what was going on. Now one can show a simulation live and even vary parameters in real time to provide insight. I have done this quite a bit with Solid State Simulations.

One simulation I like but have never used effectively is that of the Ising model.
See for example, Daniel Schroeder's simulation or James Sethna or Matt Bierbaum.
What does it help me understand?
The main ideas are the concept of symmetry breaking, the correlation length, and the divergence of the correlation length at the critical point.

1. Watching the different configurations changing with time illustrates the notion of an ensemble.
2. At high temperatures one sees the paramagnetic phase where the spins are independent of each other and so there are no domains.
3. As the temperature approaches the critical temperature (T=2.27J) from above the correlation length increases and large fluctuating domains form.
4. Below the critical temperature large domains form and fluctuate less and less as the temperature lowers.
5. The ferromagnetic ground state (blue or yellow, up or down spin) in zero external field depends on the history. This illustrates symmetry breaking

Any other things?

Basic introductions to Condensed Matter Physics

Suppose a motivated and intelligent high school student or first year undergraduate comes to you and says, ``Condensed matter physics sounds really cool! What should I read or look at to learn more about it?"

Obviously, suggesting the student look at classic graduate texts such as Ashcroft and Mermin or Chaikin and Lubensky is not helpful. They need something that will inspire them to want to learn more as well as introduce them to some of the basic ideas and topics.

I would suggest the following.

David Pines, Unit 8 in Physics for the 21st Century, an on-line course
Emergent Behavior in Quantum Matter

Robert Laughlin, A Different Universe: Reinventing Physics from the Bottom Down

Stephen Blundell, Superconductivity: A Very Short Introduction

Rodney Cotterell, The Material World

But when then have read some of these it would be nice if the student could look at something more technical. To second year undergrads I give a series of lectures on Thermodynamics and Condensed Matter Physics. They don't need to know any quantum or stat. mech., just some thermo, and they can still get some of the flavour, excitement, and scope of the subject. But, I don't know a book that lays this material out clearly and simply. I draw on Schroeder, Thermal Physics, but it has no discussion of superfluids, order parameters, or symmetry breaking.

What do you think are good resources?

I thank Alex Agedah for asking this question.

Update. Here are some slides for a talk that Danielle McDermott gave on the subject. It lists many useful resources. (She mentions it in a comment below).

Phase diagram of snowflakes

I like "collecting" interesting phase diagrams, partly because they are fun to show students when teaching introductory thermodynamics. I recently discovered the one below that I feel I really should have known about. It shows the morphology of different snow crystals as a function of temperature and water supersaturation (relative to ice).
It should be pointed out that this is a non-equilibrium phase diagram as it involves supercooled liquid water.

The figure below is taken from the beautiful review
The physics of snow crystals 
Kenneth G Libbrecht

This diagram was originally constructed by Ukichiro Nakaya in the 1930's. The physics behind it is still poorly understood.

I came across the diagram while browsing through the Forces of Nature book by Brian Cox and Andrew Cohen.

While on the subject here is a nice video.

Broken symmetry, order, and entropy

One of the greatest joys of teaching is having students ask questions that you do not know the answer to. In the last week of the course PHYS2020 Thermodynamics and Condensed Matter Physics for second year undergrads at UQ, I give two lectures about critical points, universality, critical exponents, broken symmetry, order parameters, and Landau theory.

Many students find this quite challenging. However, I think it is important that students be exposed to two of the most important ideas of theoretical physics from the twentieth century: broken symmetry and universality. Furthermore, there is no technical reason why second year undergrads cannot learn this material. Since the text, Thermal Physics by Schroeder, does not cover this material we have finally settled on a chapter from a book by Hoch.

After my last lecture, a student asked an excellent question along the lines of
"Why is it that broken symmetry occurs at lower temperatures?
How is this related to entropy and order?"

This led me to wondering whether there were any rigorous results that answer the question. I could not find anything in a quick search.
Do you know of anything?

I was wondering whether something like the following conjecture was true:

Conjecture. Consider a physically reasonable Hamiltonian H for an infinite system. Suppose H is invariant under some symmetry group G. Let rho(T) be the equilibrium density matrix at temperature T. Then for sufficiently large T, rho(T) is also invariant under G.

Maybe this is equivalent to

Lemma. At sufficiently high temperatures, the von Neumann entropy S (rho) = - Tr( rho ln (rho)) is maximal if rho is invariant under G. 

This looks to me like the kind of thing that people like Elliot Lieb, David Ruelle, Y. Sinai, ... might have tackled at some point.

I welcome ideas and suggestions.

A fascinating thermodynamics demonstration: the drinking bird

I am currently helping teach a second year undergraduate course Thermodynamics and Condensed Matter Physics. For the first time I am helping out in some of the lab sessions. Two of the experiments are based on the drinking bird.



This illustrates two important topics: heat engines and liquid-vapour equilibria.

Here are a few observations fo in random order.

* I still find it fascinating to watch. Why isn't it a perpetual motion machine?

* Several more surprising things are:
a. it operates on such a small temperature difference,
b. that there is a temperature difference between the head and bulb,
c. it is so sensitive to perturbations such as warming with your fingers or changes in humidity.

* It took me quite a while to understand what is going on, which makes me wonder about the students doing the lab. How much are they following the recipe and saying the mantra...

* I try to encourage the students to think critically and scientifically about what is going on, asking some basic questions, such as "How do you know the head is cooler than the bulb? What experiment can you do right now to test your hypothesis? How can you test whether evaporative cooling is responsible for cooling the head?" Such an approach is briefly described in this old paper.

* Understanding and approximately quantifying the temperature of the head involves the concept of humidity, wet-bulb temperature and a psychometric chart. Again I find this challenging.

* This lab is a great example of how you don't necessarily need a lot of money and fancy equipment to teach a lot of important science and skills.

The shape of nature

I watched the first episode of The Forces of Nature narrated by Brian Cox, The Universe in a Snowflake.
[Unfortunately, I don't think the whole episode is free online. It should be! I watched it streamed through my university library website].

The imagery and creativity are stunning.
The episode focuses on shapes that occur in nature: spherical planets, human towers in Spain, hexagonal snowflakes, honeycomb beeswax, and "spherical" manatees, animals with bilateral symmetry,  ...
Cox nicely discusses some of the underlying principles, including how complexity emerges from simple underlying laws.

How do bees "know" that a honeycomb structure is optimal? This relates to a simple example of symmetry breaking and the much more difficult honeycomb conjecture that was only solved in 1999.

Value of student pre-reading quizzes. II

Following up on my previous post, below are some selected comments I got from students in my thermodynamics class last semester. 

A couple (in bold) comment on how the lectures help understand the reading.

But, there is an interesting follow up. Since the students now have their grades I received the student evaluations. Some complained strongly that the lectures were poor/useless because they just repeated what was in the reading. Others complained that I did not answer all the questions they raised in the reading. 

I am sure I can do better, but this just highlights to me that it is impossible to keep all students happy. 

For some you go too fast, some too slow. 

For some you give too much detail, others not enough detail. 

For some you follow the book too closely, for others not closely enough. 

For some you repeat things too much, for others not enough.

I would really like to go through the derivations and maths in class. It's so much harder to read than it is to see it being written on the board.

Some things are much easier for me to understand after the lectures. The constant K is exponential decay depending on the change of G and inversely to the T. I'll understand Q2 better after the lecture.

The most interesting was definitely the section on the construction of the phase diagrams from the free energy graphs over various temperatures. I've used phase diagrams extensively before, but have never been taught how they are constructed bar experimental measurements of the temperatures at which solidification begins and ends over a range of compositions. It's great to finally see a theory-based, thermodynamic construction that supports the experimental measurements.

The section on the Eutectic point and eutectic phase changes was confusing at first, then really cool and interesting when I understood. This really strikes me as being a useful application of thermodynamics!

I have just studied phase diagrams for solid solutions in MECH2300 so it was nice to get a better look behind the curtain at what gives the phase diagrams their shape. Thanks Gibbs.

I wish I could learn PHYS2020 through Osmosis

I felt that the section on the osmotic pressure and the derivation of the equation was a little bit rushed and difficult to follow. Also, who lead the Israelites through a semipermeable membrane? ......Osmoses. Get it? Cus... Cus... yeah alright... that's all.

I never had any idea diffusion to was just due to a pressure difference. Now that i think about it it maes sense but it never even crossed my mind why this occured other than simply because mixing would increase entropy and the membrane was permeable. This new interpretation of the event is really interesting.

Of all the reading I was very pleased to see a derivation of the Saha eequation and how basic chemical equilibrium equations were able to be applied to other areas of physics. I've seen the equation arise extensively is astrophysics and it was nice to see how such a seemingly complex relation could be derived so simply by applying the versatility of thermodynamics in physics.

I found the derivation of Le Chatlier's principle to be extremely interesting, as we were taught this qualitatively in Year 12 chemistry, and the derivation was easy to follow and made sense and it was nice to see where this actually comes from

Magnets; how do they work? In all seriousness, paramagnetism and ferromagnetism have come up a couple times, yet we've never covered these in lectures.  Would you be able to go over a brief explanation of them and what they have to do with magnetic dipole moment?

I couldn't pull my head around the magnetic phase boundary, something about it threw me and even after reading it several times I still didn't really understand what was going on.

20 key concepts in thermodynamics and condensed matter

Tomorrow I am giving a summary lecture for the end of an undergraduate course PHYS2020 Thermodynamics and Condensed Matter. I taught the second half of the course, which has featured in some earlier posts. Here are the slides where I attempt to summarise 20 key ideas/results/concepts in the course.

My approach to the key ideas in thermodynamics is heavily influenced by Hans Buchdahl, my ANU undergraduate lecturer (and honours thesis supervisor) and his (dense) Twenty Lectures on Thermodynamics.
A similar axiomatic macroscopic approach which starts with the second law has more recently been championed by Elliot Lieb and Jacob Yngvason, and described in a nice Physics Today article.

What is the chemical potential?

I used to find the concept of the chemical potential rather confusing.
Hence, it is not surprising that students struggle too.
I could say the mantra that "the chemical potential is the energy required to add an extra particle to the system" but how it then appeared in different thermodynamic identities and the Fermi-Dirac distribution always seemed a bit mysterious.

However, when I first taught statistical mechanics 15 years ago I used the great text by Daniel Schroeder. He has a very nice discussion that introduces the chemical potential. He considers the composite system shown below, where a moveable membrane connects two systems A and B. Energy and particles can be exchanged between A and B. The whole system is isolated by the environment and so the equilibrium state is the one which maximises the total entropy of whole system.

Mechanical equilibrium (i.e. the membrane does not move) occurs if the pressure of A equals the pressure of B.

Thermal equilibrium (i.e. there is no net exchange of energy between A and B) occurs if the temperature of A equals that of B. Thus, temperature is the thermodynamic state variable that tells us where two systems are in thermal equilibrium.

Diffusive equilibrium (i.e. there no net exchange of particles between A and B) occurs if the chemical potential of particles in A equals that in B, where the chemical potential is defined as

Starting with this one can then derive various useful relations such as those between the Gibbs free energy and the chemical potential (dG= mu dN and G=mu N).
Thus, the chemical potential is the thermodynamic state variable/function that tells us whether or not two systems are in diffusive equilibrium.

Doug Natelson also has a post about this topic. He mentions the American Journal of Physics article on the subject by Ralph Baierlein, drawing heavily from his textbook. However, I did not find that article very helpful, particularly as he mostly uses a microscopic approach, i.e. statistical mechanics. (Aside: the article does have some interesting history in it though).
I prefer to first  use a macroscopic thermodynamic approach before a microscopic one as, I discussed in my post, What is temperature?

The power of simple free energy arguments

I love the phase diagram below and like to show it to students because it is so cute.

However, in terms of understanding, I always found it a bit bamboozling.

On monday I am giving a lecture on phase transformations of mixtures, closely following the nice textbook by Schroeder, Section 5.4.

Such a phase diagram is quite common.
Below is the phase diagram for the liquid-solid transition in mixtures of tin and lead.

Having prepared the lecture, I now understand the physical origin of these diagrams.

Eutectic [greek for easy melting] point is the lowest temperature at which the liquid is stable.

What is amazing is that one can understand these diagrams from simple arguments based on a very simple and physically motivated functional form for the Gibbs free energy that includes the entropy of mixing.

It is of the form

G(x) = C + D x + E x(1-x) + T [xlnx + (1-x)ln(1-x)]

where x is the mole fraction of the one substance in the mixture and T is the temperature.
The parameters C, D, and E are constants for a particular state.

The second term represents the free energy difference between pure A and pure B.
The third term represents the energy difference between A-B interactions and the average of A-A and B-B interactions. [I am not sure this is completely necessary].
The crucial last term represents the entropy of mixing (for ideal solutions).

Below one compares the G(x) curves for the three states: alpha (solid mixture with alpha crystal structure), beta, and liquid in order to construct the phase diagram.

The value of student pre-reading quizzes

How might you achieve some of the following desirable teaching goals?

• Get students to read the text book
• Find out what students are enjoying learning
• Find out what students are struggling to understand
• Keep students engaged
• Get feedback during the semester rather than at the end through student evaluations.

A key component of innovative teaching approaches such as peer assisted instruction, flipped classrooms, and just in time learning (a la Eric Mazur and Carl Wieman) are getting students before each class meeting to complete a short online quiz, based on reading the relevant part of the text. Ideally the teacher looks at the students answers before the class to get a feel for where they are at in understand and to address specific issues in the class.
Some of my UQ physics colleagues have really pursued this approach. 

I am currently teaching a second year undergraduate thermodynamics class with Joel Corney, from whom I have learnt a lot about teaching innovation.

Once a week the students complete a 3 question quiz on Blackboard (course software that all UQ courses "must" use). These do not contribute towards the final grade, but are a "hurdle" requirement: students must complete at least 70% to pass the course.
On average 80% of the students are completing these quizzes. In contrast, about 50% bother to show up for class.

The first two questions are brief basic comprehension questions base on the reading. e.g.,

Give a concise statement of the second law of thermodynamics for a system at constant temperature and volume. In your answer, refer only to system properties.

The third question is usually.

What concepts or topics did you find most difficult in the reading? If none, explain what you found most interesting.

I do find this is quite beneficial. I do believe that some of the goals above are achieved.
It does give me a much better feel for where the students are at. Some do appear to be doing the reading, thinking about it, and learning something. On the other hand, some are very confused. Others appear to not do the reading but just make wild guesses at the answers.

Below are some sample answers to the last question. The first two bring a smile to my face!

I loved how thermodynamics is used in so many areas in science. We studied Gibbs Free Energy in CHEM1100 so the term is familiar but it's fantastic to cover it in so much depth especially the mathematical reasoning behind the equations that were forced down our throat in first year with very minimal explanation. 

As an engineering student all this thermodynamic identity business does my noodle. Understanding all the theoretical stuff and "beautiful equations" is challenging coming from a world of plug and chug. 

It's really useful thinking about whether or not properties are intensive or extensive. It was always kind of a gut feeling type thing, but it's nice to finally clarify it. 

I feel like a lot of this stuff seems kind of useless at the moment, hopefully it will all fall into place soon. I know that it should be simple, but I can't seem to wrap my head around the free energy stuff and particularly how it is related to entropy.  

Fuel cells seem super cool. I don't particularly understand the Legendre transformations that were mentioned in the footer of page 157. 

I found it hard to keep up with the logic. Though i 'found the answers' to the questions above, i do not fully understand them. 

It's satisfying having the four thermodynamic potentials and identities but I feel like it's just a gateway to confusion, like all the assumptions that are made for the various derivatives of energy and entropy, etc.. Wizard 'diagrams' still don't help.

I struggled with the concept "free energy" until I really looked at the reading question. Having to think about it properly made me really understand what is meant by the term. I would still like to go over this concept in class. 

I am lost in the relationship between U, F, H and G. 

I know this is a physics course, but how much chemistry content is assumed knowledge?  

I don't get how in deriving the ds_total=-(1/T)dF form of the second law of thermodynamics for constant volume and temperature you can assume that the temperature of the system is equal to the temperature of the surroundings, and for there to still be an exchange of energy between the two. Unless its an isothermal transfer of heat between the system and surroundings, I don't get how you can have no temperature gradient, yet for there to be a transfer of energy between the system and environment in a no-work process. An explanation in the lecture would be greatly appreciated. 

i thought i understand the arguments, but i know i dont when i tried the questions.

This is very useful and helpful feedback.
However, the benefit comes with a cost... my time. It takes about 2-3 hours to read and grade the responses. Furthermore, you have to be well organised to do this before the lecture. (I didn't manage to do that for my first 2 weeks but have now caught up and so now hope to...)  If you want to change the lecture that also takes more time....
In a leisurely world what would be great would be to actually respond individually online to some of the student questions...

Incorporating scientist biographies into lectures

A few years ago I decided I wanted to include brief biographies of relevant great scientists in my undergraduate lectures. I posted (5 years ago!) about how I started with Landau but I lost momentum. This year I have put more effort into it. I just taught my second year undergraduate thermo class about Gibbs free energy and so I profiled Gibbs.

In solid state physics I have profiled Drude, Sommerfeld, von Laue, and Bloch.
I have found this quite enjoyable for myself and hopefully for the students. I have learnt quite a bit, just by reading the relevant Wikipedia pages. It also introduces students to the human dimension of science. For example, Drude died by suicide and so it is a good opportunity to flag mental health issues. Sommerfeld was a mentor of many great scientists. von Laue actively opposed the Deutsche Physik of the Nazis. Bloch was the first Director General of CERN.

Has anyone else experience at doing similar things? Any suggestions?

Mixing may not be irreversible

There is an interesting article Entropy: Order or information by Arieh Ben-Naim in the Journal of Chemical Education.
He points out two related and common misconceptions about entropy:

• mixing is always irreversible (and so must involve an increase in entropy)
• entropy is related to disorder

This is illustrated with the three processes of mixing shown below. All involve mixing, but only the first is irreversible.

What determines the entropy change is not the mixing (or amount of disorder) but the change in volume of each gas. That can be related to information (or ignorance) about the state of the gas molecules.

The value and cost of student reading quizzes

Following the example of some of my colleagues this semester I have started doing pre-lecture reading quizzes for my second year undergraduate course on Thermodynamics and Condensed Matter. Here is how it works.

A reading on the subject of the lecture (usually a Section from the textbook by Schroeder) is assigned.
A brief quiz of 2-4 questions is placed on Blackboard. These can be multiple choice and/or brief essay. The aim is to "force/encourage" students to engage with the text, think about the material, and be better prepared for the lecture. Reading the quiz results before the lecture provides some useful feedback on students levels of understanding and misconceptions. The occasional question, "What don't you understand in the reading?" provides useful feedback to the lecturer who can try and address these in the actual lecture.

The marks/grades for the quiz contribute a small amount to the formative assessment. This seems to be enough to motivate the majority of students to take the quizzes. However, it seems that about 30-50% of the class don't bother. A similar fraction don't bother to come to the lecture, which is serious problem that needs to be addressed.

Overall, I think this is a successful and worthwhile exercise. It is encouraging to see some of the students really do put the effort in and you see how they are wrestling with the material. I have been encouraged by the depth of some of the questions I have gotten in lectures which I think reflect this.

Although, valuable we should be mindful of two significant costs associated with this exercise.

First, it all takes time: designing the questions, uploading them on Blackboard, downloading the responses, assigning grades, reading the responses, and figuring out how to modify the lecture.
Blackboard will mark multiple choice quizzes automatically. For the essay questions, a graduate student, Chao Feng, has written nice software that allows one to look at all the responses in a convenient format. Nevertheless, it still take time.
A minimum of several hours a week is required. To do it really effectively one may need to devote one day a week. I don't know where I or others would find the time...

Second, are we actually hurting the students. I wonder whether this is just another exercise in babysitting students and fear-driven learning. Every year we see to be giving more and more small items of assessment to motivate students to engage with the course and learn something. But, they aren't in high school anymore. Hopefully, sometime in their life they are going to grow up and learn to be responsible, independent, and quasi-disciplined adults who do things because they actually want to or at least because they realise there is some benefit from doing it...

Students love video demonstrations

Today I gave a lecture on first-order phase transitions to undergraduates. Again I find the students love the videos I show.
 I mostly use videos from the Video Encyclopedia of Physics Demonstrations, which I got my dept. to buy a decade ago. However, now you can find virtually anything you need on YouTube! For example, here is a nice one of regelation of ice which demonstrates that the solid-liquid phase boundary has a negative slope.

Student misconceptions about entropy

I am slowly learning that many students think that because of the second law of thermodynamics that the entropy of a system must increase in any process. They forget or ignore that this is only true for an isolated system. 
Nice counter examples at fixed temperature and pressure are

• freezing of a liquid
• condensation of vapour
• slow compression of a gas
• many chemical reactions: e.g., combination of hydrogen gas and oxygen gas to form liquid water in a fuel cell

For all of these processes the entropy of the system decreases.
These are possible because there is a net decrease in the Gibbs free energy.
The entropy of the system plus surroundings increases.

I am trying to address this by continually testing understanding of this point with online quizzes and in class "clicker" quizzes.

Why temperature and pressure?

Before introducing the Gibbs free energy in my thermodynamics class I asked the students to say which variables they thought were generally the "easiest" to control in chemistry and physics experiments: volume and temperature, volume and energy, pressure and temperature, ...., or all?

Many students thought volume and temperature. (Maybe because what they mostly learn about is gases!).
I think the "correct" answer is pressure and temperature because
* these are environmental not system variables
* it is very hard to control the volume of a solid.

Am I right?
I now realise this is a rather subtle point and worth getting students to think about.
Appreciating it makes students think about experiments rather than mathematics and helps motivate why the Gibbs free energy is actually the most useful thermodynamic function.