## Welcome to Physics 4230!

### Week 17

The Final Exam is Monday 7:30-10PM in the Duane Physics Helproom (basement G2B80 area). The Final Exam is inclusive of all material in the course. See the exam page for more information.

Homework: Set yourself some interesting problem to solve and go for it! HWK is finished for this course!

### Week 16

This is the last week of lectures for the class! We continue our study of quantum ideal gases with the cases of various Bose gases, particularly photon gases, and possibly the case of Bose-Einstein condensation in gases of massive bosons: Superfluids!
The Final Exam is scheduled Monday May 8, 7:30P-10P. Location is scheduled to be in Duane G2B47, our usual lecture room, but we are working to find a better space. Stay tuned!

Reading: Schroeder Chapters 7 on Quantum Statistics

Homework: HWK 14 due on Wednesday, May 3, 2017.

### Week 15

This week we concentrate on quantum ideal gases and the case of the ideal Fermi Gas of spin 1/2 indistinguishable Fermions such as electrons, protons, and neutrons. These gases (surprisingly) are the basic model for widely varying physical systems from neutron stars (boxes of neutrons) to simple metals (boxes of electrons).

Reading: Schroeder Chapters 7 on Quantum Statistics

Homework: HWK 14 due on Wednesday, May 3, 2017.

### Week 14

Exam 2 is scored. Solutions and scores are on D2L.
This week we are extending what we learned about systems at fixed T, V, and N to the case where the number of particles is allowed to vary. That means a new type of partition function and a new free energy that are both appropriate for a new set of independent variables. The number of particles, N, is allowed to vary, so N is no longer a good independent variable. We need to learn about chemical potential! Notice that we now believe, due to quantum mechanics, that in some very fundamental way, particle number cannot be fixed (ever) except as an approximation, because we can always convert energy into mass (and visa versa), SO variable particle number is fundamental. The ideas we will cover this week are critical to understanding the thermal behavior of quantum mechanical systems.

Reading: Schroeder Chapters 7 on Quantum Statistics

Homework: HWK 13 due on Wednesday, Apr. 26, 2017.

### Week 13

Exam 2 is Tuesday evening. See the Exam tab for more information.
Now that we have a full recipe for finding the Helmholtz free energy from the quantum energy levels, let's see if we can directly calculate the properties of a gas of particles in a box. It's the Ideal Gas! Some of the important details involve the question of whether the particles are distinguishable or indistinguishable. This idea is central in quantum physics, where we find that all particles are either Bosons or Fermions. The idea that indistinguishability is an important attribute of particles first appeared in thermal physics.

Reading: Schroeder Chapters 6 on Boltzmann Statistics

Homework: HWK 11 due on Wednesday, Apr. 12, 2017.

### Week 12

Welcome back from Spring Break. We will concentrate on systems that are in equilibrium (or close to equilibrium) with a large bath at fixed TEMPERATURE. The goal is to learn about and use the probabilities of finding various energy levels occuppied at the fixed temperature. Boltamann Factors!

Reading: Schroeder Chapters 6 on Boltzmann Statistics

Homework: HWK 10 due on Wednesday, Apr. 5, 2017.

### Week 11

Spring Break. No lectures this week.

Reading: Schroeder Chapters 5 on Thermodynamic Potentials

Homework: HWK 10 due on Wednesday, Apr. 5, 2017.

### Week 10

'Free Energies' is the topic this week. There turn out to be functions that are as useful as the Entropy function of state, but that have independent variables that are up to you to choose. It's great to have more convenient independent variables. Free energies also give you new tools for understanding you systems with different constraints, say a system at fixed temperature rather than fixed energy, might behave.

Reading: Schroeder Chapters 5 on Thermodynamic Potentials

Homework: HWK 9 due on Wednesday, Mar. 22, 2017.

### Week 9

This week, we continue our study of engines and extend the ideas to engines that run in reverse, which we also call refrigerators. Refrigeration for e.g., food storage, was part of the revolution in public health care that occured in the late 19th century. We will then turn back to our basic formalism, the idea that there is an Entropy that has natural independent variables of internal energy, volume, and particle number, and discover that we can find similar functions of state, so-called 'Free Energies' that have more convenient independent variables.

Reading: Schroeder Chapters 5 on Thermodynamic Potentials

Homework: HWK 9 due on Wednesday, Mar. 22, 2017.

### Week 8

We continue our study of the 2-state paramagnet. In this example, we get to see how careful understanding of the multiplicity and it's logarithm (entropy), allows us to predict the behavior of large systems. We will hope to touch on the ideal gas and then move on to study heat engines. What are the limits of engine efficiency? Where did the word 'engineer' come from?

Reading: Start reading Schroeder Chapters 4 on heat engines and refrigerators. Outstanding!

Homework: HWK 8 due on Wednesday, Mar. 15, 2017.

### Week 7

We now turn to using the multiplicity function, the function that tells us the total number of microstates, Just knowing that such a thing exists and knowing that most of the states describe situations where energy, volume, and other properties are fully shared across the system, is enough to understand why thermal equilibrium behavior is so common. Still, if we are going to understand specific systems, we need practice building the multiplicity function, the entropy, and learning how to extract information. Our first example will be the 2-state paramagnet.

EXAM 1 is being scored. Solutions are on D2L.

Reading: Schroeder Chapters 2 and 3 on counting states, the Entropy function, and how entropy is related to measured heat flows.

Homework: HWK 7 due on Wednesday, Mar. 8, 2017.

### Week 6

This week is all about understanding the multiplicity function, the function that tells us the total number of microstates. The (logarithm of) multiplicity gives us the entropy. We don't start with much insight about the number of states and we don't start with much insight about the overwhelmingly large fraction of those states that nearly evenly distributes the energy amoung the system members. Our goal this week is to see specific examples that show us why the Einstein Solid multiplicity function is strongly peaked in this way.

EXAM 1 is being scored. Solutions are on D2L.

Reading: Schroeder Chapters 2 and 3 on counting states, the Entropy function, and how entropy is related to measured heat flows.

Homework: HWK 5 due on Wednesday, Feb. 22, 2017.

### Week 5

Boltzmann taught us that the Entropy is just the (logarithm of) the number of microscopic states that the system can have, subject to any macroscopic constraints. Thermodynamics teaches us that all thermal properties of a system are encoded in the Entropy function S(U, V, N). This week we begin learning how to count the allowed states, and see how to actually derive the entropy function of state for some simpler cases.

EXAM 1 is coming next week, Tuesday evening, Feb. 21, 7:30P-9P in Duane G1B20. Please see the exam tab for more information.

Reading: Schroeder Chapters 2 and 3 on counting states, the Entropy function, and how entropy is related to measured heat flows.

Homework: HWK 5 due on Wednesday, Feb. 22, 2017.

### Week 4

This week, we will be working with the 2nd Law of Thermodynamics. Conservation of energy (the 1st Law) is an important issue in understanding changes in thermal equilibrium system, but it does not allow us to predict even simple things like the direction of spontaneous heat flow. The 2nd Law of Thermodynamics tells us how to predict the direction of processes that will happen on their own. It does so by noticing that there is an additional function of state, the Entropy, and that function of state allows us to predict the direction of spontaneous change.

Reading: Schroeder Chapters 2 and 3 on counting states, the Entropy function, and how entropy is related to measured heat flows.

Homework: HWK 4 due on Wednesday, Feb. 15, 2017.

### Week 3

This week we are determining the -PdV Work done ON a system and the heat ADDED TO as system and using them via the 1st Law of Thermodynamics to determine the change in the internal energy of the system. Work and Heat are processes and they surely depend upon the path used. However, internal energy is a function of state and is independent of path. Fun! You can use path dependent processes to determine a function of state!

Reading: Schroeder Sections 1.5 and 1.6 in particular cover topics of compressional work and heat that we discuss later this week. Start reading Chapter 2 on Entropy as well.

Homework: HWK 3 due on Wednesday, Feb. 8, 2017.

### Week 2

This week we are continuing a quick run though why, despite the fact that it in principle should require a huge amount of information to describe a many-body system, we typically find systems in an 'equilibrium' state, where initial conditions and evolution history are apparently not important. Such systems are rather well described using only a small number of macroscopic properties, say total energy, volume, and number of particles for the Ideal Gas. This behavior is understood as a result of there being a huge number of microscopic states consistent with a given energy, volume, and number, AND that a huge percentage of those states distribute the system energy rather smoothly among the system components. The chances of finding a system NOT in this smooth distribution is vanishingly small. The (log of) number of microscopic states is the entropy and specifying it along with volume and number is enough to tell us about equilibrium behavior. We will begin talking about work and heat this week, to see how this idea came about.

Reading: Start digging into Schroeder Chapters 1-3. Sections 1.5 and 1.6 in particular cover topics of compressional work and heat that we discuss later this week.

Homework: HWK 1 due on Wednesday, Jan. 25, 2017.

### Week 1

First lecture is Wednesday, Jan. 18, 3:00P-3:50P, in room Duane G2B47.

Have a look at the course syllabus

Summary of things to do during or by the first week:
Buy the text (Daniel V. Schroeder's An Introduction to Thermal Physics).
Buy a clicker if you don't have one. Then follow these instructions to register.

Reading: Start digging into Schroeder Chapters 1-3.

Homework: HWK 1 due on Wednesday, Jan. 25, 2017.