Physics 363: Introduction to Thermal Physics

Thermal physics is perhaps the most broadly applicable of the core physics courses since it applies generally to all kinds of macroscopic phenomena. Besides being fundamental to physics, it is valuable for engineers, and central to thinking about biology.

In introductory physics courses and even in the mechanics course Physics 361, one typically learns how to solve problems that involve just a few simple objects: a point mass attached to an idealized massless spring, a point-like planet orbiting a point-like Sun, or a rigid gyroscope rotating about an axis. But most objects that the human race deals with on a daily basis, and many objects in nature such as gases, liquids, solids, planets, stars, galaxies, and even the universe itself, do not consist of one or a few simple point objects, they consist of huge numbers of particles, where huge means of order 1023 (Avogadro's number) or larger. Is there any possibility to understand the properties of an object made up of so many parts when it is already difficult to solve a problem involving, say, three objects interacting gravitationally or electrically?

In Physics 363, you discover that the answer is a remarkable yes. In fact, it is specifically when a system contains many particles and when the object has the special property of being in thermodynamic equilibrium, that a macroscopic system consisting of many pieces can be described in a different simpler way than that suggested by mechanics or by quantum mechanics in that just a few numbers such as temperature, entropy, energy, or chemical potential suffice to characterize the macroscopic object completely. And from these numbers, and how these numbers vary with experimental knobs such as external pressure or strength of an electrical field, one can understand and often predict quantitatively many properties of macroscopic objects that are valuable for day-to-day experiments or for engineers when they design and build devices.

Physics 363 also discusses and answers some basic fascinating questions related to spontaneous behavior: why does an ice cube melt but water never spontaneously freezes at room temperature? Why does a balloon filled with gaseous hydrogen and a balloon filled with gaseous oxygen spontaneously mix completely when connected by a tube? And a really deep question, which is why does time flow from past to future, when the microscopic equations of nature are symmetric with respect to the flow of time? The answers to these questions revolve around the concept of entropy, which is explained and clarified in 363. From an understanding of entropy, 363 students then gain a deeper understanding of what is meant by "temperature", and will learn that the temperature of a magnetic system can be negative, and that electrons in a metal can be moving at a percent the speed of light even at absolute zero.

Another important concept discussed in 363 is the idea of a phase transition. People are so used to ice melting into water or water boiling into steam that they are unaware of how subtle these behaviors are when looked at from a microscopic point of view: why do the same water molecules form ice or water or steam (or many other phases) under different conditions? Why do these transitions occur abruptly as some experimental knob like temperature or pressure is varied? What are the rules that govern when or how one phase changes into another as some experimental knob such as temperature or pressure or chemical concentration is varied?

In 363, students also get a glimpse of how phase transitions have become an influential metaphor for broader scientific questions about how complex structure arises from simpler structure (say crystalline ice forming from disordered water vapor). Phase transition theory in fact has guided many efforts to understand how complexity arises from simplicity, in contexts far from equilibrium physics and sometimes having nothing to do with physics directly. The origin of life or the formation of a brain that is smart enough to invent tools would be examples. Are these "phase transitions" that occurred when some critical number of chemicals in a primeval soup was exceeded, or when the network of neurons in a brain become great enough in number and in connectivity that something novel appeared, an "intelligence" phase?

Like all of the other undergraduate physics courses, one of the pleasures of taking 363 is learning how to carry out relatively short calculations (say 1-2 pages long) that provide much insight about complicated experimental phenomena and that often make experimentally correct predictions. A neat example discussed in 363 is how to calculate the maximum possible mass of a white dwarf star, which is the final stage of all stars whose initial mass is less than about eight times the mass of our Sun (this is about 97% of all stars in the Milky Way). Gravity tries to pull all the mass of a star into its center but this inward force is opposed by the large outward pressure of the small stellar core, which in turn arises from the high temperature of the core caused by fusion reactions. But eventually all the hydrogen fuel in the star's small core is used up, the fusion reactions stop, and the core cools down with the result that gravity succeeds in crushing a star that might be 100 times the diameter of our Earth into a white dwarf about the size of our Earth. But even in the absence of hot fusion reactions, the inward pull of gravity becomes opposed by a new mechanism, which is a quantum mechanical repulsion of the freely moving electrons in the white dwarf that arises when many electrons are crowded into a sufficiently small volume. This repulsion exists even at absolute zero and has nothing to do with electrical repulsion, it is a consequence of a quantum mechanical exclusion principle that prevent two electrons with the same quantum state from being near one another.

But as you learn to calculate in 363, if a white dwarf has a total mass exceeding about 1.4 times the mass of our Sun (this upper limit is known as the Chandrasekhar limit), the quantum electron pressure is not strong enough to hold back the force of gravity and the white dwarf will continue to collapse inwards. In this case, the white dwarf explodes with astounding energy (with as much energy as about 1010 stars over a period of about a week!) as carbon nuclei start to fuse everywhere throughout the star, creating a blast of light that can be seen ten billion light years away. Because all white dwarf explosions are essentially identical (they are all triggered when the Chandrasekhar limit is just exceeded), their explosions have provided astronomers with accurate beacons that allow distances to be measured accurately over long distances. It is in fact measurements based on white dwarf explosions that allowed astronomers to detect the accelerated expansion of the entire universe, leading to one of the big mysteries of current science, which is what is causing the accelerated expansion and whether it will ever stop.