There will be a revision tutorial for this course on Monday
Time and Place: 9:05 in Hall C
The exam is on Tuesday, January 17, 9:30 in the Small Sports
A schedule of content and exercises will appear below.
Homework is due on the Monday of the following week, before the
start of the Monday tutorial at 10:05, unless noted otherwise.
Notes: I gave an overview of coming
attractions. We discussed the concepts of temperature and thermal
equilibrium. (the absolute thermodynamic temperature will be defined in
detail later on), and the zeroth law of thermodynamics, which says
that if two systems are each in equilibrium with a third one, they must be
in equilibrium with one another. I introduced equations of
state, which relate the macroscopic variables in equilibrium states,
with the ideal gas law as an important example. Much of this material (but not all) can be found in the introduction and in
chapter 1 of the book by Fermi.
Notes: We introduced quasistatic
transformations and cycles, look at work performed by gases and most
importantly, introduce the first law of thermodynamics which says
that energy is conserved and heat is a form of energy. We discussed in
some detail how internal energy and heat can in principle be measured
(calorimetry) We covered the rest of chapter 1 and the first
section of chapter 2 of the book by Fermi,
Please find assignment 1
here. A lot of this is a refresher on
the uses of the ideal gas law, but there is some stuff on work done by
gases and other equations of state here too.
This assignment is due Monday, October 3, before the start of the
tutorial at 10:05.
We showed how the infinitesimal form of the first law (dQ=dU+dL) allows
one to calculate the heat absorbed or released in any quasistatic process,
if the energy and the infinitesimal work done are known (as a function
of the system variables). We introduced heat capacities and specific
heats, in general and specifically at constant volume and at constant
temperature. We also introduced the notion of extensive and intensive
This material is covered in chapter 2 of Fermi's book, mostly in
sections 4 and 5.
Please find assignment 2
This assignment is due Monday, October 10, before the start of the
tutorial at 10:05.
Notes: We note that, for an ideal gas, the energy depends only on
the temperature (in particular U=(3/2)nRT for a monatomic ideal gas
and U=(5/2)nRT for a diatomic ideal gas). We use this to calculate
the heat capacities for an ideal gas at constant pressure and temperature.
We then introduce adiabatic processes (processes where no
heat is absorbed or released). For an ideal gas, we will calculate the
adiabatic curves describing these processe in the (p,V), (p,T) or (V,T)
diagram. We will apply the result to a calculation of the temperature
gradient of the atmosphere (assuming it is due to adiabatic expansion of
rising air). This material is covered in chapters 2 and 3 of the book by Fermi,
in sections 6 and 7
We introduce the second law of thermodynamics, in two
forms, the Kelvin postulate and the Clausius postulate and argue
that these are equivalent. In the
course of the proof we introduced heat engines, in particular the
Carnot engine. We defined the efficiency ηof a heat engine as the work
done by the engine in a cycle divided by the heat absorbed from the
high temperature reservoir during the cycle. We calculated η for
the reversible Carnot engine, showing that it depends only on the
temperatures of the hot and cold reservoirs.
This material is covered in chapter 3 of the book by Fermi,
mostly in section 8
We studied the efficiency of general heat engines and used
the results to define the absolute thermodynamic temperature. We then
proved Clausius theorem on thermodynamic cycles
This material is in chapters 3 and 4 of Fermi's book, paragraphs 9
We use Clausius' theorem to define the entropy. Then we prove various
properties of the entropy, including the fact that it is non-decreasing
for isolated systems (which is another version of the second law of
thermodynamics). We also introduce the third law of thermodynamics,
which says that the entropy of any state at temperature T=0 vanishes. We
showed that, as a result, the specific heat of any substance must also
vanish as T goes to zero.
We also discuss how to calculate the entropy using the first law, in the
form of the thermodynamic identity TdS=dU+dL.
This material is in chapters 4 and 8 of Fermi's book, paragraphs
12, 13, 14, 30 and 31
We calculated the entropy for an ideal gas from the first law and the
formula for the energy. Then we showed show how to use the fact that S is a
state function to obtain equations for the energy of
the system (by equating the mixed partial derivatives of S).
We also discussed the liquid-vapor transition for a simple substance.
in particular, we introduced the p-V diagram for a typical fluid
(with liquid, gaseous and coexistence regions on the
isotherms) and introduced supercritical fluids.
Interesting Youtube videos showing the transition into the supercritical
temperature regime can be found here
One of these has some useful explanation and
the other has better picture quality for viewing the experiment
This material is in chapter 4 of Fermi's book, paragraphs
You may still hand in your solutions to assignment 6. In addition, as
assignment 7, please do problem 3 from last year's exam, which can be found
We derived Clapeyron's equation for the pressure of a
saturated vapour. We also introduced the thermodynamic
potentials (U, H, F, G) and derived the Maxwell relations. We also showed
that the maximal work that can be extracted from a system in a process in
contact with a reservoir at constant temperature is equal to the decrease of the free
energy F in the process (with equality for quasistatic processes). This material is covered in chapter 4 and 5 of
Fermi, mostly in section 15, 17 and 18.
We spent a bit more time with the
potentials H (Enthalpy) and G (Gibs free energy). Note that Fermi calls
the Gibbs free energy "the thermodynamic potential at constant pressure",
and he uses the symbol Φ. We showed that the
heat absorbed in a process at constant pressure equals the change in the
enthalpy. We also showed that the Gibbs free energy is non-increasing
(almost always decreasing) in processes at constant pressure and
temperature. In particular, we get dG=0 for equilibrium states at given
(fixed) p and T. We also treated Maxwell's construction of the
plateau where the liquid and gaseous phases coexist. In the course of
this, we mentioned superheated and supercooled liquids. The wikipedia
pages on supercooling and superheating have
some more information and links to videos of supercooled and superheated
water. You might also want to do a search for "hot ice" or "sodium
acetate" for similarly cool videos of a supercooled solution.
Some of this material is covered in
chapter 4 and 5 of Fermi, in sections 16 and 18.
Exercises: No hand in this week,
but recommended exercises are the remaining problems from
We introduce the phase diagram of a simple substance - in this
case basically a (p,T)-diagram with coexistence lines for the various
phases (liquid, gas, solid) and their intersection point (the triple
point) indicated. The critical point features as the end point of the
coexistence line between liquid and vapor.
We will also derive Gibbs' phase rule, using the Gibbs free energy. This material is covered in
chapter 5 of Fermi, in sections 18 and 19.
We spent a bit more time with Gibbs' Phase rule.
Finally, we considered chemical reactions between gases at constant
volume; in particular, we introduced the law of mass action,
gave a kinetic argument for it and
indicated how it can be derived by requiring that the Helmholtz free
energy is a minimum in equilibrium.
The material on gaseous reactions is covered in
chapter 6 of Fermi, in sections 21 and 23.