First law relations for ideal gases
condition
First law
w=
q=
constant T
E = 0; q = -w
-nRTln(V2/V1)
+nRTln(V2/V1)
constant V
E = qv
0
CvT
constant P
E = qp + w
-PV
C p T
E = w
CvT
0
adiabatic
Week 7 (14-18 Oct)
Free energy of mixing
Last week we developed the mathematical machinery to deal with chemical
reactions:
! Pi $
&
" P %
o
the chemical potential, i = i + RT ln#
and an expression for the total free energy of a system: G =
! n
i
i
i
If G
Week 6 (7-11 Oct)
Monday was midterm 1. Wednesday's lecture is summarized in the PDF file
"extremum principles".
Friday we reviewed the three kinds of systems: the constraints imposed at the
"borders" of the system, and the associated "extremum" equation:
Week 8 (21-25 Oct)
Fugacity
For an ideal gas, we wrote an expression for the chemical potential as:
!P$
= + RT ln# &
" P %
The standard state we use for a reference is ideal gas at 1 bar and the specified
temperature. The equation applies only to an i
Week 12 Boltzmann distribution law (22 Nov)
The last topic of the course is a brief introduction to statistical thermodynamics, how simple
statistical considerations can be related to the thermodynamic properties of materials. The
problem is the following
Week 12 (18-22 Nov) Electrochemical potentials
When a charged component of a system is unable to move between all the phases
present, an electrostatic potential develops. An example is a membrane, permeable only
to positive ions, dividing a solution of KC
Lectures Week 9-10 - Chapter 9, ideal and real solutions (Chemical equilibrium
next week)
Ideal solutions and Raoult's law
We consider the equilibrium between liquid and vapor phases in a system with
two components, A and B. The chemical potential of A in
Lectures week 11 (11-15 Nov)
The phase rule
We briefly covered Gibbs' phase rule. E & R bring it up in regard to one component
systems, section 8.3, and mention it again in section 9.14 without ever saying how the
rule is extended for multi-component syst
'Week' 15 (2 Dec)
The partition function of a harmonic oscillator
Monday we looked at another situation where the partition function reduces to a simple
equation, the harmonic oscillator. The example is the vibrational energy levels of a
diatomic molecule
'Week' 13 (25 Nov)
Applications of the Boltzmann distribution law
Today's class was about two applications of the Boltzmann distribution law, in which the
denominator of the law (partition function) can be written out in a simple form and used to do
some
Week 5 (30 Sept - 4 Oct)
See separate write-up on "Multiplicity" for an introduction to Chapter 5.
Historically, the idea of entropy was arrived at by thinking about the maximum
efficiency possible for a heat engine working between hot and cold temperatur
Multiplicity and the 2nd law
We can imagine processes that do not violate conservation of energy but
nevertheless are not expected to happen: the Joule paddlewheel spontaneously starts
to raise a weight, while the temperature of the water decreases; two b
Week 4 lecture summary (23-27 Sept)
Chapter 4 is all about the enthalpy, H. A change in H, H, is informative about
any kind of interaction, from weak Van der Waals to the strongest covalent
bonds, and is measured for a huge variety of chemical reactions a
Explanation of the Equipartition theorem- from Atkins & Jones, Chemical Principles
A fundamental theorem of classical mechanics called the equipartition theorem (which we shall
not derive here) states that the average energy of each degree of freedom of a
Connecting the partial derivatives in total differentials to experimental quantities
The thermodynamic functions U and H tell us how much energy a system contains. It is very
useful to know how the U or H of a system changes as we change P, V, or T associ
Extremum principles and the fundamental equations of thermodynamics
(This is an introduction to Chapter 6 of E&R. It is largely based on Chapters 7 and 8 of
Molecular Driving Forces, by Ken Dill.)
An "extremum principle" tells what configuration of a syst
Chemical Equilibria
Our fundamental equation for G gives us the machinery to ask questions about spontaneous
changes in the composition of a system, i.e., chemical reactions. The condition for equilibrium,
at constant T and P, is
dG =
! dn
i
i
=0
(4)
i
If
Connecting the partial derivatives in total differentials to experimental quantities
The thermodynamic functions U and H tell us how much energy a system contains. It is very
useful to know how the U or H of a system changes as we change P, V, or T associ
Week 1 lecture summary (4-6 Sept)
We started with a review of physics:
force: F=ma, in units of Newtons, kg-m/s2,
work: force times distance, units of Joules, kg-m2/s2,
and the way that work done on an object (such as a lifting a textbook against the
forc
Week 2 lecture summary (9-13 Sept)
Real gases
PV = nRT is called the "ideal" or "perfect" gas law. Real gases do not follow this
relation under all conditions- plots of the compressibility factor Z = pVm/RT vs.
pressure for different gases show that Z may
Multiplicity and the 2nd law
We can imagine processes that do not violate conservation of energy but
nevertheless are not expected to happen: the Joule paddlewheel spontaneously starts
to raise a weight, while the temperature of the water decreases; two b
Week 2 lecture summary (16-20 Sept)
State functions
State functions are defined in Chapter 2; they are simply quantities that depend
only on the initial and final states of the system: deltaX = X(final state) - X(initial
state). P, V, T, U, and H are all