Download Thermodynamics - Christian Hill

Thermodynamics
Introduction
The physical chemistry lecture course in the Michaelmas term of the first year is
intended to provide a background to some of the basic concepts and principles of
the subject. In particular, the course concentrates on the important but deeply
unfashionable subject of chemical thermodynamics.
Thermodynamics is one of the most powerful techniques that scientists have developed to understand the natural world. The laws of thermodynamics provide
a general and comprehensive framework within which to study the properties of
macroscopic systems (composed of many atoms or molecules), such as temperature, volume, pressure, and equilibrium constant. Thermodynamics provides
useful definitions for concepts such as energy, entropy, “heat”, and work, and
their use extends far beyond the scope of simple chemical reactions to the realms
of physics, biochemistry and meteorology (to name but three disciplines).
Yet thermodynamics has an image problem. It is a mature science, unchanged
in its essentials since the end of the nineteenth century, with a fussy and esoteric
notation. It has always traditionally been taught with the use of differentials
(even though there appears to be no terribly good reason for this) and the
derivatives that do appear look different from those found elsewhere in physics
- here’s what Bohren and Albrecht (see suggested reading) have to say about
one shocker:
δ rev Q
=T
dV
∂S
∂V
p
“What a strange hybrid creature!, a mathematical equivalent of the
centaur, half man and half horse. And you don’t have to search far
to find equally strange creatures in thermodynamics, a kind of game
reserve for mathematical unicorns, centaurs, satyrs, and sphinxes.”
Despite this, a lot of the actual mathematics involved in thermodynamics doesn’t
have to be all that complex: you will need some basic calculus, and be able to
deal with physical quantities and their units (for an introduction and some
revision of this, see the accompanying document, “Units and Some Basics”).
Another, more serious impediment to learning thermodynamics is in the definitions of some of the basic concepts themselves. “Energy” and “entropy”,
for example, cannot at this level be satisfactorily nailed down in snappy, oneline definitions; their common usage in everyday language is deceptive. They
acquire meaning through their application in making experimentally-testable
predictions about the natural world (for example, an important aspect of energy is that it is conserved in a given process; entropy is quantity which increases
in a spontaneous change).
The best approach to learning thermodynamics is to get hold of a good text
book (see below), and work through the relevant chapters slowly, gaining a good
grounding in the essentials as you go. If you find yourself having to look up too
many equations, you’re doing it wrong: you should be able to derive almost
everything you need from a very few basic definitions and the laws of thermodynamics if you understand them properly. Work through as many exercises
and problems as you can find (Atkins is good for this), and it should all begin
to make sense before long...
Suggested Reading
1. P. W. Atkins and J. de Paula, Atkins’ Physical Chemistry, any edition,
OUP.
2. E. B. Smith, Basic Chemical Thermodynamics, 5th ed., Imperial College
Press, 2004.
3. C. F. Bohren and B. A. Albrecht, Atmospheric Thermodynamics, OUP,
1998.
4. J. B. Fenn, Engines, Energy, and Entropy: a Thermodynamics Primer,
Freeman, 1982.
5. P. W. Atkins, The Second Law, Scientific American Books, 1994.
6. C. Lawrence, A. Rodger and R. G. Compton, Foundations of Physical
Chemistry, OUP Primer 40, 1996.
7. C. Lawrence, J. Wadhawan and R. G. Compton, Foundations of Physical
Chemistry: Worked Examples, OUP Primer 68, 1999.
8. H. Metiu, Physical Chemistry: Thermodynamics, Taylor and Francis,
2006.
9. A. Ben-Naim, Entropy Demystified: The Second Law Reduced to Plain
Common Sense, World Scientific, 2008.
Notation and Common Pitfalls
Units
Please read the accompanying document, “Units and Some Basics”, carefully
and make sure you understand it. The section on so-called Quantity Calculus
may be new to you and will tell you how to interpret table headings properly.
It is important to include the correct units with your answers. In thermodynamics, pay particular attention to the distinction between kJ mol−1 and J mol−1 or
your answers are likely to be three orders of magnitude out. At least to begin with, you are strongly recommended to include the units with your working
when solving problems so that, for example, the kinetic energy of a ball of mass
100 g travelling at 8 m s−1 would be calculated in SI units as:
T = 21 mv 2 = 12 (100 × 10−3 kg)(8 m s−1 )2 = 3.2 J.
Give your answers to an appropriate number of significant figures, but note that
there is usually no need to add “3 s.f.” and the like after every answer.
Graphs
When drawing a graph by hand you will almost always be looking to find a
straight-line plot. Be sure to label the axes correctly and take extra care over
the units of the gradient if you need it. Select a scale for your graph so as to
use as much of the page (use graph paper) as possible. And finally, it isn’t
considered cool to plot a straight line through two points...
Physical Constants
Some physical constants come up so frequently in Physical Chemistry that you
will find it useful to remember them- it is sufficient to do so to 3 decimal places.
Here are the ones you’ll need to get started.
Speed of light
Avogadro constant
Boltzmann constant
Gas constant
Atomic mass unit
c
NA
kB
R
u
p
= 2.998 × 108 m s−1
= 6.022 × 1023 mol−1
= 1.381 × 10−23 J K−1
= 8.314 J K−1 mol−1
= 1.661 × 10−27 kg
= 1 bar = 105 Pa
1M
= 1 mol dm−3
1 atm = 101.325 kPa = 760 Torr
Note that R = NA kB and u = 1/(1000 NA ) in kg.
Tutorial Questions
We have two tutorials this term, in Weeks 7 and 8. There is a question sheet
for each tutorial - please attempt all the questions and hand them in to my
pigeonhole in college by 5pm the afternoon before the tutorial.