1
Note 2.
Energy
2.1 Ideal gases: A simple system to play with
Ideal gases are a natural place to start learning about thermodynamics. We have some
intuition about how gases work and an “ideal” gas is a simple model of how gases work.
In particular, an ideal gas is a great model system to learn and test our understanding of
thermodynamics since all of the fundamental thermodynamic properties we will talk
about can be found in them and they allow us to study thermodynamics without getting
lost in too much math. Later on, we will study more realistic gases and see the nature of
the differences.
2.1.1 Basic properties
Like many types of matter, we characterize an ideal gas by certain properties: volume
(
V
), pressure (
P
), temperature (
T
), and how many moles of atoms are in the gas (
n
).
There is a simple expression relating these quantities:
PV = nRT
This equation is called the equation
of state
for this system, since it relates the
state
variables
(
P
,
n
,
V
, and
T
) in this case. Actually, many gases behave like ideal gases in
certain conditions (this is called “ideal” conditions).
There are two types of properties here:
1.
Extensive properties
are properties which are related to “how much stuff” there is.
For example,
n
and
V
are extensive properties. If the system is duplicated, these variables
get doubled.
2.
Intensive properties
are independent of the size of the system. For example,
P
,
T
, are
intensive properties. So is the density
ρ
= N/V
, where
N
is the total number of atoms.
2.1.2 A brief glimpse of phase transitions: Van der Waals equation
When gases cool, they condense to liquids. When liquids cool, they freeze into solids.
These are two examples of phase transitions. However, ideal gases cannot have phase
transitions. This is what is meant by “ideal.” Thus, far from the phase transition, they are
good models, but do not work well near the transition.
What makes a phase transition? Interaction between molecules. Gas particles start to
stick together at lower temperatures and form a liquid. How can we model this
interaction? We can modify the ideal gas equation to include interactions. We’ll do so in
two steps: