Introduction to Statistical Mechanics
Statistical Mechanics handles very large systems of particles, for example the air in a room
(of order 1 mole or 10
particles). As you’ll see such large systems are handled very diFerently
than a single particle or a system of a few particles.
If N is very large, tracking the position and velocity of every particle at every instant in
time becomes very cumbersome and impractical.
In many cases, we don’t even care where
every little microscopic atom is at every instant in time. We care more about the
properties of the system, such as pressure, temperature, volume, and the number of particles in
the system. Therfore, systems of many particles are treated in a fundamentally diFerent way
from the systems we’ve discussed in the course so far. These systems are treated
in other words we describe them by their average properties.
“State” of a System
±or a system of 1 particle, we need 6 parameters to de²ne the “state” of the particle
x, y, z, v
These six parameters give us the current location of the particle and enough information
to predict it’s location at a later time. If we know the forces acting on a particle, we can
specify it’s state for all future times.
If we have a system of 2 particles, we need 12 parameters to describe the system.
±or N particles, we need 6N parameters
If N is very large (like 10
particles in a solid or in this room), it’s completely impractical
to track the location and velocity of every particle.
Even with modern computers, we
can’t do it. So, we instead describe a system with a large number of particles statistically.
This way we don’t have to track the location of every particle at every instant.
In this case, we don’t need to specify all 6N positions and velocities of every individual
atom. Rather, we can describe the system by a few “macroscopic quantities” such as N,
V, P, T.
±or the rest of the term, we’ll discuss this kind of system which is treated in a funda-
mentally diFerent way from the systems we’ve discussed so far in this course.
You all have experience that energy ³ows from hot to cold.
If you grab a glass full of
hot tea, it burns your hand.
That is the ³ow of thermal energy from the hot glass to
your cold(er) hand.
The thermal energy transfer between two systems depends on the
temperature diFerence between them. This ³ow of energy due to temperature diFerence
is called “heat” and given the symbol