Biomedical Engineering Reference
In-Depth Information
10
5
0
Figure 7.4
Simple energy level diagram
C
C
B
A
B
A
Figure 7.5
Quantum states
In a macroscopic sample of matter, each particle can have many microscopic quantum
states to choose from and a key question is, for an equilibrium temperature, how do the
particles distribute themselves amongst their allowed quantum states? Let me illustrate the
problem with just three particles.
I am going to make another big assumption in order to keep the treatment simple.
I assume that the particles form a perfect gas and whilst they may collide with each
other and with the walls of the container, their energies do not change and indeed I can
find the total energy of the system just by summing over the energies of the individual
particles.
For the sake of argument, I will take the internal energy
U
as 9 D and the number of
particles
N
3 as in Figure 7.5. We have to enumerate the ways in which three particles
with these simple quantum state energies can achieve a total energy of 9 D.
The rows of Table 7.6 indicate every possible combination of integers that make up 9.
To save space, I have only included one of each possible arrangements after the first; so
for example, particle A could have 7 D with particles B and C having 1 D, particle B could
have 7 D with particles A and C having 1 D, or particle C could have 7 D with particles A
and B having 1 D. This is the origin of the integer 3 in the final column; it is the number of
=
