Consider two very cold chambers that
are completely empty except for a few argon atoms (figure 6.5 and 6.6).
Chamber 1: 4 atoms, 5 quantum states, total energy = 8 units
Chamber 2: 3 atoms, 5 quantum states, total energy =6 units
There are 5 quantum energy states available to these atoms. The lowest has an energy of
2 units, and the highest has an energy level of 10 units. The atoms in both
chambers are only free to occupy the lowest energy state. If one occupies a higher energy
state then the total energy of the system will be too high. In this case, there is only
one possible way to arrange the atoms in each chamber. The ways that the atoms are
arranged to fill the quantum energy states are called micro-states. Figures 6.5 and 6.6
illustrate this principle.
Figure 6.5: Micro-state for Chamber 1
Figure 6.6: Micro-states for Chamber 2
If chamber 2 is heated, the atoms will move faster. Assume the total energy is now 12
units. Figure 6.7 shows that the number of available micro-states is greatly increased.
Figure 6.7: Ten Micro-states Available After Heating
Entropy is often defined as a measure of disorder, but this definition
is not only misleading it is wrong. Entropy is a measure of available micro-states. So in
this example, the argon atoms that are heated have more entropy (10 micro-states available
vs. 1 micro-state available).
Entropy can also be defined as a measure of uncertainty. Because as
more micro-states become available to the system, the state of the particles becomes more
uncertain. Entropy has nothing to do with disorder.
From this example, it should be clear that there are several ways to
increase the entropy of a system. Increasing the temperature is one. Suppose 5 quantum
energy levels are added so that all of the odd energies are represented, E=1, E=3, E=5,
E=7, and E=9. The argon atoms will be able to distribute themselves in many more ways and
thus find more micro-states.
next: The second law of
thermodynamics
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