The Molecular Interpretation of Entropy

Consider the following system, where two flasks are sealed together and connected by a stopcock (Figure 1.1 “Two-Atom, Double-Flask Diagram”). In this system, we have placed two atoms of gas, one green and one blue. At first, both atoms are contained in only the left flask. When the stopcock is opened, both atoms are free to move around randomly in both flasks. If we were to take snapshots over time, we would see that these atoms can have four possible arrangements. The likelihood of all atoms being found in their original flask, in this case, is only 1 in 4. If we increased the number of atoms, we would see that the probability of finding all of the atoms in the original flask would decrease dramatically following (1/2)ⁿ, where n is the number of atoms.

Thus we can say that it is entropically favoured for the gas to spontaneously expand and distribute between the two flasks, because the resulting increase in the number of possible arrangements is an increase in the randomness/disorder of the system.

Figure 1.1. Two-Atom, Double-Flask Diagram

When the stopcock is opened between the flasks, the two atoms can distribute in four possible ways.