The quantum casino: simulations
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Arranging objects

We saw in the Entropy and disorder simulation that objects moving at random will arrange themselves equally between two boxes. This simulation looks a little more closely at why this should be. Like Entropy and disorder, it does not try to closely model a real chemical situation.

It is important to distinguish between a particular state that we might be able to observe and the way(s) that it is made up. An example is box 1 has one object and box 2 five. There are six ways of doing this – object 1 in box 1, the rest in box 2; object 2 in box 1, the rest in box 2 and so on. However, if all the objects are identical, we cannot distinguish between them and they all lead to the same state. However, some states are more probable than other because there are more arrangements that lead to them.

This simulation lets you investigate the number of ways that make up particular state and see how this varies with the number of objects.



You should notice that 50 : 50 arrangements (and those close to this) are much more likely than ones where one box has few objects and the other many. This probability increases enormously as the total number of objects increases and would become virtually certain for an everyday number of particles such as a mole (6 x 1023).

The quantum casino