Labster Logo

Entropy explained by probability

Entropy can be explained in terms of probability: Placing four different cards in a box with two rooms can be done in 16 different ways, as you can see on the image below. If you pick one of these combinations at random, chances are highest that you will pick one with an equal distribution of cards in the two rooms because the combination with two cards in each room has more microstates available. Only one of the 16 combinations have all of the cards in the left room.

Four different cards are placed into a box with two rooms. There are sixteen of these boxes and they are arranged into five rows. The distribution of boxes over these rows is based on the number of cards in each room. Row one and five have one box each and the boxes have all four cards in one room. Rows two and four have four boxes each and the boxes have three cards in one room and one card in the other room. Row three has six boxes and the boxes have an equal number of cards are in each room. Since row three has the greatest number of boxes, these boxes will be preferred statistically. There is a six out of sixteen chance of choosing a box with an equal number of cards in each room.

Figure 1: Entropy can be explained by statistics.

Now think of the cards as gas molecules and the box with two rooms as two connected gas containers. Instead of 4 particles inside, there are now billions of billions. The number of combinations for placing all the gas molecules in either of the two containers is approaching infinity but still, only one of those combinations have all of the particles in the left container. The chances of an equal distribution of gas particles between the two containers are much, much higher. We say that the expansion of a gas into a connecting empty container is spontaneous because it increases the entropy of the system.

Referred from:

Article
Entropy