Chemistry · Chapter 16

Entropy: Counting the Ways

Entropy is the spread of matter and of energy. Move the particles, hand out the energy, and watch the number of microstates climb. The formula S = k ln W turns that count into joules per kelvin.

One microstate4 left, 4 right

Each dot is one particle. Each small bar above a dot is one quantum of energy. The whole picture is a single microstate, which means one exact way the sample can be.

Ways to split the particlesheight = number of arrangements

The countS = k ln W

0× 10−23 J/K W = 1
ways to place the particles 
ways to share the energy 
total W 
ln W 

Position count is 2N. Energy count is the number of ways q matching quanta land on N particles. Here the two are independent, so they multiply.

Controls

What this shows
Spread out has more ways
Try the two buttons above. The even split and the one-sided pile are both single microstates, so each one is equally likely on its own. The even split wins because so many different arrangements look like it.