Free Expansion of an Ideal Gas into twice the Volume.

A. Thermodynamic Approach
For an Ideal Gas the entropy change when T_f = T_o is,

For one mole ΔS = 5.76 J/K.

B. Information Approach
Two states - A molecule can be in the left half of the container or it can be in the right side of the container. We know less about the system after the free expansion since it can be in either side.

Measured in bits, the change in entropy for one mole

C. Probability Approach
The probability that N molecules will be in the left half of the container is (1/2)^N while the probability that all N molecules are in the container is just one.

The same as before.