# Extracting Work From Mixing Of Ideal Gases?

Consider two identical boxes of ideal gases, at the same temperature, volume, and pressure. I will assume that gas A and gas B are distinguishable, but do not react with each other (maybe this is a lie).

We remove a wall between the two boxes. The gases will tend to mix over time, since that tends to increase entropy.

Because entropy is increasing, Gibbs energy should be decreasing. I have read that "The Gibbs free energy change is the maximum amount of non-expansion work that can be extracted from a closed system."

However, in my example, where there is no change in enthalpy, I don't see how the work can be extracted from simply the change in entropy (the arrangement of the gases).

Clearly I have missed something, as I am new to these terms. I hope my question is not too naive.

• Determining change in entropy and enthalpy during mixing of gases Jun 4, 2022 at 7:20
• You need to devise a reversible process for going from two individual gases at T, P , and V to a mixture of the gases as T, P, and 2V (and partial pressures P/2). Hint: such a process might involve use of semipermeable membranes and three cylinders. Jun 4, 2022 at 10:47