Entropy of Mixing and Separation Work
We consider mixing and separation of ideal mixtures at constant tempera- ture T . The combined first and second law for a closed system at constant temperature T reads
where Sgen = r S˙gendt is the total entropy generation for the process.
We consider mixing first, where state 1 is the unmixed state, and state 2 is the mixed state. Then, since Umix = 0 for an ideal mixture,
When the mixing is fully irreversible, no work is drawn, W12 = 0, and the entropy generation is just the entropy of mixing, Sgen = Smix. However, the equation shows that it is possible to generate the work
In a real device, the irreversibilities of the process diminish the work by T Sgen. The maximum work is obtained from a fully reversible process as
Note that more work can be produced at higher temperature.
Now we consider separation, where state 1 is the mixed state, and state 2 is the unmixed state. Then, again with Umix = 0,
work is required for separation at lower temperatures.
Section 21 will present a closer look at desalination plants, which separate salt from water, and osmotic power plants, which use mixing for power generation. 21.5.