1. Thermodynamics of separation What is the minimum work to separate a mixture into it’s pure components? Ex. Mining, Desalination, Material Purification, Recycling.

2. Balance Eq’ns for Mass, Energy & Entropy S irr

3. Minimum Work of Separation

4. Gibbs Free Energy of Mixing*  g o mix =  h o mix – T 0  s o mix.  g o mix  – T 0  s mix = – T 0 (s 12 – x 1 s 1 – x 2 s 2 ) For non-interacting molecules entropy can dominate often resulting in a negative Gibbs Free Energy and hence spontaneous mixing. I.e.  g o mix < 0 * at standard conditions

5. S = k ln  Boltzmann’s entropy equation How many ways can “r” atoms be positioned in a lattice with “n” locations?

6. w min = T 0  s mix = k T 0 (ln  12 ) Ex. 4 atoms in 8 locations

7. Using Stirling’s Approximation Where x is mol fraction r/n, and R = k N avo ln N! = N ln N - N

8. Multi-component System

9. “Separation”

10. “Extraction”

11. Separation Examples From the atmosphere From the Ocean Solutions –Polymer –Water based –Liquid metals (activity coef)

12. The minimum work to separate O 2 from the atmosphere In wet air you get 3.97 kJ/mol : compare with Szargut Table from the EngineeringToolBox.com

14. energy requirements for mining and milling, possible future trends Chapman and Roberts p 113 & 116 underground ~ 1000/g (MJ/t metal) open pit ~ 400/g (MJ/t metal)

15. Sherwood plot showing the relationship between the concentration of a target material in a feed stream and the market value of (or cost to remove) the target material [Grübler 1998].

16. Exergy of a Mixture

17. CRUST at T o, p o Ore value at mine Pure ore (e.g. Fe 2 O 3 ) Pure metal Metal alloy Mixing in product Mixing in waste stream Further mixing and corrosion Exergy Purification Stages Recycle to pure metal Theoretical Exergy Values for a metal extracted from the earth ’ s crust shown at various stages of a product life cycle (not to scale)