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Thermodynamics of separation

Thermodynamics of separation. What is the minimum work to separate a mixture into it’s pure components? Ex. Mining, Desalination, Material Purification, Recycling. Balance Eq’ns for Mass, Energy & Entropy. S irr. Minimum Work of Separation. Gibbs Free Energy of Mixing*.

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Thermodynamics of separation

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  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 Sirr

  3. Minimum Work of Separation

  4. Gibbs Free Energy of Mixing* Dgomix = Dhomix–T0Dsomix. Dgomix  –T0Dsmix = –T0(s12–x1s1– x2s2) For non-interacting molecules entropy can dominate often resulting in a negative Gibbs Free Energy and hence spontaneous mixing. I.e. gomix < 0 * at standard conditions

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

  6. Ex. 4 atoms in 8 locations wmin = T0Dsmix = k T0 (ln 12)

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

  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 O2 from the atmosphere Table from the EngineeringToolBox.com In wet air you get 3.97 kJ/mol : compare with Szargut

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

  14. 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].

  15. Exergy of a Mixture

  16. Pure metal Exergy Metal alloy Mixing in product Mixing in waste stream Further mixing and corrosion Recycle to pure metal Pure ore (e.g. Fe2O3) Ore value at mine CRUST at To, po Purification Stages Theoretical Exergy Values for a metal extracted from the earth’s crust shown at various stages of a product life cycle (not to scale)

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