Presentation on theme: "Thermodynamics of separation What is the minimum work to separate a mixture into it’s pure components? Ex. Mining, Desalination, Material Purification,"— Presentation transcript:
Thermodynamics of separation What is the minimum work to separate a mixture into it’s pure components? Ex. Mining, Desalination, Material Purification, Recycling.
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
S = k ln Boltzmann’s entropy equation How many ways can “r” atoms be positioned in a lattice with “n” locations?
w min = T 0 s mix = k T 0 (ln 12 ) Ex. 4 atoms in 8 locations
Using Stirling’s Approximation Where x is mol fraction r/n, and R = k N avo ln N! = N ln N - N
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)