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Unformatted text preview: 4.10. IRREVERSIBLE ENTROPY PRODUCTION IN A CLOSED SYSTEM 137 the second law requiring dσ ≥ 0. Equation (4.387) in terms of dσ is dσ = − 1 T N summationdisplay i =1 μ i dn i ≥ . (4.388) Now, while most standard texts focusing on equilibrium thermodynamics go to great lengths to avoid the introduction of time, it really belongs in a discussion describing the approach to equilibrium. One can divide Eq. (4.387) by a positive time increment dt to get − 1 T N summationdisplay i =1 μ i dn i dt ≥ . (4.389) Since T ≥ 0, one can multiply Eq. (4.389) by − T to get N summationdisplay i =1 μ i dn i dt ≤ . (4.390) This will hold if a model for dn i dt is employed which guarantees that the left side of Eq. (4.390) is negative semi-definite. One will expect then for dn i /dt to be related to the chemical potentials μ i . Elimination of dU in Eq. (4.383) in favor of dH from dH = dU + PdV + V dP gives dH − PdV − V dP bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright...
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This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Park-sou during the Fall '11 term at FSU.
- Fall '11