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che294f01hmwrk08 - October 8 2001 CHE/MAE 294 F01...

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October 8, 2001 CHE/MAE 294 F01, Assignment 8 due Friday, October 12 Extra credit will be given for those problems marked with if they are solved using a computer program. Solidification 1. Nucleation is controlled by the formula G T 4 3 π r 3 G v 4 π r 2 γ , where G T (J)is the total Gibb’s energy of the nucleus that forms, G v (J/m 3 ) is the bulk Gibb’s energy per unit volume of solid, γ (J/m 2 ) is the Gibb’s energy per unit surface area of solid (surface tension), and r is the radius of the nucleus. The critical radius for nucleation r c is determined at the point where d G T dr 0. Prove that r c 2 γ T m H f us T where T m (K) is the melting temperature, H f us (J/mol) is the molar enthalpy of solidification, and T T m T (K) is the degree of undercooling. Hints: At T m , the value of G v H f us T S f us is identically zero. 2. For Cu, T m 1356 K, H f us 1826 J/cm 3 , and γ 17 7 μ J/cm 3 . Determine the critical radius for nucleation (in nm) at undercoolings of 10 o C, 20 o C, 100 o C, 200 o C, and 500 o C.
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