(Solution) - a Rewrite the expression for the total free energy change -(2025 Original AI-Free Solution)

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(a) Rewrite the expression for the total free energy change for nucleation (Equation 10.1) for the case of a cubic nucleus of edge length a (instead of a sphere of radius r). Now differentiate this expression with respect to a (per Equation 10.2) and solve for both the critical cube edge length, a*, and also ?G*.
(b) Is ?G* greater for a cube or a sphere? Why?