Consider a given volume of liquid at a temperature ∆T below Tm with a free energy G₁, figure a. If Vs is the volume of the solid sphere, V, the volume of liquid, Asl is the solid/liquid interfacial area, GS and G are the free energies per unit volume of solid and liquid respectively, and γsl, the solid/liquid interfacial free energy. 

(a) The free energy of the system without any solid present is G₁=_______ 

(b) If some of the atoms of the liquid cluster together to form a small sphere of solid, figure b, the free energy of the system will change to G₂ =_____ 

(c) Therefore, the formation of solid results in a free energy change ∆G =_______ 

(d) Determine the energy barrier ∆G* for homogenous nucleation using the information above.

 

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