Question $3)$ Answer the following questions: $(\%20)$

a$)$ For a homogeneous nucleation process, sketch the dependence of the surface and bulk

free energies on the radius of a spherical embryo using the equation below. $(\%10)$

$G_n=4r^2-\frac{4}{3}{r}^3\frac{kT}{V}lnS$

b$)$ Sketch the dependence of the free energy changes $(G_n)$ on the radius of a spherical

embryo when the supersaturation ratio $($S$)$ is greater than $1,$ equal to $1$ and less than $1.(\%$