Question

(a) For the solidification of iron, calculate the critical radius r* and the activation free energy ΔG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are –1.85 × 109 J/m3 and 0.204 J/m2, respectively. Use the supercooling value ΔT = 273 K, and the melting point of iron is 1538°C.

Answer 1

Answer:

$r = 1.46 *10^{-9} m$

$\Delta G^* = 1.828 *10^{-18} j$

Explanation:

given data:

latent heat of fusion $\Delta H_f = -1.85*10^9 j/m2$

surface free energy = 0.204 j/m2

meltinf point = 1538 degree celcius

$\Delta T_c = 273 K$

critical radius is given as

$r^* = \frac{-2rT_m}{\Delta H_f} *\frac{1}{\DeltaT_c}$

$= \frac{-2*0.204*(1538+273)}{-1.85*10^9} *\frac{1}{273}$

$r = 1.46 *10^{-9} m$

activation free energy is given as

$\Delta G^* = \frac{16\pi r^3 t_m^2}{3\Delta H^2_f} * \frac{1}{\Delta T^2_C}$

       $= \frac{16\pi 0.204^3*(1538+273)^2}{3*(-1.85*10^9)^2} * \frac{1}{273^2}$

$\Delta G^* = 1.828 *10^{-18} j$