Near room temperature, the diffusion coefficient of $C$ in $Fe$ is $D=(2{10}^{-5}\frac{m^2}{s})exp(-\frac{10120}{T}).$

Assume that the average vibrational frequency of $C$ atoms in the lattice is $5{10}^{13}\frac{1}{s}.$ Given a lattice

parameter $a_0=0\mathrm{.}287nm,$ calculate the entropy of the activated state for interstitial diffusion.

$D=a_{0}w,=\frac{1}{6},$

$w=w_0$exp$(-\frac{G_M}{R}T),w_0=5{10}^{13}\frac{1}{s},R=8\mathrm{.}314\frac{J}{m}$ole $K$