Naphthalene ball with $5cm$ diameter is placed in a stagnant air at $40C$ and $1$atm. Molar evaporation flux of this ball is $1\mathrm{.}47{10}^{-3}mo\frac{l}{m^2}.$s$.$ The vapor pressure of naphthalene is $15\mathrm{.}2$kPa at $40C$ and it has a negligible concentration in the bulk phase. Calculate the mass transfer coefficient $(k_c).($Assume that the system is dilute$){}_{\text{a}\text{i}\text{r}}=1\mathrm{.}8{10}^{-5}k\frac{g}{m}.s$;$,{}_{\text{a}\text{i}\text{r}}=1\mathrm{.}123k\frac{g}{m^3}$;$R=82\mathrm{.}06c{m}^3.$atm $\frac{?}{\text{m}\text{o}\text{l}}.$ K at process conditions.

For spherical surfaces: $Sh=2+0\mathrm{.}6(Re{)}^{0\mathrm{.}5}(Sc{)}^{0\mathrm{.}33}$