Consider the iron film of thickness $x$ shown in figure below, which separates two volumes of hydrogen gas. The gas on the left side of the film is at pressure $P_1$ and the gas on the right side of pressure $P_2.$

$($a$)$ Calculate the flux of hydrogen through the iron film at steady state at $400C.$ You are given the following information:

i$.x=0\mathrm{.}001m$;$p_1=1\mathrm{.}013{10}^{5}Pa(1$atm$)$;$p_2=0$;$D_{H-Fe}={10}^{-8}\frac{m^2}{s}$ at $400C$;${}_{Fe}=7600k\frac{g}{m^3}$ temperature $(T)$ as

$logK=\frac{1905}{T}-2\mathrm{.}401(Tin$ Kelvin $)$

Assume hydrogen dissolved in steel at the gas$-$solid interface $($on the left face$)$ to be in equilibrium with the hydrogen gas present outside. Also, assume Henrian behaviour for hydrogen dissolved in steel.

$($b$)$ Now consider a cubical iron tank of wall thickness $0\mathrm{.}001m$ and volume $0\mathrm{.}1m3$ that contains hydrogen gas at a pressure of $1$atm. If the pressure outside the tank is negligibly small, after what time has the diffusion of hydrogen through the tank occurred to the extent that the pressure in the tank has decreased to half of its original value?