Problem statement $3$

Gaseous hydrogen at $200$ psia and $300C$ is stored in a small, $10-cm-$diameter, steel pressure

vessel having a wall thickness of $0\mathrm{.}125in.$ The solubility of hydrogen in steel, which is

proportional to the square root of the hydrogen partial pressure in the gas, is equal to $3\mathrm{.}8{10}^{-6}$

$mo\frac{l}{c}{m}^3$ at $14\mathrm{.}7a$ and $300C.$ The diffusivity of hydrogen in steel at $300C$ is $5{10}^{-6}c\frac{m^2}{s}.$

If the inner surface of the vessel wall remains saturated at the existing hydrogen partial pressure

and the hydrogen partial pressure at the outer surface is zero, estimate the time, in hours, for

the pressure in the vessel to decrease to $100$ psia because of hydrogen loss by dissolving in and

diffusing through the metal wall.