An unglazed porcelain plate \(5 \mathrm{~mm}\) thick has an average pore diameter of \(0.2 \mu \mathrm{m}\). Pure oxygen gas at an absolute pressure of \(20 \mathrm{~mm} \mathrm{Hg}, 400 \mathrm{~K}\), on one side of the plate passed through at a rate of \(0.10 \mathrm{~cm}^{3}\) (at \(20 \mathrm{~mm} \mathrm{Hg}, 400 \mathrm{~K}\) ) \(/ \mathrm{cm}^{2}\)-s when the pressure on the downstream side was so low as to be considered negligible.

(a) Calculate the Knudsen number for flow inside the pores.

(b) Estimate the rate of passage of hydrogen gas through the plate at \(300 \mathrm{~K}\) and an absolute pressure of \(10 \mathrm{~mm} \mathrm{Hg}\), with negligible downstream pressure.