(Solved): 14-48 The solubility of hydrogen gas in steel in terms of its mass fraction is given as \( w_{H_{2} ...

14-48 The solubility of hydrogen gas in steel in terms of its mass fraction is given as \( w_{H_{2}}=2.09 \times 10^{-4} \exp (-3950 / T) P_{H_{2}}^{0.5} \) where \( P_{H_{2}} \) is the partial pressure of hydrogen in bars and \( T \) is the temperature in K. If natural gas is transported in a 1-cmthick, 3-m-internal-diameter steel pipe at \( 500 \mathrm{kPa} \) pressure and the mole fraction of hydrogen in the natural gas is 8 percent, determine the highest rate of hydrogen loss through a 100-mlong section of the pipe at steady conditions at a temperature of \( 293 \mathrm{~K} \) if the pipe is exposed to air. Take the diffusivity of hydrogen in steel to be \( 2.9 \times 10^{-13} \mathrm{~m}^{2} / \mathrm{s} \). Answer: \( 3.98 \times 10^{-14} \mathrm{~kg} / \mathrm{s} \)