Answer
$P_{M} = 2.93 \times 10^{-14} \frac{cm^{3}STP-cm}{cm^{2}-s-Pa}$
Work Step by Step
Given:
Carbon dioxide diffuses through a high-density polyethylene (HDPE) sheet 50 mm thick at a rate of $2.2 \times 10^{-8} (cm^{3} STP)/cm^{2}-s $ at 325 K. The pressures of carbon dioxide at the two faces are 4000 kPa and 2500 kPa, which are constant.
Required:
The permeability coefficient at 325 K assuming steady state conditions.
Solution:
Using Equation 14.9 and knowing that $P_{1} = 250000 Pa$ and $ P_{2} = 4000000 Pa$, it follows:
$P_{M} = \frac{JΔx}{ΔP} = \frac{JΔx}{P_{2} -P_{1}} = \frac{(2.2 \times 10^{-8} \frac{cm^{3}STP}{cm^{2}-s}) (5 cm)}{(4000000 Pa) - (250000 Pa)} = 2.93 \times 10^{-14} \frac{cm^{3}STP-cm}{cm^{2}-s-Pa}$
