Question

Compute the number of kilo- grams of hydrogen that pass per hour through a 6-mm-thick sheet of palladium having an area of 0.25 m^2 at 600°C. Assume a diffusion coefficient of 1.7 x 10^8 m^2/s, that the concentrations at the high- and low-pressure sides of the plate are 2.0 and 0.4 kg of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained.

Answer 1

Answer:

The number of kilo- grams of hydrogen that pass per hour through this sheet of palladium is $4.1 * 10^{-3} \frac{kg}{h}$

Explanation:

Given

x1 = 0 mm

x2 = 6 mm = 6 * $10^{-3}$ m

c1 = 2 kg/$m^{3}$

c2 = 0.4 kg/$m^{3}$

T = 600 °C

Area = 0.25 $m^{2}$

D = 1.7 * $10^{8} m^{2}/s$

First equation

J = - D $\frac{c1 - c2}{x1 - x2}$

Second equation

J = $\frac{M}{A*t}$

To find the J (flux) use the First equation

J = - 1.7 * $10^{8} m^{2}/s$ * $\frac{2 kg/m^{3} - 0.4 kg/m^{3}}{0 - 6 * 10^{-3} } = 4.53 * 10^{-6} \frac{kg}{m^{2}s }$

To find M use the Second equation

$4.53 * 10^{-6} \frac{kg}{m^{2}s}$ = $\frac{M}{0.25 m^{2} * 3600s/h}$

M = $4.1 * 10^{-3} \frac{kg}{h}$