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-BARSIC- [3]
3 years ago
5

Compute the number of kilograms of hydrogen that pass per hour through a 5-mm-thick sheet of palladium having an area of 0.20 m^

2 at 500°C. Assume a diffusion coefficient of 1.0 x 10^8 m^2 /s, that the concentrations at the high- and low-pressure sides of the plate are 2.4 and 0.6 kg of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained.
Engineering
1 answer:
Nat2105 [25]3 years ago
3 0

Answer:

The answer is "\bold{ 259.2 \times 10^{11} }".

Explanation:

The amount of kilograms, which travel in a thick sheet of hydrogen:

M= -DAt \frac{\Delta C}{ \Delta x} \\\\

D =1.0 \times 10^{8} \ \ \ \frac{m^2}{s} \\\\ A = 0.20 \ m^2\\\\t = 1\ \ h = 3600 \ \   sec \\\\

calculating the value of \Delta C:

\Delta C =C_A -C_B

  = 2.4 - 0.6 \\\\    = 1.8 \ \ \frac{kg}{m^3}

calculating the value of \Delta X:

\Delta x = x_{A} -x_{B}

     = 0 - (5\ mm) \\\\ = - 5 \ \ mm\\\\= - 5 \times 10^{-3} \ m

M = -(1.0 \times 10^{8}  \times 0.20 \times 3600 \times  (\frac{1.8}{-5 \times 10^{-3}})) \\\\

    = -(1.0 \times 10^{8}  \times 720 \times  (\frac{1.8}{-5 \times 10^{-3}})) \\\\= -(1.0 \times 10^{8}  \times \frac{ 1296}{-5 \times 10^{-3}})) \\\\= (1.0 \times 10^{8}  \times 259.2 \times 10^3)) \\\\= 259.2 \times 10^{11} \\\\

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The first thing we must consider to solve this problem is the continuity equation that states that the amount of mass flow that enters a system is the same as what should come out.

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