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If I make a box from aluminum (0.5 mm thickness) and put air in it (about 2 bar or 3 bar), would the box lose the air over time (10 years period) or not?

Assuming the temperature will change constantly between 0 to 100 Celsius. I found this equation $J = KD (\sqrt{p_2} − \sqrt{p_1}) / \delta$. Is it the right equation to work with?

I'm a student (Electrical engineering) working on project. I don't need to calculate the exact value I just need to know if it is possible. Please feel free to correct the question (I have never studied fluid dynamics).

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Your equation for gas permeation mostly applies to hydrogen, which will dissociate into hydrogen atoms before entering the material. For nitrogen (major component of air), the equation has no square roots. Nitrogen permeation is extremely slow; if the box is welded shut and there are no cracks, then this process will be negligible, even over a 10-year period.

Note that packages for fruit juice, long-life milk, and such use a very thin film of aluminum to keep the oxygen out and achieve a shelf life of several years.

Lafferty, Foundations of Vacuum Science and Technology (1998) provides the equation for the gas flow rate (in pressure*volume/time units) $$ Q = {kA\over d} (p_1-p_2) $$ where $A$ is the surface area, $d$ the wall thickness, $p_{1,2}$ the pressures on either side of the wall, and $k$ is the permeation conductivity. For nitrogen through steel at 100 °C, the value is $k=10^{-20}~\mathrm{m^2/s}$ (actually extrapolated off-scale).

If the box is sealed with some rubber-like seal, then the seal will likely be the major leak, with a permeation conductivity that is many orders of magnitude higher.

Note that with just 0.5 mm thickness, it is hard to guarantee that there are no microscopic cracks anywhere.

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