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Hi there,

I'm having a problem interpreting how a velocity interval defined by [itex]dv^3 = dv_x dv_y dv_z[/itex], being an isotropic case, why do we write it like this:

[itex] dv^3 = 4 \pi v^2 dv [/itex]

And also, how can I derive the molecular impingement rate over a surface? I saw at a book, but I don't understand it, that, considering only particles with velocity [itex] v_x [/itex] will hit the surface, in order to get the molecular impingement rate, [itex] J [/itex], we have to:

[itex] J = \frac{1}{V} \int_ 0^{\infty} v_x dN = \frac{n\, v_{avg}}{4} [/itex]

Where [itex] dN [/itex] is the number of molecules, [itex] n = N/V [/itex], being [itex] V [/itex] the volume and [itex] v_{avg} [/itex] the average velocity.

Thank you!

I'm having a problem interpreting how a velocity interval defined by [itex]dv^3 = dv_x dv_y dv_z[/itex], being an isotropic case, why do we write it like this:

[itex] dv^3 = 4 \pi v^2 dv [/itex]

And also, how can I derive the molecular impingement rate over a surface? I saw at a book, but I don't understand it, that, considering only particles with velocity [itex] v_x [/itex] will hit the surface, in order to get the molecular impingement rate, [itex] J [/itex], we have to:

[itex] J = \frac{1}{V} \int_ 0^{\infty} v_x dN = \frac{n\, v_{avg}}{4} [/itex]

Where [itex] dN [/itex] is the number of molecules, [itex] n = N/V [/itex], being [itex] V [/itex] the volume and [itex] v_{avg} [/itex] the average velocity.

Thank you!

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