Hello everyone,
This is a master degree problem that is applicable for thin films, its highly appreciated if anyone help me in the derivation of the equations. The equation are written in the attached file.
Thank you in advance.
I mean, this is a pressure divided through the thermal de Broglie wavelength, so it is probably derived via statistical thermodynamics. For more info, please tell us what the "e" index means.
Hello, do you want a partial derivation of Ne over the variable Pe ? because in this case, it's a linear function, so the derivation is a "constant".
If the other variables M and T are not constants, then you should do a total derivative.
The formula that you are interested in is the effusive flow rate. It tells us how many gas molecules pass through a window with a unit area per unit time. This implies, its dimension is 1/m²/s.
The formula is valid for ideal gasses that obey the Maxwell's velocity distribution (https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution), from which it can be derived. You may check the following Wikipedia contribution: https://en.wikipedia.org/wiki/Effusion#Physics_in_Effusion, where you can find the description of this quantity.
A more detailed description of the kinetic theory of gases can be found here: https://en.wikipedia.org/wiki/Kinetic_theory_of_gases, it is based on the abovementioned Maxwell's velocity distribution. Have a look especially at the paragraph "Collisions with container wall", where the collision rate = the effusive flow rate is derived.
I hope these hints will help you.
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