- #1

Pushoam

- 962

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## Homework Statement

Derive the flux of molecules i.e. no. of molecules striking a surface per unit area per unit time.

## Homework Equations

## The Attempt at a Solution

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Let's say that there are n molecules per unit volume.

The no. of molecules which will touch the surface in the +ve x direction in time ##d t ## is

dN = n A dx = n A <v

_{x}> dt .

So, the flux should be ##\phi = n <v_x>##.

##< v_x> = < v_y> = < v_z> \neq \frac {<v>} 3##

The probability of getting a particle with speed between ##v_x## and ## v_x + dv_x## is given by

##g(v_x) dv_x ## ## \propto ## ## e ^ \left( - \frac {m{v_x}^2}{2 k_B T} \right) ##.

Then,

## <v_x> = \int_{0 }^{\infty } v_x C## ##e^{ \left( - \frac { m{v_x}^2 } {2 k_BT } \right) }## ## dv_x ##

Where C is the appropriate constant.

I have to express ## < v_x >## into ## <v>##. For this I should express ##<v_x>## as ## v \sin { \theta } \cos { \phi } ## and then take integration.

Is this correct?

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