7/30/2019 Physics Formula 40

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32 Physics Formulary by ir. J.C.A. Wevers

7.5 Collisions between molecules

The collision probability of a particle in a gas that is translated over a distance dx is given by ndx, where is

the cross section. The mean free path is given by =v1

nu with u =

v21 + v22 the relative velocity between

the particles. Ifm1 m2 holds: uv1

=

1 +

m1m2

, so =1

n. Ifm1 = m2 holds: =

1

n

2. This means

that the average time between two collisions is given by =1

nv. If the molecules are approximated by hard

spheres the cross section is: = 14

(D21 + D22). The average distance between two molecules is 0.55n

1/3.

Collisions between molecules and small particles in a solution result in the Brownian motion. For the average

motion of a particle with radius R can be derived:

x2i

= 13

r2

= kTt/3R.

A gas is called a Knudsen gas if the dimensions of the gas, something that can easily occur at lowpressures. The equilibrium condition for a vessel which has a hole with surface A in it for which holds that

A/ is: n1

T1 = n2

T2. Together with the general gas law follows: p1/

T1 = p2/

T2.

If two plates move along each other at a distance d with velocity wx the viscosity is given by: Fx = Awx

d .The velocity profile between the plates is in that case given by w(z) = zwx/d. It can be derived that =13

v where v is the thermal velocity.

The heat conductance in a non-moving gas is described by:dQ

dt= A

T2 T1

d

, which results in a temper-

ature profile T(z) = T1 + z(T2 T1)/d. It can be derived that = 13CmVn v /NA. Also holds: = CV.A better expression for can be obtained with the Eucken correction: = (1 + 9R/4cmV)CV with anerror