1. PHYSICS ENGINEERING DEPARTMENT
FIZ341E - Statistical Physics and Thermodynamics
Laboratory
Name of Exp. : Maxwellian Velocity Distribution
Date of Exp. : 22.10.2014
BARIŞ ÇAKIR
090100235
2. Introduction
Maxwell’s velocity theory says that, molecules which have different
velocity and energy and also they move different directions (fig1.). In each
direction distribution of velocity vectors are same so molecules behavior is
isotropic.
Figure1. Velocities
If we explain theory by equations, Maxwell-Boltzmann distribution
function is,
( ) ∝ =
These 3 velocity vectors are not related to each other so and they take values
between plus and minus infinite. Maxwell equation should be normalized
between v+∆v and v.
( ) = 1
From the equation, normalization constant equals,
=
2
Finally when we multiply probability densities of 3 different dimension equals
always three dimension probability density.
( ) = ( ) ( )
3. This is a clear result of isotropic condition.
Experimental Procedure
Tools and devices: The circle with 24-zone to keep the balls, power
supply, digital stroboscope, chronometer, test tubes, cables.
Figure2. Experimental Setup
Procedure: First, we set the frequency of oscillator to 50s^-1, and we put
100 glass balls in experimental setup. During 60 seconds, number of pushed
glass balls calculated. This step is repeated for 2 times and we calculate average
number of glass balls pushed from apparatus.
In second step we put 100 glass balls in to the apparatus again but this
time we just add 35 glass balls for each minute, for 9 minutes, after 9 minutes,
we determine the number of glass balls in each of the 24 compartments.
Data Analysis
First we calculate how many glass balls pushed out from the apparatus
and calculate average value of these glass balls.
= 38 ; = 32
= 35
Second, we add 35 glass balls in each minute for the 9 minutes than we
determine number of glass balls in the compartments of reciever (Table1.). We
know for jumping over each stage molecules need to raise their velocity to
0.078(m/s).
We calculated the possible ∆v value using equation for each part
(f=50Hz, =10.72 mg, h=60mm, ∆s=1cm, g=9,81 / ) ;
∆v=∆s.
/
= 0.078 m/s
4. Place
Number of glass
balls V(m/s) f(v)
1 6 0,078 0,699301
2 7 0,156 0,815851
3 18 0,234 2,097902
4 21 0,312 2,447552
5 16 0,39 1,864802
6 20 0,468 2,331002
7 8 0,546 0,932401
8 5 0,624 0,582751
9 3 0,702 0,34965
10 2 0,78 0,2331
11 2 0,858 0,2331
12 1 0,936 0,11655
20 1 1,56 0,11655
Table1. Experimental Calculations
If we plot the graph of velocity-probability density;
Graphic1. Expected Positions of Particle
Conclusion
Our expectation is plotting probability density graph similar to real one,
for example following graphic is a probability density graph for different
temperatures,
-0,5
0
0,5
1
1,5
2
2,5
3
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8
f(v)
V(m/s)
Probability Density
5. Figure 3. Probability Densities for Different Temperatures
Our graphic is very similar to T1 temperatures graph, if we would
increase the temperature we can get similar results to T2 and T3.
Resources
Thermodynamics LAB FÖY
http://galileo.phys.virginia.edu/classes/252/kinetic_theory.html
http://www.tannerm.com/maxwell_boltzmann.htm
Answers
1. From the average velocity formula;
< > = ( )
< > = 4
2
< > =
8
2. If the molecular weight increases, the average speed decreases.
If the molecular weight decreases, the number of molecules with average
speed decreases.
If the temperature increases, average speed increases.
If the temperature decreases the number of molecules with average speed
increases.
