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Maxwellian distribution in Fig. 10.1 is equal to unit (S= 1).
To find the most probable speed v pob that corresponds to the maximum

of the function  vf (Fig. 10.1) it's necessary to investigate this graph on
extremums, namely to find the derivative and to find the solution of the

following equation:
df  v
 0 (1.10.4)
dv

Hence the most probable speed is equal to :

2 kT 2 RT
v   (1.10.5)
prob
m M

The average speed of a molecule (see fig.10.1) is :

8 kT 8 RT
 v   (1.10.6)
 m  M
And the root-mean-square speed is equal to

3 kT 3 RT
v rms   (1.10.7)
m M

The temperature T increases the
Maxwelian distribution changes as it is

shown in Fig. 10.2: v prob 2 vprob 1 , the

area under both curves is the same

Figure 1.10.2

1.11. Barometric Formula. The Boltzmann Distribution

In the previous chapter we have considered the behaviour of an ideal

gas not liable to be influenced by external force fields. Due to gravity

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