(II) Given the Maxwell speed distribution function, the aver- age value of v" is U² = Un f(v) du N v" where N is the total number of particles. (a) Show that the average speed is 8kT Vav = Vam Note that fo x³ exp(-ax²)dx = 1/2a².

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Chapter1: Units, Trigonometry. And Vectors
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(II) Given the Maxwell speed distribution function, the aver-
age value of un is
Un
v² = 5" v² f(v) du
N
where N is the total number of particles.
(a) Show that the average speed is
8kT
Vav = V πM
Note that fo x³ exp(-ax²)dx = 1/2a².
Transcribed Image Text:(II) Given the Maxwell speed distribution function, the aver- age value of un is Un v² = 5" v² f(v) du N where N is the total number of particles. (a) Show that the average speed is 8kT Vav = V πM Note that fo x³ exp(-ax²)dx = 1/2a².
(b) Show that the rms speed is
Urms =
3kT
m
Note that fo x*exp(-ax²)dx = √9π/64a³.
Transcribed Image Text:(b) Show that the rms speed is Urms = 3kT m Note that fo x*exp(-ax²)dx = √9π/64a³.
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