HOMEWORK ASSIGNMENT 11
Problems Chapter 11
11-7
The Maxwell speed distribution (number of particles with speed in the range
dv) is
N(v)dv = 4πN m
2πkT 3/2
v2e−mv2
2kT dv
a) Define
x=v
vm
, dx =dv
vm
, vm=2kT
m1/2
Then
N∗(x)dx =N(xvm)d(xvm) = 4N
√πx2e−x2dx
b) The total number of particles with v < v0is
P(v0) = Zv0
0
dvN (v) = Zx0
0
dxN∗(x)
=4N
√πZx0
0
x2e−x2dx
=−2N
√πZx0
0
xde−x2
dx dx
=−2N
√πZx0
0
dxe−x2
dx −d(x)
dx e−x2
dx
=−2N
√πx0e−x2
0−Zx0
0
e−x2dx
c) For v0=vm, x0= 1 and
P(vm)
N=−2
√πe−1−Z1
0
e−x2dx= 0.428
11-8 The definitions are
vm=2kT
m1/2
,v=8kT
πm 1/2
, vrms =3kT
m1/2
For the Oxygen molecule
m= 32 ∗1.67 ∗10−27
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