18.83:
a) See Problem 18.80. Because
dv
v
f
)
(
is the probability that a particle has a
speed between
dv
v
f
dv
v
v
)
(
,
and
+
is the fraction of the particles that have speed in that
range. The number of particles with speeds between
dv
v
v
+
and
is therefore
dv
v
Nf
dN
)
(
=
and
.
)
(
dv
v
f
N
N
v
v
v
∆
+
∫
=
∆
b)
,
2
mp
m
kT
v
=
and
.
4
2
2
4
)
(
mp
1
mp
2
3
v
π
e
e
m
kT
πkT
m
π
v
f
=
=

For oxygen gas at
,
0421
.
0
)
(
and
s,
m
10
95
.
3
K,
300
2
mp
=
∆
×
=
v
v
f
v
keeping an extra
figure.
c) Increasing
v
by a factor of 7 changes
.
10
94
.
2
)
(
and
,
7
of
factor
a
by
21
48
2


×
=
∆
v
v
f
e
f
d) Multiplying the
temperature by a factor of 2 increases the most probable speed by a factor of
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 Fractions, Fraction, probable speed

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