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()
(
)
26
3
3
2 0.16 9.8m s
1.74 10 m 32.0 10 kg mol
7.0 10 K.
38
.31Jmo
lK
T
−
××
==
×
⋅
(e) The temperature high in Earth's atmosphere is great enough for a significant number
of hydrogen atoms in the tail of the Maxwellian distribution to escape. As a result the
atmosphere is depleted of hydrogen.
(f) On the other hand, very few oxygen atoms escape. So there should be much oxygen
high in Earth’s upper atmosphere.
37. The rms speed of molecules in a gas is given by
3
rms
vR
T
M
=
, where
T
is the
temperature and
M
is the molar mass of the gas. See Eq. 1934. The speed required for
escape from Earth's gravitational pull is
2
e
vg
r
=
, where
g
is the acceleration due to
gravity at Earth's surface and
r
e
(= 6.37
×
10
6
m) is the radius of Earth. To derive this
expression, take the zero of gravitational potential energy to be at infinity. Then, the
gravitational potential energy of a particle with mass
m
at Earth's surface is
2
e
e
UG
M
m
r
m
g
r
=−
,
where
2
e
gG
M
r
=
was used. If
v
is the speed of the particle, then its total energy is
2
1
2
e
E
mgr
mv
+
. If the particle is just able to travel far away, its kinetic energy must
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Acceleration, Mass

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