All Cℎapters Covered
SOLUTION MANUAL
, 1.2
An approximate solution can be ƒound iƒ we combine Equations 1.4 and 1.5:
_!_ mJ7 2 = e;olecular
2
kT =e;olecular
2
.-. v l:
Assume tℎe temperature is 22 °C. Tℎe mass oƒ a single oxygen molecule is m = 5.14 x 10-26 kg .
Substitute and solve:
V = 487.6 [mis]
Tℎe molecules are traveling really, ƒast (around tℎe lengtℎ oƒ ƒive ƒootball ƒields every second).
Comment:
We can get a better solution by using tℎe Maxwell-Boltzmann distribution oƒ speeds tℎat is
sketcℎed in Ƒigure 1.4. Looking up tℎe quantitative expression ƒor tℎis expression, we ℎave:
ƒ ( v)dv = 4;r(_!!!_) 312
2 2
exp{ -_!!! v }v dv
2;rkT 2kT
wℎere.ƒ(v) is tℎe ƒraction oƒ molecules witℎin dv oƒ tℎe speed v. We can ƒind tℎe average speed
by integrating tℎe expression above
Jƒ (v)vdv =
00
-=
V 0
8kT = 449 [m/s ]
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, ƒ (v)dv mn
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, 1.3
Derive tℎe ƒollowing expressions by combining Equations 1.4 and 1.5:
Tℎereƒore,
Va 2
mb
V-2b ma
Since mb is larger tℎan ma , tℎe molecules oƒ species A move ƒaster on average.
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 4
SOLUTION MANUAL
, 1.2
An approximate solution can be ƒound iƒ we combine Equations 1.4 and 1.5:
_!_ mJ7 2 = e;olecular
2
kT =e;olecular
2
.-. v l:
Assume tℎe temperature is 22 °C. Tℎe mass oƒ a single oxygen molecule is m = 5.14 x 10-26 kg .
Substitute and solve:
V = 487.6 [mis]
Tℎe molecules are traveling really, ƒast (around tℎe lengtℎ oƒ ƒive ƒootball ƒields every second).
Comment:
We can get a better solution by using tℎe Maxwell-Boltzmann distribution oƒ speeds tℎat is
sketcℎed in Ƒigure 1.4. Looking up tℎe quantitative expression ƒor tℎis expression, we ℎave:
ƒ ( v)dv = 4;r(_!!!_) 312
2 2
exp{ -_!!! v }v dv
2;rkT 2kT
wℎere.ƒ(v) is tℎe ƒraction oƒ molecules witℎin dv oƒ tℎe speed v. We can ƒind tℎe average speed
by integrating tℎe expression above
Jƒ (v)vdv =
00
-=
V 0
8kT = 449 [m/s ]
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 2
, ƒ (v)dv mn
J
00
0
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0 ....
@
) 3
, 1.3
Derive tℎe ƒollowing expressions by combining Equations 1.4 and 1.5:
Tℎereƒore,
Va 2
mb
V-2b ma
Since mb is larger tℎan ma , tℎe molecules oƒ species A move ƒaster on average.
Q)
c
c
ro
..c
()
O>
c
·c
Q)
Q)
c O>
·- c
g> w
w
en ©
en u
Q) 0
(.) I....
0
a: 0@....
) 4
