10.3 Solutions
427
(b) R = N 0 k = 6.02 × 10
23
× 1.38 × 10
−23
= 8.3 J/mol K
(1)
PV = NRT
(2)
1.01 × 10
5 V = 8.13 × 373 N
(3)
whence N = 33.3 mol/m
3
n = number/m
3
= 33.3 × 6.02 × 10
23
= 2 × 10
25
/m
3
λ =
1
nσ
√
2
=
1
2 × 10 25 × 4π
10 −10
2 √
2
= 10
−7 m.
10.4 (a) For curve f 1 , v mp = 425 m/s; for curve f 2 , v mp = 850 m/s (Fig. 10.5).
Fig. 10.5 Maxwell–
Boltzman velocity
distribution
(b) v mp ∝
√
T
∴ T 2 =
T 1 v 2
mp (1)
v 2
mp (2)
= 300
850
425
2
= 1200 K
(c) ¯
v =
4/πv mp
¯
v 1 = 1.1287 × 425 = 480 m/s
¯
v 2 = 1.1287 × 850 = 959 m/s
¯
v 1 / ¯
v 2 = 1/2
(d) and (e)
v mp =
2kT
m