71.
(a) Since an ideal gas is involved, then ∆E
int
= 0 implies T
1
= T
0
(see Eq. 20-62). Consequently, the
ideal gas law leads to
p
1
= p
0
V
0
V
1
=
p
0
5
for the pressure at the end of the sudden expansion. Now, the (slower) adiabatic process is described
by Eq. 20-54:
p
2
= p
1
V
1
V
2
γ
= p
1
(5
γ
)
as a result of the fact that V
2
= V
0
. Therefore,
p
2
=
p
0
5
(5
γ
) =
5
γ
−1
p
0
which is compared with the problem requirement that p
2
= 5
0.4
p
0
. Thus, we find that γ = 1.4 =
7
5
.
Since γ = C
p
/C
V
, we see from Table 20-3 that this is a diatomic gas with rotation of the molecules.
(b) The direct connection between E
int
and K
avg
is explained at the beginning of
§20-8. Since ∆E
int
= 0
in the free expansion, then K
1
= K
0
.
(c) In the (slower) adiabatic process, Eq. 20-56 indicates
T
2
= T
1
V
1
V
2
γ
−1
= 5
0.4
T
0
=
⇒
(E
int
)
2
(E
int
)
0
=
T
2
T
0
= 5
0.4
≈ 1.9 .
Therefore, K
2
= 1.9K
0
.
Document Outline
- Main Menu
- Chapter 1 Measurement
- Chapter 2 Motion Along a Straight Line
- Chapter 3 Vectors
- Chapter 4 Motion in Two and Three Dimensions
- Chapter 5 Force and Motion I
- Chapter 6 Force and Motion II
- Chapter 7 Kinetic Energy and Work
- Chapter 8 Potential Energy and Conservation of Energy
- Chapter 9 Systems of Particles
- Chapter 10 Collisions
- Chapter 11 Rotation
- Chapter 12 Rolling, Torque, and Angular Momentum
- Chapter 13 Equilibrium and Elasticity
- Chapter 14 Gravitation
- Chapter 15 Fluids
- Chapter 16 Oscillations
- Chapter 17 Waves—I
- Chapter 18 Waves—II
- Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
- Chapter 20 The Kinetic Theory of Gases
- 20.1 - 20.10
- 20.1
- 20.2
- 20.3
- 20.4
- 20.5
- 20.6
- 20.7
- 20.8
- 20.9
- 20.10
- 20.11 - 20.20
- 20.11
- 20.12
- 20.13
- 20.14
- 20.15
- 20.16
- 20.17
- 20.18
- 20.19
- 20.20
- 20.21 - 20.30
- 20.21
- 20.22
- 20.23
- 20.24
- 20.25
- 20.26
- 20.27
- 20.28
- 20.29
- 20.30
- 20.31 - 20.40
- 20.31
- 20.32
- 20.33
- 20.34
- 20.35
- 20.36
- 20.37
- 20.38
- 20.39
- 20.40
- 20.41 - 20.50
- 20.41
- 20.42
- 20.43
- 20.44
- 20.45
- 20.46
- 20.47
- 20.48
- 20.49
- 20.50
- 20.51 - 20.60
- 20.51
- 20.52
- 20.53
- 20.54
- 20.55
- 20.56
- 20.57
- 20.58
- 20.59
- 20.60
- 20.61 - 20.70
- 20.61
- 20.62
- 20.63
- 20.64
- 20.65
- 20.66
- 20.67
- 20.68
- 20.69
- 20.70
- 20.71 - 20.80
- 20.71
- 20.72
- 20.73
- 20.74
- 20.75
- 20.76
- 20.77
- 20.78
- 20.79
- 20.80
- 20.81 - 20.90
- 20.81
- 20.82
- 20.83
- 20.84
- 20.85
- 20.86
- 20.87
- 20.88
- 20.89
- 20.90
- 20.91 - 20.92
- 20.91
- 20.92
- 20.1 - 20.10
- Chapter 21 Entropy and the Second Law of Thermodynamics
- Chapter 22 Electric Charge
- Chapter 23 Electric Fields
- Chapter 24 Gauss’ Law
- Chapter 25 Electric Potential
- Chapter 26 Capacitance
- Chapter 27 Current and Resistance
- Chapter 28 Circuits
- Chapter 29 Magnetic Fields
- Chapter 30 Magnetic Fields Due to Currents
- Chapter 31 Induction and Inductance
- Chapter 32 Magnetism of Matter: Maxwell’s Equation
- Chapter 33 Electromagnetic Oscillations and Alternating Current
- Chapter 34 Electromagnetic Waves
- Chapter 35 Images
- Chapter 36 Interference
- Chapter 37 Diffraction
- Chapter 38 Special Theory of Relativity
- Chapter 39 Photons and Matter Waves
- Chapter 40 More About Matter Waves
- Chapter 41 All About Atoms
- Chapter 42 Conduction of Electricity in Solids
- Chapter 43 Nuclear Physics
- Chapter 44 Energy from the Nucleus
- Chapter 45 Quarks, Leptons, and the Big Bang
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