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| Owen D. — A First Course in the Mathematical Foundations of Thermodynamics (Undergraduate Texts in Mathematics) |
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| Предметный указатель |
Accumulation function 52 54—57 61 83 111 112 128
Accumulation Inequality 58 59 61—65 67 68 79 83
Accumulation integral 112 119
Accumulation Theorem 62 74
action 33 35 68 69 73 75 77 79 80 82 84 86 87 89 93 94 98 104 109 111 127—129
Adiabat 6—8 16 24 48 50 125 126
Anomalous behavior of water 23
Caloric 36
Caloric theory of heat 12 14 15 20 35 36
Calorimetry 122
Caratheodory 43
Caratheodory's theory of thermodynamics 21
Carnot 11 12 14 36 42 53 64
Carnot — Clapeyron relation 20 22
Carnot, heat engine 9 13 14 16 18 19 22 24 25 39 47 48 50
Carnot, ontrivial 14
Carnot, refrigerator 9 39 48 50 128
Clausius 12 14 43
Clausius inequality 56
Clausius property 68—77 80 83 84 128 129
Clausius — Planck Inequality 75
Coleman 69
Compressive force 85
Conservation property 80—82 87 128
Constitutive equations 121
Constitutive equations, thermodynamical restrictions on 121
Control 33
Convex combination 75
Convex set 84 100
Curve, oriented 3
CYCLE 8 10 14 20 21 24 26 32 36 39 40 49—51 55 56 58—60 63 65 67—69 74 79 80 83 86 98 105 116 118 126 128
Cycle, approximate 69
Cycle, Carnot 8 9 25 36 47 51 66
Cycle, interior of 8
Cycle, Isothermal 83 105
Cycle, negatively oriented 8
Cycle, positively oriented 8
Cycle, reversal of 63
Cycle, Sargent 126 128
Cycle, simple 8 9
Cycle, standard parameterization 24
Deformation, residual 95 101
density 23
Dissipation property 83 84 86 89 90 98 128
Dissipative 120
Efficiency 26 130
Efficiency, estimate 24 42
Efficiency, Kelvin's formula for 18 24
Elastic filament 90
Elastic modulus 95
Elastic segment 97 98
Elastic system 97 99
Empirical temperature scale 44—46 52 63 128
Energy 122
Energy, conservation of 13
Energy, function 12 67 68 82 113 115 118
Energy, potential 87
Energy, stored 87
Enthalpy 106
entropy 24 56 121 122
Entropy function 23 67 68 74 75 79 118 119 126
Environment 33 35
Equation of state 10 87 89
Equilibrium response function 93
Extra force 117 120
Filament 85 96 104
Filament, approximating elastic 106—108
Filament, elastic 86—90 95 96 101 104—106
Filament, elastic-perfectly plastic 95 130
Filament, elastic-plastic 98 99
Filament, external force on 85
Filament, force on 87 89
Filament, homogeneous 85 104
Filament, length of 85—88 91 104
Filament, viscous 90 94—96 106—109 118
Filament, work done on 87 97
First law 10 13—15 18 20—23 25 35 36 38 39 42 52 58 65 67 80 82 85 105 106 113—117 120 122 126 127
First law of thermodynamics 11
First Law, preservation of 38—40
force 85 89 95 96 98 104
Force, compressive 85
Force, equilibrium 95
Force, external 85 87
Force, extra 95
Force, tensile 85
Force, yield 95
Heat 14 42
Heat, absorbed 5 17 18 22 33 43 65 104 120
Heat, capacity 2
Heat, emitted 5 18 33 43 65 104
Heat, engine, Carnot 9 13 14 16 18 19 22 24 25 39 47 48 50 126
Heat, engine, efficiency of 120
Heat, gained 3 11 13 33 35 80 104—106
Heat, gained at or below a hotness level 52
Heat, gained at or below a temperature 52
Heat, gained, net 2 4 5 18 24 46 47 53 112 113 117 118 120
Heat, mechanical equivalence of 122
Heat, net gained 36 40
Heat, rate of gain of 5 41
Heating 5 10 11 20 22 25 42 62 125
Heating measure 122
Helmholtz free energy function 84 86 87 91—94 99 101 102 104 118 130
Homogeneous fluid bodies 35 42 109
Homogeneous fluid bodies with viscosity 109
Homogeneous fluid body 2 3 5 9—14 16—18 20—23 25 30 33 36 38 53 65—67 75 79 80 84 85 105 111—114 117—120 125—128
Homogeneous fluid body, approximating 117 120
Homogeneous fluid body, latent heat function of 2
Homogeneous fluid body, pressure function of 2
Homogeneous fluid body, state of 2
Homogeneous fluid body, state space of 2
Hotness 42 43 54
Hotness, level 43—46 52 53 57—59 111 112 118
Hotness, level, ordering of 44
Hotness, manifold 44 45 52
Ideal gas 10 12 16 39—41 43 45 46 53 54 57—59 64 65 74 79 82 110 113 118 125 126
Integral, accumulation 75 79 80
Integral, line 4 9 71 80 82 98
| Integral, Riemann 61
Internal energy 24 121
Internal energy, function 13 23 106 107 126
Isobar 22 23 126
Isotherm 7—9 18
Isothermal path 84
Joule 12
Joule's constant 105
Joule's relation 38—41 58 67 68 80 83 86 116 122
Kelvin 43 55
Kelvin's formula for efficiency 126
Latent heat 2 20 105 107 108
Latent heat with respect to pressure 125
Latent heat, function 109 119
Length, residual 95 100
Line integral 4 34 35 46 63
Lower potential 84 128
Materials with fading memory 122
Materials with memory 121
Mathematical systems theory 122
Mechanical equivalent of heat 12
Mechanics 121
Melting 107
Order relation 44
Path 3 4 8 13 14 23 24 28 33 46 60 63 77 95 97
Path, adiabatic 6—9 24 43
Path, Carnot 8 25 26 50 66
Path, closed 61
Path, equilibrium 111
Path, isothermal 7 8 17 24
Path, reversal of 15 69 77
Path, simple 7
Path, standard parameterization of 3—6 20 46 47 62
Phase 104—106
Phase, change of 104 105 107 108
Phase, transition 104 106 117
Planck 43 55
Plastic segment 97 98 101
Plastic system 97 99
Potential 23 82 93 94 129
Pressure 2 22 23
Pressure, function 109 127
Process 28—30 32 35 37 53 68 74 77 78 86 88 94 95 97—101 104 106 107 111 112 115 117 120 127 128
Process, cyclic 36 43 68
Process, generator 28 29 31 32 37 69—74 76 78 79 82 83 86 90 92 94 96 103 109—111 113
Process, generator, successive application 88 89
Process, isothermal 84—86
Process, retarded 91
Process, reversal of 79
Product of systems 36 57
Product operation 38 40 113 118
Product system 36—39
Rate of expansion 110 117
Rate-dependent 112
Rate-independent 2 112
Refrigerator, Carnot 9 39 48 50 128
Restorability 79
Retardation 106 107 112 113
Reversal 97
Reverse triangle inequality 81
Reversibility 77—79
Second law 10 13—18 20—25 35 36 38 42 52 55—57 59 61—63 67 68 74 80 85—87 89 90 94 95 98 105 117—120 122 126 128
Second law of thermodynamics 11 12
Second Law, preservation of 58
Second Law, verbal forms of the 43
Semi-system 129
Serrin 43 53 55 65
Silhavy 43
Specific heat at constant pressure 125
Specific heat, constant 125 126
Specific heat, function 109 119
Specific heats, difference in 125
Specific heats, ratio of 125
State 7 9 12 14 15 23 24 28—30 32 43 67 69—72 76—78 80 81 84—87 89 90 91 94—96 99—101 111 113 115 119 122 126 128 129
State, final 28 30
State, initial 28 29 33
State, space 28—30 45 67 85 86 95 109 114 118 119 130
State, standard 23 99
State, transformation function 88
States 109
States, accessible from a state 29
Step function 49 50
Successive application 33
Supply 33
system 32 33 35 43 53 68 79 80 85 86 95 97 109 116
System with perfect accessibility 28—30 32 33 35 37 53 57 68 69 75 77 80 83 86 88 89 97 109—112 127—129
System, coupled 15
System, isolated 75
System, product 36—39
System, thermodynamical 35—38 40 41 52 53 56—58 62 64 65 67—69 74 75 77 80 82—84
System, thermometric 43
Temperature 2 3 9 14—16 18 20 22 24—26 37 42—44 54 65 66 80 110 125—127
Temperature, absolute 121 122
Temperature, Celsius scale 2
Temperature, Kelvin scale 2
Temperature, scale 59 62—65
Temperature, scale, absolute 18 43 64 65
Temperature, scale, empirical 44—46 52 63
Tensile force 85
Thermodynamical system 35—38 40 41 52 53 56—59 62 64 65 79 111 112 118 122
Thermodynamical systems, union of 122
Thermomechanics 122
Thermometer 18 44 45
Thermometer, gas 46
Thermometry 46 122
Transformation 29
Triangle inequality 72
Universal constant 36
Universal factor 41
Universal function 16 17
Upper potential 73—76 78 83 84 128 129
van der Waals fluid 126
Vector field, conservative 80
Viscous body 110—115 117—120
Volume 2 3 5 22 46 110
Water, anomalous behavior of 3
Work 2—4 11 13—15 18 22 24 33 35 36 57 83 84 86 95 98 99 111 112 117 120 127
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