Index
683
Residual entropy, 336–341
Reverse Carnot engine, 64–66
S
Second law of thermodynamics, 37, 52–54,
82–88
Semiconductor
electrons in metals, 148
intrinsic, 554–559
n−type impurity, 559–564
Simple harmonic oscillator (SHO), 235–240
anharmonicity effects, 267–271
approximation, 264–266
degrees of freedom, 240–242
model partition function, 266–267
one-dimensional, 683
polyatomic molecules, 313–322
rigid-rotor approximation, 311–313
Solid state concepts
effective mass, 660–664
energy bands, 653–656
Feynman model, 653–656, 656–660
Spectrum
isotropic radiation, 9
microdensitometer trace, 334
optoacoustic overtone absorption, 332
pure rotational infrared, 331
Raman, 325
vibrational frequencies, 245
vibration–rotation Raman, 327
Spherical/symmetric top molecules, 647–651
linear molecules, 645–646
top rotor, 646–647
Spin systems
ground level atoms or ions, 449–454
magnetic susceptibilities, 459–463
multi-electron atoms/ions, 445–449,
455–459
setting, 434–436
statistical mechanics, 436–445
State functions, 32, 40–48
reversible adiabatic expansion, 32
thermodynamic, 29, 40–48
Stirling approximations
lowest-level approximation to n!, 629–631
to n!, 631–633
Susceptibility
adiabatic demagnetization, 428–433
electric, 423
magnetic, 428–433
second-order Zeeman contribution, 461
Symmetry
1:3 and 3:1 distributions, 14
electronic state nuclear interchange,
286–288
nuclear
interchange, 285
spin, 332
T
Thermodynamics
definitions, 28–30
engines (see Engines)
entropy, 33–40
equating expressions, 31
heat capacity difference, 48–51
ideal gas particles, 28
integrals, 33
internal energy, 33–40
laws of, 32
multicomponent systems, 88–96
natures of, 27
N -particle classical ideal gas, 30
real gases, 96–121
second law, 82–88
stability, 82–88
state functions, 32, 40–48
thrust of, 27
See also Canonical ensemble
Traditional calculus
Euler–Maclaurin summation formula,
614–617
fundamental theorem, 617–618
inverse differential operator, 611–612
multivariate functions, 602–611
regression of series concept, 618–620
single variable, 601–602
Taylor and Maclaurin series, 612–614
variations, 624–626
Transition state, 483, 502, 506
Translational states
continuum approximation, 146–151
independent degrees of, 360
internal state contributions, 219–221
quantum correction, 374
rotational degrees of freedom, 380
Van der Waals gas, 100
V
Van der Waals model, 98–101, 108, 464
Variance
heat capacity, 235
internal energy, 259
number of photons, 581
photon energy state, 581
and standard deviation, 23–24, 171
683
Residual entropy, 336–341
Reverse Carnot engine, 64–66
S
Second law of thermodynamics, 37, 52–54,
82–88
Semiconductor
electrons in metals, 148
intrinsic, 554–559
n−type impurity, 559–564
Simple harmonic oscillator (SHO), 235–240
anharmonicity effects, 267–271
approximation, 264–266
degrees of freedom, 240–242
model partition function, 266–267
one-dimensional, 683
polyatomic molecules, 313–322
rigid-rotor approximation, 311–313
Solid state concepts
effective mass, 660–664
energy bands, 653–656
Feynman model, 653–656, 656–660
Spectrum
isotropic radiation, 9
microdensitometer trace, 334
optoacoustic overtone absorption, 332
pure rotational infrared, 331
Raman, 325
vibrational frequencies, 245
vibration–rotation Raman, 327
Spherical/symmetric top molecules, 647–651
linear molecules, 645–646
top rotor, 646–647
Spin systems
ground level atoms or ions, 449–454
magnetic susceptibilities, 459–463
multi-electron atoms/ions, 445–449,
455–459
setting, 434–436
statistical mechanics, 436–445
State functions, 32, 40–48
reversible adiabatic expansion, 32
thermodynamic, 29, 40–48
Stirling approximations
lowest-level approximation to n!, 629–631
to n!, 631–633
Susceptibility
adiabatic demagnetization, 428–433
electric, 423
magnetic, 428–433
second-order Zeeman contribution, 461
Symmetry
1:3 and 3:1 distributions, 14
electronic state nuclear interchange,
286–288
nuclear
interchange, 285
spin, 332
T
Thermodynamics
definitions, 28–30
engines (see Engines)
entropy, 33–40
equating expressions, 31
heat capacity difference, 48–51
ideal gas particles, 28
integrals, 33
internal energy, 33–40
laws of, 32
multicomponent systems, 88–96
natures of, 27
N -particle classical ideal gas, 30
real gases, 96–121
second law, 82–88
stability, 82–88
state functions, 32, 40–48
thrust of, 27
See also Canonical ensemble
Traditional calculus
Euler–Maclaurin summation formula,
614–617
fundamental theorem, 617–618
inverse differential operator, 611–612
multivariate functions, 602–611
regression of series concept, 618–620
single variable, 601–602
Taylor and Maclaurin series, 612–614
variations, 624–626
Transition state, 483, 502, 506
Translational states
continuum approximation, 146–151
independent degrees of, 360
internal state contributions, 219–221
quantum correction, 374
rotational degrees of freedom, 380
Van der Waals gas, 100
V
Van der Waals model, 98–101, 108, 464
Variance
heat capacity, 235
internal energy, 259
number of photons, 581
photon energy state, 581
and standard deviation, 23–24, 171