1374 Index
Partial molar quantities (cont.)
in nonideal solutions, 275–276
in one-component ideal gas, 186–187
in one-component system, 185–186
Partial molar volume, of nonideal solutions,
276
Partial pressure
of dilute gas pressure, 415
of one-component ideal gas, 187
Partial vapor pressure
of benzene and toluene, 240, 240f
of hydrochloric acid, 329–330, 330f
Raoult’s law, 238
Particle in a box, 663–673
free particle in one dimension, 670–672
free particle in three dimensions,
672–673
probability density, 705
one-dimensional, 663–666, 664f
classicalvs. quantum mechanics, 664
equations for, 664–665
probability density, 701–702, 701–702f
solution for, 665–666, 666f
uncertainty product, 711–712, 712t
Schrödinger equation and de Broglie
waves, 664
specification of state of, 668–669
in three-dimensions, 669–670, 669f,
1276–1278
time-dependent wave function for, 668
Pascal, 8, 622
Pascal, Blaise, 8, 622
Path-independent, line integral, 48
Pauli exclusion principle, 763, 766–768,
785, 1011
Pauli, Wolfgang, 768
Pauling, Linus, 862
PEP.SeePhosphoenolpyruvic acid
Period, of oscillations, 626
Periodic boundary conditions, 1175
Periodic function, 1253
Periodic motion, of harmonic oscillator,
626, 626f
Periodic table of elements, 789, 813–818,
815–816f, 820
Peritectic point, 289–290
Permeability, 1002, 1275
Permittivity, 270, 1275
Perpendicular band, of vibrational spectra,
977, 977f
Perpetual motion machine of the first kind, 57
Perpetual motion machine of the second
kind, 106
Perrin, Jean Baptiste, 469
Perturbation method, 789, 799, 819,
1283–1287
degenerate case, 803–805, 1285–1287
helium ground state application of,
800–802, 800f
nondegenerate case, 1283–1285
variation methodvs., 802
Perturbation theory
degenerate, 803–805, 1285–1287
time-dependent, for electric dipole
transitions, 951–953
Petit, Alexis Thérèse, 77
Pfaffian differential equations, 1245, 1245f
Pfaffian form, 1238
pH measurement
cell for, 372–373, 373f
glass electrode for, 373–374, 373f
pH meters, 374
Phase(s), 27, 200, 203
coexistence of, 3, 27–35, 27f
counting of, 203–204
equilibrium of, 199–235
fundamental fact of, 200–202
Gibbs energy and phase transitions,
215–221
Gibbs phase rule, 202–204
multicomponent system surfaces, 230–234
one-component system surfaces, 222–229
in one-component systems, 205–213
transitions of, 27, 27f
Phase diagram(s), 27, 27f
Clapeyron equation for, 208–210
Clausius and Clausius–Clapeyron equation
and, 199
with DSC, 287–288
Gibbs phase rule for, 199
of helium, 207, 207f
of ideal solutions
pressure-composition, 243–245, 244f
temperature-composition, 245–246,
245–246f
two-component, 243
for nonideal mixtures, 282–290
liquid-vapor, 282–284f, 282–285
solid-liquid, 285–288, 285–288f
solid-liquid with compounds, 288–289f,
288–290
three-component, 290, 290ffor phase equilibrium, 237
of two-component ideal solutions, 243
of water, 206, 206f
Phase equilibrium, 199–235, 234
fundamental fact of, 200–202
Gibbs phase rule, 202–204
of multicomponent systems
phase diagrams, 237
surfaces, 230–234
one-component system surfaces, 222–229
energy attributed to, 222–224
Laplace equation, 227–229
surface tension, 224–227, 225–226f
in one-component systems, 205–213
Clapeyron equation, 208–210
Clausius–Clapeyron equation, 210–212
vapor pressure and total pressure,
212–213
Phase transitions, 27, 27f
absolute entropy and, 141
classification of, 216–218
Clausius–Clapeyron equation and,
211–212
entropy changes of
irreversible, 127–128
reversible, 123–124
first-order, 216
Gibbs energy and, 215–221
liquid-vapor transition critical point,
218–219
Maxwell equal-area construction,
219–220, 219f
temperature dependence, 220–221
heat transfer during, 54
second-order, 217
Phenomenological law, Fourier’s law of heat
conduction, 445–446
ΦFunctions
in Born–Oppenheimer approximation, 825
in relative Schrödinger equation, 731–732
zero value in, 745–746, 746f
Phlogiston, 55
Phonons, 1165
Phosphoenolpyruvic acid (PEP), hydrolysis of,
344–345
Phosphorescence, 978–980, 980f
Photoacoustic spectroscopy, 993
Photochemical chain reactions, 558, 981
initiation of, 523
Photochemical reaction, 981
Photochemistry, 949, 951, 981–983, 982f