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APPENDIX: UNITS This appendix explains some of the abbreviations1•2 used for units in this book and gives conversion factors to SI units and atomic units: length 1 a0 = 1 bohr = 0.5291771 X 10-10 m 1 A= 1 Angstrom= lo-10 m = 1.889727 ao mass 1 me = 1 atomic unit of mass = mass of an electron 9.109534 X 10-31 kg = 5.485803 X 10-4 U 1 u 1 universal atomic mass unit = one twelfth the mass of a 12c atom 1.6605655 x lo-27 kg = 1822.887 me time 1 t Eh 1 = 1 atomic unit of time = 2.418884 x l0-17 s 1 s = 1 second = 4.134137 x 1016 t/Eh temperature 1 K = 1 Kelvin amount of substance 1 mol = 1 mole 6.022045 x 1023 atoms, molecules, or formula units energy 1 cm-1 = 1 wavenumber 1 kayser 1.986477 x lo-23 J 4.556335 x 10-6 Eh 857 858 APPENDIX: UNITS 1 kcal/mol = 1 kilocalorie per mole 4.184 kJ/mol = 1.593601 x 10-3 Eh 1 eV 1 electron volt = 1.602189 x lo-19 J 3.674902 X 10-2 Eh 1 Eh 1 hartree = 4.359814 x lo-18 J Since so many different energy units are used in the book, it is helpful to have a conversion table. Such a table was calculated from the recommended values of Cohen and Taylor3 for the physical censtants and is given in Table 1. REFERENCES 1. "Standard for Metric Practice", American Society for Testing and Materials, Philadelphia (1976). 2. D. H. Whiffen, Expression of results in quantum chemistry, Pure Appl. Chem. 50: 75 (1978). 3. E. R. Cohen and B. N. Taylor, The 1973 least-squares adjustment of the physical constants, J. Phys. Chem. Ref. Data 2: 663 (1973). )> "'tl "'tlm z 0 X c z Table 1 Energy conversion factors. uJ cm-l kJ/mol kcal/mol eV E h 1 cm- 1 = I 1.0 1.196266 X 10-2 2.859144 X 10-3 l_. 239852 X 10-l; 4, 556335 X 10-G 1 kJ/mol = 83.59347 1.0 2, 39005 7 X ]_0-l 1. 036436 X 10-2 3.808798 x Jo-1+ 1 kcal/mol = 349.7551 4.184a 1.0 4. 336445 x 10-2 1.593601 X Jo-3 1 eV = 8065.479 96.48455 23.06036 1.0 3.674902 x 1o-2 1 Eh = 219474.7 2625.500 627.5095 27.21161 1.0 a. exactly (by definition) CXlc, '() INDEX action-angle variables, 8, 21, effect of inelastic events, 292, 293, 640, 793, 794 835-839, 849 activation energy, 3, 139, 142- optical potential calculations, 146, 153, 155, 156, 162, 835-839 170, 172-175, 177, 179, average ~-labelling of CS, 718, 180, 248, 249, 255, 311, 719, 722, 723 332, 351, 353, 359, 434, 441-445, 447, 448, 469, basis set effe~ts, 169, 172-176, 478, 485, 487, 523-526, 186-190, 194, 245, 248, 253, 531, 599, 653, 654, 658 344, 540, 544, 654, 662, 663, activation energy, state­ 665-667, 776-778 selected, 448, 469, 478, bimolecular rate constants, 39, 40, 485 289, 290, 294, 296-300, 331, active orbitals, 333 332, 338-340, 345-347, 371, adiabatic energy transfer, 692, 432, 438, 439, 441-445, 456, 693, 696 469, 477, 478, 556, 587-631 adiabatic theory of reactions, bond-energy-bond-order (BEBO) 366, 593 model, 294-297, 595, 597 alkyl radical dissociations, bond strengths, calculated, 141- 37-69 144, 153-155, 176-179, 351, angular momentum effects on 557, 665, 666, 675 unimolecular decay, 24, bottleneck region of potential 46, 62, 64, 225-227, 570 energy surfaces, 2, 24, 273- anharmonic oscillators, 19, 20, 278, 587-631 107, 236, 237, 292, 332, branching reactions, 11, 24, 27, 449, 775, 793, 794 146, 156-161, 519, 520, 522- anharmonic state counting, 19, 531, 551-584, 600, 601, 606, 20, 26, 27, 51, 52, 595, 609, 610, 619, 626, 627, 850 596, 604, 613 bulge effect, 753 anharmonicity effects on unimolecular decay, 19, capture cross sections, 232-234 20, 236, 237 carbene insertions, 170, 177 apse quantization axes, 719, carbene rearrangements, 185, 251 731, 733 catalysis, 639, 654, 676-681, 813 Argand diagrams, 388-391 centrifugal sudden approximation, atom-surface scattering, 290, 291, 298-300, 376, 692, accurate calculations, 831-839 717-733 attractive hard-wall classical cross sections, 741, 744- calculations, 832-835 746, 753, 754 861 862 INDEX classical model for laser, 639- double mass spectrometer system, 641 536, 538-540 combustion, 139, 294, 330, 331, 359 edges of microcrystallite, 844 contour diagrams of potential effective core potentials, 261, energy surfaces, 109, 119, 662 126, 204, 208, 211, 361, effective cross sections, 435, 362, 401, 409, 411, 501, 436 527-530, 541, 542, 557- eigenphase-shift analysis, 394- 560' 688 397 Coriolis coupling, 21, 267, Einstein model, 711 268, 313 ejection yields, 844-851 coupled-cluster methods (CCM electron correlation, 132-156, and CCD), 133-139 161, 162, 169, 171-180, 187-189, 194, 245, 248, decay rates of quasibound 253, 535-538, 653, 656, clusters, 223-232, 577 663-675, 772-779 decoupling approximations, 476, electronic excitation energies, 692, 693 133, 147-155, 161, 162, degeneracy-averaged differential 187-194, 337, 763, 779-783 cross sections, 722-724 electronic-field representation, derivatives as input in inter­ 759-762 polation, 204, 205 electronic representations, 687 detailed balance, 438, 440 electronically nonadiabatic diatomics-in-molecules (DIM) processes, 193, 293, 297, method, 294-297, 315, 486, 488, 548, 639-641, 359-363, 367-371, 520- 646-649, 686-688, 691-693, 531, 553-559, 688 695, 713, 763-768, 853 DIM-3C method, 522 energy minimization pathway, 654, differential cross sections 655, 657 (differential in scat­ energy partitioning, tering angle), 312, 314, in products of surface reactions, 319, 320, 327, 413-415, 809-812 421-429, 450, 451, 496, in unimolecular reactions, 40, 570-576, 704, 707, 710, 41, 57-67, 86, 192 711, 714, 720-724, 737- experimental reaction cross 755, 808, 811, 812, 846, sections, 535, 536, 546-548 850-853 dissociation reactions, 2, 15, factorization of the CVT recrossing 140-145, 152-156, 179, coefficient, 613-631 249, 287, 431-433, 445, Fermi resonance, 121-127 456, 466-469, 548, 564- filtering techniques, 422-428 570, 686, 694, 695 Fourier series expansion, 421-425 distinguished coordinate, 655, Franck-Condon model of electronic 658 energy transfer, 693 distorted wave approximation, Franck-Condon structure, 11, 106, 291, 298-300, 463, 495, 107, 115-121, 291, 640, 642, 496' 692' 693 643, 645, 650 INDEX 863 fundamental dynamical assumption laser-induced chemistry, 639-651, of TST, 588, 596, 603 759-768 laser inhibition of reaction, generalized relaxation cross 640, 645-648, 650 sections, 721, 723-728 local modes, 20, 22, 106, 123, generalized valence bond wave­ 126-128 functions, 24, 253, 331, London-Eyring-Polanyi-Sato (LEPS) 333, 334, 340, 341, 347- and extended LEPS potential 350, 464, 552, 560, 662- energy surfaces, 294-296, 681 359, 370, 371, 376, 422- gradient method, 172, 243-261, 429, 520, 551, 560, 597, 265, 595 600, 601, 618-629, 641, 645, 807 Hammond's postulate, 615 lifetimes of collision complexes, hydrogen bond, 76, 79-81, 89, 11, 48, 391-394, 415, 552, 90 560, 571, 572, 576-578 impulse model, 704, 708, 714, magnetic transitions, 320-324, 733 693, 718, 719, 730-733 inactive orbitals, 334 many-body approach to atom­ information-theoretic methods, molecule collisions, 687, 287, 301, 568, 569, 691, 694-696, 703, 704 795-797, 811 many-body expansion, 772, 785-793 interpolation of derivatives, many-body perturbation theory 204, 205 (MBPT) of electronic interpolation of potential structure, 133-139, 161, energy surfaces, 206-210, 772-779 294, 361 minimum-energy path (MEP), 43, intramolecular vibrational 243, 250, 330, 405, 409, energy redistribution, 1, 513, 590, 591, 595, 598, 7, 10-23, 40, 42, 49-57, 604, 606, 607, 612-615, 620 121-128, 230, 251, 255, molecular beam experiments, 10, 259, 572, 577, 584 40, 249, 415, 495, 496, intrinsic reaction coordinate 703, 753, 806, 811-813 (IRC), 243, 250-259, 265, M~ller-Plesset theory, 171 590 moments of final-state distri­ isotopic selectivity via laser butions, 59, 301, 323-325, field, 639, 649, 650 421, 449-453, 455, 456, inversion problem, 687, 694, 691, 795-797 754 multicenter potentials, 688, 689, 704, 706-708, 710, 713, kinetic isotope effects, 249, 845, 846 291, 298-300, 547, 548, multi-configuration-self­ 606-611, 623, 624, 626, consistent-field (MCSCF) 627, 630, 639, 640 method, 206, 244, 331, 656-658, 663 Langevin equation, 278-284, 808 multiple-collision expansion, laser effects on collision 694, 708 processes, 287, 639-651, multivalued interpolation, 205 686, 725, 759-768 864 INDEX natural collision coordinates, quantal reaction probabilites, 251, 497, 498 289-291, 297-300, 360, negative ion-neutral reactions, 363-369, 375-383, 405, 536, 538-549 406, 411-413, 432, 437, non-RRKH lifetimes, 4, 11-20, 438, 467, 589, 596, 612, 49-57 630 number states, 759 quantal scattering wavefunction, 398-400, 405, 495, 499- orbital concepts for chemical 503, 509-513 reactions, 188-192, 333, quasibound clusters, definition 334, 340, 341, 347-350 of, 221, 222 orbital phase continuity quasibound states of diatomics, principle, 333 433, 455, 456, 468 organic radical processes, 37, quasiclassical trajectory 179, 185 calculations, 287-293, osculating complex model, 570- 296-302, 311-327, 359, 575, 578 370, 379, 380, 421-429, 431-469, 479-482, 484-487, partial retention of diatomic 495, 551-584, 597, 639-650, differential overlap 690, 703, 704, 753, 793-800 (PRDDO) method, 620 quasiperiodic trajectories, 7, 9, periodic orbits, 121-128, 294, 21, 51, 53-56, 292, 793 366 photoabsorption, 10, 11, 104, R-matrix propagation method, 506, 105, 107-111, 649, 650, 507' 691, 765 725 rainbow scattering, 737-755 photodesorption, 98 atoms from atoms, 694, 741-743 photodissociation, 108-110, 173, atoms from diatomic molecules, 185-195, 251-255 693, 694, 744-751 photon angular momentum, 762 atoms from polyatomic molecules, polarization CI method, 294- 751' 752 297, 331, 335-338, 341- gases
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  • Are the Kelvin and Clausius Statements of Second Law of Thermodynamics Mutually Consistent?

    Are the Kelvin and Clausius Statements of Second Law of Thermodynamics Mutually Consistent?

    1 Are the Kelvin and Clausius statements of second law of thermodynamics mutually consistent? Radhakrishnamurty Padyala #282, Duomarvel Layout, Yelahanka, Bangalore -560064, India. Email: [email protected] Abstract: The most standard and fundamental statements of the second law of thermodynamics are those of Kelvin and Clausius. They form the foundation for the structure of thermodynamics. Essentially they are statements of impossibility of certain processes in nature. Every standard book on thermodynamics ritualistically demonstrates the consistency between these two statements by showing violation of one leads to violation of the other. We show in this note, that the two statements are mutually inconsistent. That is, we show violation of one does not lead to violation of the other. We adopt a procedure similar to the one used by Fermi for our demonstration. Keywords: Thermodynamics, Second law, Kelvin’s proposition, Clausius proposition, Inconsistent second law statements. 1. Introduction Thermodynamics occupies a very important place in the arena of modern science, engineering, and technology. Its importance stems mainly from the second of the four laws of thermodynamics. It has one and a half centuries of history and remains most controversial among the laws of physics even to this day. It plays crucial role in philosophical discussions on evolution, origin of universe, Black holes and so on. The importance attached to thermodynamics can be understood from the fact that, unlike any other subject (with the exception of mathematics perhaps) it is taught to the students of Physics, chemistry, biology, astronomy, geology, chemical, mechanical, metallurgical, automobile, architecture engineering & technology. There is, however, another side to thermodynamics (see next paragraph) that must be kept in mind while dealing with thermodynamics: No other part of science has contributed as much as to the liberation of the human spirit as the second law of thermodynamics.