## Plant Energy Transformations-Photosynthesis - …

### Oxygen is a chemical element with symbol O and atomic number 8

Thermodynamics vs kinetics; Homogeneous and heterogeneous reactions - chemical reaction control rate equation, reaction rate constant, reaction order, non-elementary reactions; Solid State Diffusion -Fick’s Law, mechanisms of diffusion, uphill diffusion, Kirkendall effect, steady and transient diffusion; External mass transfer -fluid flow and its relevance to mass transfer, general mass transport equation, concept of mass transfer coefficient, models of mass transfer -film theory and Higbie’s penetration theory; Internal mass transfer-ordinary and Knudsen diffusion, mass transfer with reaction; Adsorption –physical adsorption vs. chemisorption, adsorption isotherms - Langmuir, BET; Adsorption as the rate limiting step examples - gasification of C by CO2, dissolution of N2 in molten steel; Porous solids - specific surface area and pore size distribution; Reactor design -batch vs continuous reactors, ideal stirred tank and plug flow reactors; Mass balance in ideal reactors, residence time distribution; Models of industrial reactors; Electrochemical kinetics-concept of polarization, activation over potential, Butler-Volmer and Tafel’s equation, applications in electro-deposition and corrosion.

### Glossary of Scientific Terms - What is Life HOME

Open, closed, and isolated thermodynamic systems; state and process variables; extensive and intensive thermodynamic properties; first, second and third law of thermodynamics; condition and criterion for equilibrium; introduction to statistical thermodynamics; single component systems and introduction to potential phase diagram, Clausius-Clapeyron equation; multicomponent systems and solution thermodynamics, mixing process, ideal, regular and non-regular solution, behavior of dilute solutions, partial molal properties, chemical potential, Gibbs-Duhem equation; homogeneous and heterogeneous systems, Gibbs phase rule, composition-temperature phase diagrams, lever rule; thermodynamics of phase diagrams, reference states, free-energy composition curves, common tangent construction; thermodynamics of surfaces and interfaces, surface excess properties, capillarity effects on phase diagram, thermodynamics of point defects.

Finite and infinite dimensional vector spaces, Hilbert space, operators in infinite dimensional spaces, Matrix algebra, Cayley-Hamilton theorem; Gram-Schmidt orthogonalization, commuting matrices with degenerate eigenvalues. Algebra of complex numbers, Schwarz inequality, function of a complex variable, Cauchy- Riemann equations and their applications, harmonic functions, complex integrals, Cauchy's theorem and its corollaries, Taylor and Laurent expansion, classification of singularities, branch point and branch cut, residue theorem and evaluation of integrals. Theory of second order linear homogeneous differential equations, Frobenius method, Fuch's theorem, Sturm-Liouville theory, Hermitian operators, orthogonal expansion and completeness. Inhomogeneous differential equations, Green's functions, special functions (Bessel, Legendre, Hermite and Laguerre functions) and properties. Integral transforms: Fourier and Laplace transforms and their inverse transforms, solution of differential equations using integral transform. Elementary group theory, point symmetry groups, group representations reducible and irreducible representations, Lie groups and Lie algebra with SU(2) as an example.

## NOVA - Official Website | Origins: Series Overview

Wave functions, superposition principle, wave packets, Schrodinger equation, probability and current densities, expectation values and Ehrenfest"s theorem. Linear vectors and operators in Hillbert space, observables, commuting operators, momentum representation and uncertainty principle, unitary transformations, Schrodinger and Heisenberg representations, equations of motion. Applications: one-dimensional potential problems, linear harmonic oscillator with polynomial solutions, and creation and annihilation operators. Central forces, free and bound states in a Coulomb potential, angular momentum, spherical harmonics, Stern-Gerlach experiment for spin ½ system, spin, addition of angular momenta, Clebsch-Gordan coefficients. Time independent perturbation theory, first and second order corrections to the energy eigenvalues, degenerate perturbation theory, application to one-electron system, Zeeman effect and Stark effect. Variational methods: Helium atom as example, Ritz principle for excited states. Special topics like Quantum dots, coherent and squeezed states, lasers, Aharonov-Bohm effect, Berry phases, quantum entanglement and EPR paradox.

## 28/02/2004 · Origins: Series Overview

Postulates of Thermodynamics; Conditions of thermal, mechanical and chemical equilibrium, examples; Maxwell relations, Thermodynamics stability; Statistical basis of thermodynamics, microscopic and macroscopic states. Classical ideal gas, Boltzman H theorem and irreversibility. Ergodic process; Micro canonical ensemble, counting of states and phase space volume; Canonical Ensemble, equilibrium between system and heat reservoir, canonical partition function, Helmholtz free energy, Grand canonical Ensemble, partition function, particle number and energy fluctuations; Quantum statistical ensemble theory: density matrix formulation; system of identical particles, manybody wavefunctions for non-interacting fermions and bosons; ideal quantum gases: Bose-Einstein statistics, Fermi-Dirac statistics; Bose systems, Bose Einstein Condensation (BEC ) in non-interacting gases. BEC in Interacting systems- experimental observation in Rb atoms; Photon gas, and thermodynamics of Blackbody radiation. Elementary excitations of liquid Helium –II; Ideal Fermi gas description, Paramagnetism and Landau diamagnetism, electron gas in metals, Specific heat of metals; Phase transitions, Condensation in Van der Waals gas, Ising model and Ferromagnetism. Landau Phenomenological theory; Non-Equilibrium statistical mechanics, Brownian motion, random walks, Langevin equation, Markov process.