The Constant Entropy Path for a Chemical Reaction

Aims. The knowledge of physical conditions in young radio sources is important for defining the framework of models describing radio source evolution. We investigate whether young radio sources are in equipartition (i.e. minimum energy) conditions by comparing the equipartition magnetic fields of 5 High Frequency Peakers (HFP) with values directly inferred from the spectral peak assumed to be produced by synchrotron self absorption. Methods. Multi-frequency VLBA observations of 5 HFPs were carried out in both the optically thick and thin part of the spectrum to determine the spectral shape and angular size of the components for which individual radio spectra were obtained. Results. We find that the magnetic fields measured using observations agree well with those obtained by assuming equipartition, which implies that these sources are in minimum energy condition and the turnover in their spectra is due probably to SSA. In two source components, we found that the peak of the spectrum is caused by absorption of a thermal plasma instead of being due to SSA. The magnetic fields found in the various components range from 10 to 100 mG. In the presence of such high magnetic fields, electron populations with rather low γ emit in the GHz-regime. In one source, we detect low-surface brightness extended emission at low frequency located ∼30 mas (∼50 pc) from the main source. This feature may be related to either an earlier episode of radio activity or a discontinuous start of the radio activity (sputtering). By comparing our data with previous VLBA observations, we estimate the hotspot advance speed to be in the range 0.1–0.7c and kinematic ages of a few hundred years.

The concept and properties of partial molar quantities are presented and discussed in a generalized fashion within a thermodynamic framework. X being any thermodynamic extensive property of a homogeneous phase of fixed composition, it is proposed to consider text-decoration:overlineXB(y, z) as a generalized partial molar property of substance B with respect to constant (y, z) whenever text-decoration:overlineXB(y, z)=(∂X/∂nB)y,z,n′ where n′ indicates that all n are held constant apart from nB, complies with the condition [graphic omitted]. This is shown to be true whenever the independent variables y and z, one thermal and the other mechanical, are intensive properties of the system.Concerning common partial molar properties, those defined at constant temperature and pressure, particular attention is paid to the partial molar isochoric thermal capacity text-decoration:overlineCV,B(T, p) and to the partial molar isentropic compression text-decoration:overlineKS,B(T, p). Contrary to generally accepted views, their relations with text-decoration:overlineCp,B(T, p) and with text-decoration:overlineKT,B(T, p), respectively, which are rederived directly from the equations relating the parent extensive properties, are far from being similar to the relations involving the corresponding molar properties. To express this behaviour, text-decoration:overlineCV,B(T, p) and text-decoration:overlineKS,B(T, p) are designated as non-Lewisian properties. A summary of thermodynamic relations among the usual text-decoration:overlineXB(T, p) properties (those of the Lewisian type) is presented, and it is suggested that non-partial molar quantities be defined in order to fill the place of non-Lewisian partial molar properties in the thermodynamic formalism for Lewisian ones.Generalized partial molar properties at constant temperature and molar volume text-decoration:overlineXB(T, Vm), at constant molar entropy and pressure text-decoration:overlineXB(Sm, p), and at constant molar entropy and molar volume text-decoration:overlineXB(Sm, Vm) are introduced and briefly discussed. Their general relations to text-decoration:overlineXB(T, p) are given and non-Lewisian properties are identified for each kind of partial molar properties. The origin of the non-Lewisian behaviour is ascribed to purely mathematical reasons. The concept of a ‘partial fractional property’ is introduced to allow intensive properties of the system which are not independent variables to be treated in a similar fashion to the extensive ones.Finally, some observations concerning the thermodynamic meaning of a partial molar property are made.

Experimental measurements of the equilibrium in the S-1 Spheromak by use of magnetic probes inside the plasma show that the final magnetic equilibrium is one which has relaxed close to the Taylor (minimum-energy) state, even though the plasma is far from that state during formation. The comparison is made by calculating the two-dimensional ..mu.. profile of the plasma from the probe data, where ..mu.. is defined as ..mu../sub 0/j/sub parallel//B. Measurements using a triple Langmuir probe provide evidence to support the conclusion that the pressure gradients in the relaxed state are confined to the edge region of the plasma.

We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the chemical potential is constant in the two sets of parallel formalisms, where the fundamental thermodynamic equations with dual interpretations of thermodynamic quantities are derived for the open systems. By introducing parallel structures of Legendre transformations, other thermodynamic equations with dual interpretations of quantities are also deduced in the open systems, and then several dual thermodynamic relations are inferred. One can easily find that there are correlations between the dual relations, from which an equivalent rule is found that the Tsallis factor is invariable in calculations of partial derivative with constant volume or constant entropy. Using this rule, more correlations can be found. And the statistical expressions of the Lagrange internal energy and pressure are easily obtained.

In this paper, we define the state of minimum energy while the expectation values of the field operators and their time derivatives in a determined moment in such a state are constrained. As an axiom, we consider such a state as the background of the quantum field theory. As an example, we consider the scalar field with [Formula: see text] interaction. To the third-order of perturbation, we obtain the equation of motion of the dynamic expectation value of the scalar field in the defined state.

The key to the understanding of polymer properties is the principle of rotational isomeric states. Each state is weighted according to an internal energy which depends on intramolecular non-bonded interactions. Each chemically regular, linear polymer species has a minimum energy state wherein the torsional angles defining this rotational isomeric state are repeated regularly along the polymer chain. This leads to a helical conformation which is generally the same as found in the crystalline polymer. X-ray diffraction has been the single most useful experimental tool for providing data concerning this “crystalline” minimum energy state.

INFORMATION on macromolecules may conveniently be found by application of the Kerr electro-optic effect. When an electric field in the form of a pulse of rectangular shape is applied to a solution the molecules will attempt to line up to a state of minimum potential energy during the rise period of the pulse. Once lined up they will remain stationery in alignment when the field amplitude is constant and then become disorientated by Brownian motion when the field ceases. If the orientation is sufficient the solution will exhibit birefringence, but since large molecules will take time to come into alignment and to return to a state of random array the rise and decay of the birefringence will lag behind that of the applied field. In general, therefore, a gradual increase of birefringence occurs, which may or may not reach a steady value according to the duration of the pulse, followed by a decay. Observations of the rise can give information on dipole moments and the steady value can be related to the Kerr constant and to molecular anisotropy. The decay for a solution of k types of molecules occurs according to the equation1: in which Δn is the birefringence at any time t, δni is the maximum birefringence shown by molecules of type i and τi is a relaxation time which is a measure of the time the molecule takes to depart from its position of minimum potential energy. If it be assumed that the effect of the field is to produce rotation of the entire molecule then the polar or non-polar nature of the molecule is made manifest by the symmetry or asymmetry of the birefringence rise and fall, and τi can be related1 to the rotary diffusion constant Di by the equation τi = 1/6Di. Values of relaxation times and diffusion constants obtained in this laboratory are reported here.

\n Context. The paper is concerned with heating of the solar corona by nanoflares: a superposition of\nsmall transient events in which stored magnetic energy is dissipated by magnetic reconnection.\nIt is proposed that heating occurs in the nonlinear phase of an ideal kink instability, where\nmagnetic reconnection leads to relaxation to a state of minimum magnetic energy.\n Aims. The aim is to investigate the nonlinear aspects of magnetic relaxation on a current loop with zero net axial current.\nThe dynamical processes leading to the establishment of a relaxed state are explored. The efficiency of\nloop heating is investigated. \n Methods. A 3D magnetohydrodynamic numerical code is used to simulate the evolution of coronal\nloops which are initially in ideally unstable equilibrium. The initial states have zero net current.\nThe results are interpreted by comparison both with linear stability analysis\nand with helicity-conserving relaxation theory.\n Results. The disturbance due to the unstable mode is strongly radially confined when the loop carries\nzero net current. Strong current sheets are still formed in the nonlinear phase with dissipation of\nmagnetic energy by fast reconnection. The nonlinear development consists first of\nreconnection in a large scale current sheet, which forms near the quasi-resonant surface of the equilibrium field.\nSubsequently, the current sheet extends and then fragments, leading to multiple\nreconnections and effective relaxation to a constant α field.\n Conclusions. Magnetic reconnection is triggered in the nonlinear phase of kink instability in loops with zero net current.\nInitially, reconnection occurs in a single current sheet, which then fragments into multiple\nreconnection sites, allowing almost full relaxation to the minimum energy state.\nThe loop is heated to high temperatures throughout its volume.\n

Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order mp ∼ 10 M⊕. Motivated by the observational sample, this paper determines the tidal equilibrium states for this class of extrasolar planetary systems. We start by considering two-planet systems with fixed orbital spacing and variable mass ratios. The basic conjecture explored in this paper is that the planet formation process will act to distribute planetary masses in order to achieve a minimum energy state. The resulting minimum energy configuration – subject to the constraint of constant angular momentum – corresponds to circular orbits confined to a plane, with nearly equal planetary masses (as observed). We then generalize the treatment to include multiple planet systems, where each adjacent pair of planets attains its (local) tidal equilibrium state. The properties of observed planetary systems are close to those expected from this pairwise equilibrium configuration. In contrast, observed systems do not reside in a global minimum energy state. Both the equilibrium states of this paper and observed multiplanet systems, with planets of nearly equal mass on regularly spaced orbits, have an effective surface density of the form σ ∝ r−2, much steeper than most disc models.

Jet physics is again flourishing as a result of Chandra’s ability to resolve high-energy emission from the radio-emitting structures of active galaxies and separate it from the X-ray-emitting thermal environments of the jets. These enhanced capabilities have coincided with an increasing interest in the link between the growth of super-massive black holes and galaxies, and an appreciation of the likely importance of jets in feedback processes. I review the progress that has been made using Chandra and XMM-Newton observations of jets and the medium in which they propagate, addressing several important questions, including: Are the radio structures in a state of minimum energy? Do powerful large-scale jets have fast spinal speeds? What keeps jets collimated? Where and how does particle acceleration occur? What is jet plasma made of? What does X-ray emission tell us about the dynamics and energetics of radio plasma/gas interactions? Is a jet’s fate determined by the central engine?

Elements, Atoms, and Electrons Matter and Elements Atoms Atomic Structure Isotopes The Periodic Table Electron Structure of Atoms Covalent Bonding and Molecules Interactions between Atoms Covalent Bonds Are Formed by Sharing Outer Electrons Formulae of Compounds Covalent Bonds Formed by Combining Atomic Orbitals Single Overlap, the Sigma-Bond Double Overlap, the Pi-Bond Molecules with s- and p-Bonds Hybrid Molecular Orbitals Forces Within and Between Molecules Ionic Bonding Polar Covalent Bonds Dipole-Dipole Forces The Hydrogen Bond van der Waals Forces The Hydrophobic Effect Coordinate Bonds Chemical Reactions Rates of Reaction Factors Affecting Rate of Reaction Rate Equations Integrated Forms of Rate Equations Zero-Order Reactions Integrated Form of the Zero-Order Rate Equation First-Order Reactions The Integrated Form of the First-Order Rate Equation Second-Order Reactions Integrated Forms of Second-Order Rate Equations Pseudo-First-Order Reactions Reversible Reactions Equilibrium Water The Water Molecule Ice Water Solutions The Mole Concept Calculating Molar Masses Molarity Colloidal Solutions Diffusion and Osmosis Acids, Bases, and Buffers Ionisation of Water The Hydrogen Ion Acids and Bases Strong Acids and Strong Bases Weak Acids and Weak Bases Ka and Kb Relationship between Ka and Kb pH, pOH, pKw, pKa, pKb Solutions of Weak Acids and Bases Salts and Salt Hydrolysis Buffer Systems Calculating the pH Values of Buffers Indicators Titrations Gases Pressure Measurement of Pressure Ideal Gas Laws Partial Pressures Solubility of Gases Diffusion in Gases Aliphatic Carbon Compounds Simple Molecules Containing Carbon Organic Compounds Alkanes and Alkyl Groups Alkenes Alcohols Thiols Aldehydes and Ketones Carboxylic Acids Amines Lipids, Sugars, and Linkages between Reactive Groups Fatty Acids Esters Glycerol Esters Hemiacetals and Hemiketals Simple Sugars Chirality in Simple Sugars Straight-Chain Sugars Spontaneously Form Rings Sugar Hydroxyls Can Be Chemically Modified Sugars Are Joined Together by Glycosidic Bonds Aromatic Carbon Compounds and Isomerism Benzene Bioactive Aromatic Compounds Isomerism Structural Isomerism Chain, Positional, and Functional Group Isomerism Tautomerism Stereoisomerism Geometrical Isomerism Optical Isomerism Organic and Biological Reaction Mechanisms Reactive Sites and Functional Groups Describing Reaction Mechanisms Bimolecular Nucleophilic Substitution Electrophilic Addition to a Nonpolar Double Bond Elimination to Form an Alkene Nucleophilic Addition to a Polar Double Bond Free Radical Reactions Carbon-Carbon Bond Formation in Biosynthesis Sulphur and Phosphorus The Electron-Shell Structure and Valency of Phosphorus and Sulphur Sulphur The Thiol Group and Thiol Esters Phosphate, Pyrophosphate, and Polyphosphate Phosphate Esters The Role of Phosphate Esters and ATP in Cellular Energy Metabolism Oxidation and Reduction Reactions Oxidation Is Linked to Reduction The Chemical Changes in the REDOX Process Splitting REDOX Reactions Standardising REDOX Half-Reactions Predicting Electron Flow Free Energy and Standard Reduction Potentials Redox Reactions and Nonstandard Conditions Metals in Biology General Properties of Metals in Biology Some Properties of Alkali Metals The Alkaline Earth Metals Transition Metals Role of Metal as Oxygen Carrier Metals Facilitate Biocatalysis The Role of Metal Ions as Charge Carriers The Toxicity of Metals Energy The First Law of Thermodynamics Units of Energy Measurement of Energy Internal Energy, U, and Enthalpy, H Calorimetry Hess's Law Enthalpies of Formation The Second Law of Thermodynamics Free Energy Interaction of DeltaH with TDeltaS Reactions and Equilibrium DeltaG and Equilibrium Activation Energy The Effect of the Temperature on Reaction Rate The Arrhenius Equation Catalysis Enzyme Catalysis Kinetics of Enzyme Reactions Finding Vmax and KM Light Light Is Part of the Electromagnetic Spectrum Wavelength and Frequency The Quantum Theory of Light The Absorption of Light The Relationship between Light Absorption and Concentration The Spectrophotometer The Fate of Absorbed Light Appendix: Derivations of Equations Index

Results of earlier studies on the decomposition of activated sec-butyl radicals formed in nonequilibrium systems by the addition of H or D atoms to trans-butene-2, to cis-butene-2, and to butene-1 are summarized together with new data. The work constitutes a program of study in which butyl radicals have been produced at six different levels of minimum internal excitation energy. Two choices of ambient temperature (300° and 195°K), together with pressure variation over the (ideal) limiting range of zero to infinity, give rise in these systems to a further increase in the number of values of the average energy of the reacting radicals; these energies correspond to a range from 7.2 to 14.2 kcal mole—1 for the average excess energy of the radicals with respect to decomposition. Twenty-one of such average energy states out of the possible twenty-four values, corresponding to two pressure extremes at each of two temperatures, have been obtained experimentally. These data permit a more consistent test of the theoretical models which were presented in the earlier work. A comparison and discussion of the observed rates is given. The agreement is satisfactory. An ``energy'' isotope effect which arises upon replacement of reactant H atom by D is well accounted for. It is concluded that the merits of the chemical activation technique for clarifying the nature of unimolecular reaction, at high levels of vibrational excitation of polyatomic species, are well borne out. The present evidence, together with other work, shows the usefulness of the Marcus—Rice rate expression in all systems where the assumptions may apply, when accurate calculations are made with quantum statistical models. The effect of variation of thermochemical and molecular parameters on the calculations is described. Not only are all vibrational degrees of freedom to be taken as active, as the best a priori assumption, but there is evidence that where they exist, internal rotations and possibly one of the over-all rotations should be so treated also.

Criterion for silicon formation in transition metal-silicon diffusion couples

Photoinduced phase-transition materials, such as chalcogenides, spin-crossover complexes, photochromic organic compounds and charge-transfer materials, are of interest because of their application to optical data storage. Here we report a photoreversible metal-semiconductor phase transition at room temperature with a unique phase of Ti(3)O(5), lambda-Ti(3)O(5). lambda-Ti(3)O(5) nanocrystals are made by the combination of reverse-micelle and sol-gel techniques. Thermodynamic analysis suggests that the photoinduced phase transition originates from a particular state of lambda-Ti(3)O(5) trapped at a thermodynamic local energy minimum. Light irradiation causes reversible switching between this trapped state (lambda-Ti(3)O(5)) and the other energy-minimum state (beta-Ti(3)O(5)), both of which are persistent phases. This is the first demonstration of a photorewritable phenomenon at room temperature in a metal oxide. lambda-Ti(3)O(5) satisfies the operation conditions required for a practical optical storage system (operational temperature, writing data by short wavelength light and the appropriate threshold laser power).

The development of reservoirs that are not in hydrostatic equilibrium or that have suffered deviations from primary drainage over geological time requires appropriate challenges to standard assumptions in order to optimize the field's full potential. Such circumstances are more frequent than usually acknowledged since the Earth is not static, structures get buried or change with tectonic activity and fluids re-arrange themselves to achieve a state of minimum potential energy. The focus of this paper is three fold: a) highlight geological processes that may affect fluid distribution and pressure regime in a reservoir; b) provide a template workflow and diagnostic tools for identification of alternative fluid-fill cycle and equilibrium state scenarios; c) illustrate through actual field examples the relevance of recognising tectonic imprint on fluid distribution, in particular for reservoirs with low permeability, oil wettability or low porosity. A companion paper1 published at the same time discusses methods to model saturation changes in some of such complex fields. In summary, the interpretation of variable contacts within a field can result in changes to development decisions (see fig 1): consequences are not limited to volumetric assessment but they can actually change the development, well count and well placement as well as impacting the design of the facilities. Based on risk and opportunity management optimization we advise against indiscriminate standard assumptions of primary drainage or hydrostatic equilibrium for all reservoirs in all basins.