Values Of Internal Energy Research Articles

A study of relevant parameters in collisional‐activation of ions in the ion‐trap mass spectrometer

AbstractVariously substituted aryl ketones served as models to gain insight into the collisional‐activation process in an ion‐trap mass spectrometer. The effects of different targets (helium, argon) at different pressures were examined. The investigation also involved the comparison of the results of tandem mass spectrometry experiments in the ion trap with those obtained in high‐energy collision and mass‐analysed ion kinetic energy experiments in a sector instrument. Use of argon and low helium pressures in the ion trap results in both an increase of the average internal energy of the activated ion and, presumably, a less broad energy deposition profile. The results indicate that the maximum value of internal energy achieved by an ion through multiple collisions in the ion‐trap mass spectrometer is limited by the presence of low‐energy reaction channels.

Nonlinear reciprocity and the maximum entropy formalism

The maximum entropy formalism calculates a phase-space distribution, p(x) , which maximizes the information-theoretic entropy subject to specified values of internal energy and state variables α i and η i ( i = 1, …, n). The latter are averages, calculated from p , of dynamical functions A i and A i ≡ iLA i , respectively, where L is the Liouville operator. From p , one extracts a fluctuation distribution g(a, v) for the values of the A and A ̊ . A kinetic equation for the fluctuation distribution has been derived by Grabert using projection operators appropriate to a system in thermal contact with its surroundings, and g is proposed as an ansatz for its solution. From the first moments of the kinetic equation, after introduction therein of g , one extracts phenomenological equations for ⋗a i and ⋗h i whose terms can be grouped to exhibit Onsager symmetry, even when nonlinear terms are included. The groupings can be affected exactly, but not uniquely.

Chemical effects of β-decay in95Zr-Alizarin S and95Zr-TTA complexes

The chemical behaviour of the95Nb atoms formed by the beta decay of the95Zr-Alizarin S and95Zr-TTA (2-thenoyltrifluoracetone) complexes were investigated. The retention values of95Nb which not complexed with organic reagents at working pH were determined. The values observed were 100% and 80%, respectively. The results are discussed and interpreted to explain the different behaviour on the basis of internal energy values and solvent effects.

Experimental appraisal of the maximal-entropy theory of multiphoton ionization-fragmentation: The alternative ionization pathway test

An experimental test of the Silberstein–Levine (SL) maximal-entropy theory of multiphoton ionization-fragmentation has been devised and applied to a diverse group of polyatomic molecules. The MPI fragmentation pattern of a given compound is strongly dependent upon the laser wavelength (which governs the ’’pathway’’ to the continuum) and the laser power density (and pulse energy). Nevertheless, it is found possible to obtain similar fragmentation patterns at several wavelengths (i.e., via different pathways) by adjusting the laser power so as to excite the molecule/ion system to the same average value of internal energy 〈E〉. Data are presented for benzene, toluene, t-butylbenzene, triethylenediamine, quinuclidine, and iodomethane, all of which tend to confirm the major premise of the SL theory that the branching fraction pattern is governed by the single parameter 〈E〉.

Statistical Mechanical Theory of Rod-Like Molecular Fluids with Kihara-Type Interactions. II. Thermodynamic Properties

Abstract Expressions for thermodynamic properties as functionals of a pair distribution function depending only on the shortest distance between molecular cores are presented. Values of internal energy, entropy, enthalpy and pressure, by two ways, were computed for a linear core and for a spherical core of CO2 molecule. Pair distribution function for linear core is taken from a new approximation derived by the authors in a previous paper, to solve Percus-Yevick equation for linear molecules. Pair distribution function for spherical core is calculated from the Percus-Yevick equation by standard methods. The comparison with experimental results shows non-spherical theory improves considerably the agreement. A brief discussion about the scope of the approximations made in the derivation of non-spherical theory is presented.

The enthalpies of sublimation and internal energies of solid argon, krypton, and xenon determined from vapor pressures

The vapor pressures of solid argon, krypton and xenon were measured from 74.653 to 83.804 K for argon, from 103.719 to 115.727 for krypton, and from 142.826 to 161.332 K for xenon. The enthalpy of sublimation ..delta.. H was determined at various temperatures from the Clausius-Clapeyron equation: ..delta..H = (dp/dT)sub(sat)T(Vsub(g)-Vsub(s)). The internal energies Usub(s) were calculated using the thermodynamic relation: Usub(s) -..delta..H + psub(sat)(Vsub(g)-Vsub(s)sup(s))-RT/sup 2/B'(T)/Vsub(g), (R = 8.31441 J K/sup -1/mol/sup -1/), where B'(T) is the derivative with respect to temperature of the second virial coefficient and subscript 'sat' refers to saturated vapor conditions. The results are presented. The derived values of internal energy are compared with those calculated by Monte Carlo techniques.

Energy transfer in collisional activation of gaseous organic ions

The amounts of translational energy lost in the collisional activation (CA) of CH 4 +, CD 4 +, CH 3 +, and CD 3 + to form the possible C(H,D) 0–3 + products have been measured. These values are consistent with the gain in internal energy required to produce the observed decomposition in unimolecular reactions, as predicted by the quasi-equilibrium theory. Further, there appear to be marked differences in the distribution of internal energy values of CH 4 + produced by electron ionization of CH 4 and the distribution produced by CA of low energy CH 4 + ions.

Thermodynamics of solid argon at high temperatures

Recent high-pressure equation-of-state data for Ar are analysed to obtain entropy, internal energy, and specific heat values for solid Ar from 84K to the melting curve at molar volumes from 21 to 24 cm3 mol-1. These equation-of-state data are also used to reanalyse earlier specific heat data along the vapour-pressure curve. The resulting thermodynamic properties are compared with theoretical calculations based on the best intermolecular potentials for Ar, and some minor inadequacies in the potentials are pointed out. These data along with the theoretical calculations provide the basis for an extensive analysis of anharmonic effects in solid Ar, and it is concluded that all the high-temperature data are consistent with a quadratic temperature dependence for the anharmonic contribution to the Helmholtz potential.

Thermodynamic Properties of Helium 4 from 2 to 1500 K at Pressures to 108 Pa

Tabular values of density, internal energy, enthalpy, entropy, heat capacity, and speed of sound for liquid and gaseous helium are presented for temperatures from 2 to 1500 kelvin at pressures from 1.0 × 104 to 1.0 × 108 pascals. Diagrams of temperature vs entropy are also given. The properties presented are calculated from an equation of state which was fitted to experimental P—V—T and other thermodynamic data from the world's literature. The equation of state was fitted to these data in three separate regions of pressure and temperature. The regional equations are forced to join smoothly at the preconceived boundaries. Extensive comparisons between the equation of state and experimental data have been made, and deviation plots are presented. A particularly careful determination of the second virial coefficient over the full temperature range 2–1500 kelvin is presented. The Joule-Thomson inversion curve has been calculated and comparisons made with other sources. Equations for the density of the saturated liquid and vapor are included as well as an equation which represents the 1958 helium vapor pressure temperature scale.

Triple-dipole dispersion forces in dense fluids

The contribution of triple-dipole dispersion forces to thermodynamic properties of fluid argon is determined from an analysis of computer-generated configurations of atoms. For states of liquid argon lying near the liquid-vapour equilibrium line the effect of triple-dipole interactions is to increase both internal energy and volume by several per cent. The inclusion of the triple- dipole contribution largely accounts for the discrepancies which are found between the experimental values of internal energy and pressure and the values calculated from a potential chosen to simulate the true pair potential between argon atoms. Accurate values are also obtained for the contribution of the triple-dipole potential to medium-dependent effective pair potentials of the type developed by Sinanoglu (1967). Results are given in tabular form for six states of fluid argon and for the corresponding states of krypton and xenon.

Specific Heats of Oxygen at Coexistence.

Specific heats of saturated liquid, along the coexistence path, are useful for computing thermodynamic properties throughout the compressed liquid phase. We report 86 experimental heat capacities of oxygen for the two-phase system, liquid plus vapor, from the triple-point to near the critical-point and corresponding derived values for the liquid phase. These results are represented by a formula which can be integrated for heat absorbed and for entropy. The changes in value of internal energy, enthalpy, and entropy of the saturated liquid are tabulated from the triple-point to the critical-point.

Numerical calculation of supersonic wake flow.

The particle-in-cell method has been used to obtain numerically the full, time-dependent development of the plane or cylindrical wake behind the flat base of a projectile moving with supersonic speed through air. Viscous and real-gas effects were neglected, but it is indicated how they could be incorporated into the calculation. Particular attention is paid to the case of Mach 1.89, arising from the passage of a very strong shock over a projectile at rest. Many features are shown of the transient build-up to statistically steady state, as well as of the late-time flow behavior. Comparisons between plane and cylindrical projectiles reveal a number of differences. Effects at higher Mach numbers are discussed briefly. I. Introduction H IGH-SPEED photographs of the flow of air about a supersonic projectile usually show the prominent structure indicated in Fig. 1. From these and other visible features, a number of details about the flow can be calculated or inferred, especially in the region outside of the wake. Within the wake itself, however, the behavior is less easily amenable to precise experimental analysis. Such properties as the timeaveraged fields of velocity, temperature, and density are difficult to obtain. Recent experimental papers1 ~3 show some of the techniques that have been successfully tried and include references to much of the earlier work. Other authors have introduced idealized models of the wake flow whose properties could be examined numerically,4 or analytically.57 The advantage of such an approach is that the achievement of agreement with some of the measured flow properties tends to confirm the physical basis of the model and to strengthen faith in the prediction of unmeasurables. The disadvantage of most models is that the restrictions required for analytical tractability are too stringent to reveal some of the most interesting flow features. Models for which numerical solution is accomplished by high-speed computer may not be so restricted, and it is the purpose of the present paper to show that such a model can be quite detailed in its presentation of the time-dependent flow throughout the entire near-wake region. We have used the particle-in-cell (PIC) method for numerical, multidimensional, time-dependent fluid dynamic studies to calculate several typical wake-flow problems. Transient effects were investigated for those examples in which flow was initiated by the diffraction of a shock about the projectile base. In those and higher Mach-number flows, the late-time statistically steady state was analyzed in detail. The calculations were performed without the inclusion of viscous or real-gas effects, but it is shown that one of the great advantages of the numerical model is that these effects are almost trivially simple to include. Use has been made of the symmetry of both the plane and cylindrical flows to reduce the number of spatial variables to two. The PIC method is well suited to hydrodynamic calculations in which multidimensional compressible flow involves large fluid distortions. We made use of a PIC code called VALLE which was written for the IBM 7030 (Stretch) Data Processing System. The computing method has been described in detail in previous literature811; thus, only a brief description will be given here. , The differential equations on which the computing method is based are those of mass, momentum, and energy conservation (dp/5*) + (u-V) P = -pV-u p(5u/50 + p(u-V) u = -Vp P(57/50 -f P(U-V)/ = -pV-u in which all symbols have their usual meanings. In the version of the method reported here, the effects of true viscosity and heat conduction have been neglected. The calculational system is based upon a rectangular mesh of fixed Eulerian cells through which the fluid moves. The fluid is represented by Lagrangian mass points called particles, each of which carries a fixed mass of fluid. The mass of each cell is represented by the sum of the particle masses within that cell. The calculation proceeds through a sequence of finite time steps in which the field variables are changed as follows: first, cell pressures are calculated from cellwise values of mass, volume, and specific internal energy. (For this problem we chose the simple gas equation of state with a fixed specific heat ratio.) From the gradients of these pressures, tentative new values of the two components of velocity are calculated, each of which is compared with a maximum allowable value. If the new value is too large, the calculation would become unstable, and so the time cycle interval is cut and the velocity calculation is restarted. Tentative new values of specific internal energy are also computed. In both cases, the values are tentative because o'f omission of transport

``Improved'' Free-Volume Theory of Liquids. V. Worm Model Calculations for the 12–6 Potential

The worm or super-cell model has been used to estimate the equilibrium properties of a fluid whose molecules interact according to the Lennard-Jones 12–6 potential. The integral equation for the radial part of the cell-cluster distribution function has been solved by an iterative method. Values of the configurational energy, configurational entropy, and of the compressibility factor are tabulated for a wide range of temperatures and densities. The results are compared with those of other theoretical studies. The calculated values of pressure, internal energy, and entropy agree remarkably well with the available experimental data.

The internal energy of inflammable mixtures of coal-gas and air after explosion

The results of experiments upon the heat lost by radiation and by conduc­tion during the explosion and subsequent cooling of inflammable gaseous mixtures have been recorded in previous papers. In the first section of the present paper the experimental results for mixtures of coal-gas and air of various strengths have been combined, and an empirical law of cooling formulated. In the second section of the paper the combined results have been applied to the estimation of the internal energy of the exploded mixtures at the maximum temperatures developed and at various stages during cooling. A study of the internal energy values for the different mixtures so obtained appears to throw into fair perspective the various causes responsible for the so-called “suppression of heat” in gaseous explosions—or, at any rate, in explosions of mixtures of coal-gas and air.