Change In Internal Energy Research Articles

Variational principles of continuum — to the memory of István Gyarmati

The variational principle, which allows the deduction of the basic equation system of continuum mechanics from the local form of Gyarmati’s integral principle is presented in this paper. Following the approach of irreversible thermodynamics, the principle the kinetic energy is described like the fundamental equation of thermodynamics as the internal energy change, namely intensive quantity multiplied by the changing of extensive quantity. As the internal energy is objective so that is an independent quantity from the coordinate system, this description to the internal energy can be done. However, the kinetic energy is coordinate-dependent quantity. To resolve this contradiction the stress tensor can be divided into elastic and dissipative stress components by using the laws of thermodynamics.

Stepwise Internal Energy Change of Protonated Methanol Clusters By Using the Inert Gas Tagging.

Structural isomer population of a hydrogen-bonded cluster generally depends on temperature. Therefore, determination of an isomer population profile in a wide temperature range is important to understand the nature of hydrogen bond networks of the cluster. To explore an isomer population profile, stepwise changes of internal vibrational energy of a protonated hydrogen-bonded cluster are performed by inert gas tagging. We observe infrared spectra of the protonated methanol pentamer with various tag species. The bare protonated methanol pentamer practically has only two possible isomer types. With the tagging, the relative population of the two isomer types changes according to the binding energy with the tag species. The observed relative population follows its theoretically predicted temperature dependence.

Thermodynamics of the adsorption of organic molecules on graphitized carbon black modified with a monolayer of 5-hydroxy-6-methyluracil

Thermodynamic characteristics of the adsorption of alkanes, alcohols, arenes, and esters on graphitized carbon black with a deposited monolayer (0.17%) of 5-hydroxy-6-methyluracil are studied by means of inverse gas chromatography at infinite dilution. It is established that size effects (violation of the additivity of molar changes in internal energy and the entropy of adsorption for pairs of molecules of one homologous series that differ by one methyl group) are observed when organic molecules are adsorbed on the surface of the resulting adsorbent. The size effects are similar to those observed when 1% 5-hydroxy-6-methyluracil is deposited on graphitized carbon black. It is concluded that the observed violation of additivity is associated with cavities in the supramolecular structure.

Finite volume solution of 2-D hyperbolic conduction in a heterogeneous medium

ABSTRACTFinite volume method that has been shown to be an effective tool for the study of non-Fourier conduction in one-dimensional heterogeneous material is extended to two-dimensional (2D) heterogeneous materials. The accuracy of 2D numerical formulation is examined by comparing the numerical results with the exact solutions for a homogeneous material with constant thermal properties. The effects of temperature-dependent properties due to both heating and cooling of the medium on the wave propagation are investigated. Transient energy balance shows significant effects of finite thermal wave speed on the transient behavior of internal and wave energy changes in the system. The effects of finite thermal wave speed on the entropy production for the cooling case are examined by invoking the second law of thermodynamics. The 2D transient temperature distributions in a heterogeneous medium show the expected effects of flux lagging constant on the thermal wave propagations through heterogeneous material.

Aerodynamic and Radiative Controls on the Snow Surface Temperature

Abstract The snow surface temperature (SST) is essential for estimating longwave radiation fluxes from snow. SST can be diagnosed using finescale multilayer snow physics models that track changes in snow properties and internal energy; however, these models are heavily parameterized, have high predictive uncertainty, and require continuous simulation to estimate prognostic state variables. Here, a relatively simple model to estimate SST that is not reliant on prognostic state variables is proposed. The model assumes that the snow surface is poorly connected thermally to the underlying snowpack and largely transparent for most of the shortwave radiation spectrum, such that a snow surface energy balance among only sensible heat, latent heat, longwave radiation, and near-infrared radiation is possible and is called the radiative psychrometric model (RPM). The RPM SST is sensitive to air temperature, humidity, ventilation, and longwave irradiance and is secondarily affected by absorption of near-infrared radiation at the snow surface that was higher where atmospheric deposition of particulates was more likely to be higher. The model was implemented with neutral stability, an implicit windless exchange coefficient, and constant shortwave absorption factors and aerodynamic roughness lengths. It was evaluated against radiative SST measurements from the Canadian Prairies and Rocky Mountains, French Alps, and Bolivian Andes. With optimized and global shortwave absorption and aerodynamic roughness length parameters, the model is shown to accurately predict SST under a wide range of conditions, providing superior predictions when compared to air temperature, dewpoint, or ice bulb calculation approaches.

The contribution of various network knots during the deformation of ethylene copolymers and nanocomposites based on them

An analysis of the deformation mechanism and changes in mechanical parameters of low-crystallinity ethylene–octene copolymers of various densities and modified with detonation nanodiamonds is performed through the use of models based on the statistical theory of rubber-like elasticity. Experimental data were processed in terms of the Haward model with allowance for the non-Gaussian statistics of macromolecules at high strain and limited extensibility and the so-called “slip-link” model, which considers the density of labile knots and permanent entanglements. Despite obvious simplifications, both models attribute the discovered extrema of the concentration dependences of mechanical properties at low concentrations of nanodiamonds to the change in the number of segments between network knots and the following change in elastic modulus (Haward model) or to the number of labile and permanent knots (“slip-link” model), a circumstance that verifies the nucleating effect of nanodiamonds. It was found that the relative increase in density of each type of knot significantly depends on the degree of crystallinity of the matrix and the concentration of the modifier. Deformation calorimetry showed that tensile and cyclic loading of the investigated systems are followed by changes in internal energy. The roles of its intramolecular and intermolecular components at the various stages of deformation and the causes of their changes were estimated. The correlation between energy effects and the transformation of the structuring and parameters of the used models was determined.

Progressive collapse analysis of steel frame structure based on the energy principle

The progressive collapse potential of steel moment framed structures due to abrupt removal of a column is investigated based on the energy principle. Based on the changes of component's internal energy, this paper analyzes structural member's sensitivity to abrupt removal of a column to determine a sub-structure resisting progressive collapse. An energy-based structural damage index is defined to judge whether progressive collapse occurs in a structure. Then, a simplified beam damage model is proposed to analyze the energies absorbed and dissipated by structural beams at large deflections, and a simplified modified plastic hinges model is developed to consider catenary action in beams. In addition, the correlation between bending moment and axial force in a beam during the whole deformation development process is analyzed and modified, which shows good agreement with the experimental results.

Pre-Melt Energy Budget of an Arctic Snowpack on Landfast First-Year Sea Ice

ABSTRACTThe pre-melt energy budget of a snowpack on landfast first-year sea ice at a remote site in the Canadian Arctic Archipelago was analyzed. Over a 19-day period, the total heat conducted into the snowpack at the snow–sea-ice interface was the largest single energy transfer to the snowpack, while each of the turbulent heat fluxes removed comparable amounts of energy. The total energy transferred from the snowpack (∑Q ≈ −7027 kJ m−2) should have reduced its temperature; however, the opposite occurred. The snowpack’s temperature at both the 7 and 13 cm depths increased over the pre-melt period. The total change in internal energy and latent heat of the snowpack (ΔUsnowpack), derived from 15-minute changes in the snowpack’s temperature over the pre-melt period, was approximately 672 kJ m−2. Closure of the energy budget was not achieved for either the daily or the total pre-melt period. The terms of the energy budget were determined independently; thus, the failure to close the energy budget was the result of the accumulation of errors associated with all the terms. However, for snow on first-year sea ice, the parameterization of the salinity and temperature dependence of the “specific heat” of the basal layer of the snowpack was likely the primary source of error. The snowpack plays a central role in the transfer of energy across the ocean–sea-ice–atmosphere interface, but an adequate method for modelling the evolution of snow on Arctic sea ice including the energy budget, which determines the warming rate and subsequent melt rate of the snow, has yet to be developed.

An evaluation method to predict progressive collapse resistance of steel frame structures

In the current work, a probabilistic assessment method of a steel framed building under abrupt removal of a column due to catastrophic events is developed. A multi-story steel framed model taking into account the influence of catenary effect has been analyzed. Uncertainties in the structural variables are incorporated in the probabilistic simulation approach. Based on the changes of component internal energy, the progressive collapse sensitivity to abrupt removal of a column has been investigated. Besides, a simplified beam damage model is proposed to analyze the energies absorbed and dissipated by structural beams under large deflections. In addition, the correlation incorporating catenary action between bending moment and axial force in a beam during the whole deformation development process is studied. With the methodologies adopted for progressive collapse assessment under removal of a column, a deterministic method has been developed, framed within the Advanced First Order Reliability Method (AFORM). A robustness index (RI) is proposed to evaluate the structural robustness performance based on the acceptable probability of global failure and structural collapse probability.

Electronic, Optic and Dynamic Properties of Rhombohedral BiTeBr

Electronic, optic and thermodynamic properties of rhombohedral BiTeBr crystal were investigated under the local density approximation (LDA) using the density functional theory. No spin-orbit interaction (SOI) were taken into account during calculations and band gap of 0.946 eV was found as which is different from experimental results but in good agreement with previous theoretical studies without SOI. For this new type ferroelectric BiTeBr from ground states features lattice parameters, electronic total density of states (TDOS), partial density of states (PDOS) and electronic band structure, from optical properties dielectric function, refraction index, extinction, reflection and absorption coefficients, number of effective valance electrons, volume and surface loss functions, among thermodynamic properties change in Helmholtz free energy, internal energy, entropy and constant volume specific heat as a function of temperature were studied.

Highly Extensible Supramolecular Elastomers with Large Stress Generation Capability Originating from Multiple Hydrogen Bonds on the Long Soft Network Strands.

Highly extensible supramolecular elastomers are prepared from ABA triblock-type copolymers bearing glassy end blocks and a long soft middle block with multiple hydrogen bonds. The copolymer used is polystyrene-b-[poly(butyl acrylate)-co-polyacrylamide]-b-polystyrene (S-Ba-S), which is synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization. Tensile tests reveal that the breaking elongation (εb ) increases with an increase in the middle block molecular weight (Mmiddle ). Especially, the largest S-Ba-S with Mmiddle of 3140k, which is synthesized via high-pressure RAFT polymerization, achieves εb of over 2000% with a maximum tensile stress of 3.6 MPa, while the control sample without any middle block hydrogen bonds, polystyrene-b-poly(butyl acrylate)-b-polystyrene with Mmiddle of 2780k, is merely a viscous material due to the large volume fraction of soft block. Thus, incorporation of hydrogen bonds into the large molecular weight soft middle block is found to be beneficial to prepare supramolecular elastomers attaining high extensibility and sufficiently large stress generation ability simultaneously. This outcome is probably due to concerted combination of entropic changes and internal potential energy changes originating from the dissociation of multiple hydrogen bonds by elongation.

Change in Internal Energy and Enthalpy of Spinning Black Hole with Half Spin Parameter in XRBs

Mahto et al. gave an expression for the change in enthalpy and internal energy with corresponding change in the radius of the event horizon of black holes of spin parameter a* = 1 (2013). On the basis of this research work, we have proposed an expression for the change in the internal energy and enthalpy of the spinning black holes to assume spin parameter a* = 1/2 and calculated their values for different test spinning black holes existing in XRBs.

Understanding gate adsorption behaviour of CO2 on elastic layer-structured metal-organic framework-11.

We demonstrate that CO2 gate adsorption behaviour of elastic layer-structured metal-organic framework-11 (ELM-11: [Cu(BF4)2(4,4'-bipyridine)2]), which is a family of soft porous crystals (SPCs), can be described by a thermodynamic model by free energy analysis with the aid of an adsorption experiment and a molecular simulation. The structures of ELM-11 (closed structure) at 273 K after its evacuation and CO2-encapsulated ELM-11 (open structure) at 195-298 K were determined by the Rietveld analysis using in situ synchrotron X-ray powder diffraction data. We then performed grand canonical Monte Carlo (GCMC) simulations for CO2 adsorption on the open host framework structures of ELM-11 from the Rietveld analysis. The temperature dependence of the Helmholtz free energy change of host ΔF(host) from the closed structure to the open structure was obtained by the free energy analysis using the GCMC data. We show that there is a linear correlation between ΔF(host) and temperature, and thus, the internal energy and entropy changes of host, ΔU(host) and ΔS(host), respectively, can be obtained. The obtained ΔU(host) value is in good agreement with that obtained from the quantum chemical calculations using the closed and open host framework structures, which demonstrates that the thermodynamic model for gate adsorption is highly appropriate. Moreover, our result suggests that the gate adsorption pressure depends on not only the guest-host interaction and the internal energy change of host, but also the entropy change of host, which should be one of the key factors for the tailored synthesis of SPCs.

On the Need to Insert the Concept of Relativity in Thermodynamics Courses

<p>Contrary to the first law of thermodynamics which is generally considered as easily understandable, the second law is often felt as raising conceptual difficulties. It can be noted that their usual presentation is not homogeneous, since the expressions referring to the first law are generally energy equations, while those referring to the second law are entropy equations. If we give to the second law the form of an energy equation, it seems that we are led to extend the significance of the first law. The reason is that, doing so, the change in internal energy corresponding to a given process appears to be different as we are in conditions of irreversibility or of reversibility. In thermodynamic language, this is a way to say that the equality <em>dU<sub>irr</sub> = dU<sub>rev</sub></em> classically interpreted as the formulation of the first law must be substituted by the inequality <em>dU<sub>irr</sub> > dU<sub>rev</sub></em>. Writing this last expression under the form<em> dU<sub>irr</sub> = dU<sub>rev</sub></em> <em>+ dU<sub>add</sub></em>, the question asked concerns the origin of the additional energy noted <em>dU<sub>add</sub></em>,. The suggested answer is that <em>dU<sub>add</sub></em> is a consequence of the Einstein mass-energy relation <em>E = mc<sup>2</sup></em>. This would mean that the laws of thermodynamics are closely linked to the concept of relativity and that the difference <em>dU<sub>irr</sub> - dU<sub>rev</sub></em> can also be formulated <em>dU<sub>irr</sub> = dU<sub>rev</sub></em> <em>- c<sup>2</sup>dm. </em>Such an interpretation was evidently impossible for the creators of the thermodynamic theory, since relativity was unknown at that time. The aim of the present paper is to detail the reasons which lead to this hypothesis, with the hope that it can be felt as a clarification and extension of the theory.</p>

Path integral Monte Carlo simulations of H2 adsorbed to lithium-doped benzene: A model for hydrogen storage materials.

Finite temperature quantum and anharmonic effects are studied in H2-Li(+)-benzene, a model hydrogen storage material, using path integral Monte Carlo (PIMC) simulations on an interpolated potential energy surface refined over the eight intermolecular degrees of freedom based upon M05-2X/6-311+G(2df,p) density functional theory calculations. Rigid-body PIMC simulations are performed at temperatures ranging from 77 K to 150 K, producing both quantum and classical probability density histograms describing the adsorbed H2. Quantum effects broaden the histograms with respect to their classical analogues and increase the expectation values of the radial and angular polar coordinates describing the location of the center-of-mass of the H2 molecule. The rigid-body PIMC simulations also provide estimates of the change in internal energy, ΔUads, and enthalpy, ΔHads, for H2 adsorption onto Li(+)-benzene, as a function of temperature. These estimates indicate that quantum effects are important even at room temperature and classical results should be interpreted with caution. Our results also show that anharmonicity is more important in the calculation of U and H than coupling-coupling between the intermolecular degrees of freedom becomes less important as temperature increases whereas anharmonicity becomes more important. The most anharmonic motions in H2-Li(+)-benzene are the "helicopter" and "ferris wheel" H2 rotations. Treating these motions as one-dimensional free and hindered rotors, respectively, provides simple corrections to standard harmonic oscillator, rigid rotor thermochemical expressions for internal energy and enthalpy that encapsulate the majority of the anharmonicity. At 150 K, our best rigid-body PIMC estimates for ΔUads and ΔHads are -13.3 ± 0.1 and -14.5 ± 0.1 kJ mol(-1), respectively.

MONTE CARLO NEUTRINO TRANSPORT THROUGH REMNANT DISKS FROM NEUTRON STAR MERGERS

We present Sedonu, a new open source, steady-state, special relativistic Monte Carlo (MC) neutrino transport code, available at bitbucket.org/srichers/sedonu. The code calculates the energy- and angle-dependent neutrino distribution function on fluid backgrounds of any number of spatial dimensions, calculates the rates of change of fluid internal energy and electron fraction, and solves for the equilibrium fluid temperature and electron fraction. We apply this method to snapshots from two-dimensional simulations of accretion disks left behind by binary neutron star mergers, varying the input physics and comparing to the results obtained with a leakage scheme for the case of a central black hole and a central hypermassive neutron star. Neutrinos are guided away from the densest regions of the disk and escape preferentially around 45 degrees from the equatorial plane. Neutrino heating is strengthened by MC transport a few scale heights above the disk midplane near the innermost stable circular orbit, potentially leading to a stronger neutrino-driven wind. Neutrino cooling in the dense midplane of the disk is stronger when using MC transport, leading to a globally higher cooling rate by a factor of a few and a larger leptonization rate by an order of magnitude. We calculate neutrino pair annihilation rates and estimate that an energy of 2.8e46 erg is deposited within 45 degrees of the symmetry axis over 300 ms when a central BH is present. Similarly, 1.9e48 erg is deposited over 3 s when an HMNS sits at the center, but neither estimate is likely to be sufficient to drive a GRB jet.

Thermodynamically consistent description of mass transfer in porous media by a singular surface

AbstractPhase transition processes are important and ubiquitous physical phenomena. These processes are not limited to systems like batch reactors, but can also appear inside porous solids such as in the sequestration of CO2 or in the food industry. In these processes, mainly first‐order transitions between the liquid and the gaseous phases of a certain fluid occur and are characterised by a jump in density and the coexistence of both phases during phase change. This jump is numerically handled by introducing a singular surface, which allows for a thermodynamically consistent description of the mass transfer during phase transition. The mass transfer is driven by the change in internal energy and couples the two mass balance relations of the two fluid phases.The formulation of a model for a multiphasic porous aggregate in a non‐isothermal environment, while accounting for the thermodynamics of the fluids and the phase transition, requires a potent theory for its description. Here, the Theory of Porous Media (TPM) provides a well‐founded, continuum‐mechanical basis to model deformable, fluid‐saturated porous media. In this particular case, a three‐phasic model is proposed, consisting of the thermoelastic solid phase, which is percolated by the compressible gaseous and liquid fluid phases. The representation of the interface between the fluid phases by a singular surface results in additional terms in the balance relations. The evaluation of these terms leads to a consistent formulation of the mass transfer, which basically compares the energy added to the system with the latent heat of the phase transition. This mass‐transfer term is furthermore dependent on the interfacial area, a factor defined by porosity and saturation.Finally, the proposed model for phase transition inside a porous medium is based on the mixture momentum balance, the volume balances of the fluid phases and the energy balance. Consequently, the four primary variables are the solid deformation, the effective pore pressures of the two fluid phases and the temperature. The numerical simulation of condensation or evaporation of CO2 in a porous solid rock, which can be either caused by changes in temperature or in pressure, allows for the demonstration of possible application areas for the presented model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Trajectory and Model Studies of Collisions of Highly Excited Methane with Water Using an ab Initio Potential.

Quasi-classical trajectory studies have been performed for the collision of internally excited methane with water using an accurate methane-water potential based on a full-dimensional, permutationally invariant analytical representation of energies calculated at a high level of theory. The results suggest that most energy transfer takes place at impact parameters smaller than about 8 Bohr; collisions at higher impact parameters are mostly elastic. Overall, energy transfer is fairly facile, with values for ⟨ΔEdown⟩ and ⟨ΔEup⟩ approaching almost 2% of the total excitation energy. A classical model previously developed for the collision of internally excited molecules with atoms (Houston, P. L.; Conte, R.; Bowman, J. M. J. Phys. Chem. A 2015, 119, 4695-4710) has been extended to cover collisions of internally excited molecules with other molecules. For high initial rotational levels, the agreement with the trajectory results is quite good (R(2) ≈ 0.9), whereas for low initial rotational levels it is only fair (R(2) ≈ 0.7). Both the model and the trajectories can be characterized by a four-dimensional joint probability distribution, P(J1,f,ΔE1,J2,f,ΔE2), where J1,f and J2,f are the final rotational levels of molecules 1 and 2 and ΔE1 and ΔE2 are the respective changes in internal energy. A strong anticorrelation between ΔE1 and ΔE2 is observed in both the model and trajectory results and can be explained by the model. There is evidence in the trajectory results for a small amount of V ↔ V energy transfer from the water, which has low internal energy, to the methane, which has substantial internal energy. This observation suggests that V ↔ V energy transfer in the other direction also occurs.

Theoretical analysis of the interconnection between the shear elasticity and heat effects in metallic glasses

Changes of the shear modulus and heat effects occurring upon structural relaxation and crystallization of metallic glasses are analysed within the framework of two approaches, the Interstitialcy theory and elastic dipole model. The former approach assumes that elastic and heat effects are determined by dumbbell interstitial defects inherited from the melt. The analysis within this framework is based on the postulate that the internal energy change is proportional to the shear modulus and defect concentration change. The elastic dipole model takes into account that dumbbell interstitials are in fact elastic dipoles and the change of the internal energy is determined by their elastic strain fields, which are considered within the framework of non-linear theory of elasticity. In spite of fully different phenomenology, both approaches lead to very similar theoretical expressions for the elastic and heat effects. The interconnection between these approaches, their advantages and problems are discussed.

Influence of Mass and Radius of Ice Crystals on Hydrometeors, Internal Energy, and Kinetic Energy: A Numeric Model Study

AbstractTwo cloud-scale experiments with two different ice-phase schemes were carried out for a precipitation event that occurred in eastern China in 2005. The results were analyzed to examine the influences of the change of ice-particle mass and radius on hydrometeors, internal energy, and kinetic energy, as well as the primary factors responsible. It was found that the ice content increases notably and the snow content decreases due to the change. This is the consequence of the modulation of cloud microphysical processes. In particular, the Bergeron process and the accretion of snow and cloud ice are markedly influenced. The differences of internal energy and kinetic energy between the two experiments are caused by adjustments to pressure-flux divergence, the coupling of temperature and divergence, and gravitational work, and the reason is that these three factors result in differences of local changes of internal and kinetic energy.