Entropic Equation Research Articles

Effect of Plasma Electric Field Assistance on the Freezing Process and Ice Crystal Formation of Bactrian Camel Meat

Background: The longissimus dorsi muscle of the camel was chosen as the experimental material in order to investigate the impact of plasma electric field assisted freezing on the quality and freezing process of Bactrian camel meat. Methods: The effect of the auxiliary plasma electric field of different field strengths (1 kV/m, 3 kV/m and 5 kV/m) on the freezing velocity of the camel meat and the distribution of ice crystals as well as the diameter and roundness of ice crystal in the frozen meat were studied and analyzing them with the help of the thermodynamic theory. Result: The findings demonstrated that the meat samples in the auxiliary 5 kV/m plasma field environment took 60 min and 30 min, respectively, at -20°C and -35°C, to pass the maximal ice crystal production zone. The tissue sections revealed that at -20°C and -35°C assisted 5 kV/m plasma field freezing, the smallest ice crystal area and grain size were formed, the roundness of the ice crystals was highest. Using Boltzmann’s entropic equation to calculate the system’s entropy, the results revealed that the meat samples frozen by the aided 5 kV/m plasma electric field had the lowest entropy at -20°C and -35°C. The electric field assisted freezing requires less energy to improve the subcooling degree and accelerate the freezing rate of meat samples, proving that the auxiliary 5 kV/m plasma electric field can significantly improve the system frozen meat moisture vitrification degree and can make the crystallization process more controllable.

A New Thermodynamic Model to Approximate Properties of Subcritical Liquids.

In order to obtain the thermodynamic properties of compressed liquids, it is usual to consider them as incompressible systems, since liquids and solids are well represented by this thermodynamic model. Within this model, there are two usual hypotheses that can be derived in two different submodels: the strictly incompressible (SI) model, which supposes a constant specific volume v=v0, and a more general model, called temperature-dependent incompressible (TDI) model, which relates a specific volume to temperature, v=vT. But, usually, this difference ends here in the thermal equation of state, and only the SI model was developed for caloric and entropic equations. The aim of this work is to provide a complete formulation for the TDI model and show where it can be advantageously used rather than the SI model. The study concludes that the proposed model outperforms the traditional model in the study of subcritical liquid. One conceivable utilization of this model is its integration into certain thermodynamic calculation software packages (e.g., EES), which integrate the more elementary SI model into its code for certain incompressible substances.

New conserved integrals and invariants of radial compressible flow in n > 1 dimensions

Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in n > 1 dimensions. Apart from entropy, which is a well-known invariant, three additional invariants are found from an explicit determination of invariants up to first order. One holds for a general equation of state, and the two others hold only for entropic equations of state. A recursion operator on invariants is presented, which produces two hierarchies of higher-order invariants. Each invariant yields a corresponding integral invariant, describing an advected conserved integral on transported radial domains. In addition, a direct determination of kinematic conserved densities uncovers two ‘hidden’ non-advected conserved integrals: one describes enthalpy-flux, holding for barotropic equations of state; the other describes entropy-weighted energy, holding for entropic equations of state. A further explicit determination of a class of first-order conserved densities shows that the corresponding non-kinematic conserved integrals on transported radial domains are equivalent to integral invariants, modulo trivial densities.

Symmetries and Casimirs of radial compressible fluid flow and gas dynamics inn > 1 dimensions

Symmetries and Casimirs are studied for the Hamiltonian equations of radial compressible fluid flow inn>1dimensions. An explicit determination of all Lie point symmetries is carried out, from which a complete classification of all maximal Lie symmetry algebras is obtained. The classification includes all Lie point symmetries that exist only for special equations of state. For a general equation of state, the hierarchy of advected conserved integrals found in the recent work is proved to consist of Hamiltonian Casimirs. A second hierarchy that holds only for an entropic equation of state is explicitly shown to comprise non-Casimirs, which yield a corresponding hierarchy of generalized symmetries through the Hamiltonian structure of the equations of radial fluid flow. The first-order symmetries are shown to generate a non-abelian Lie algebra. Two new kinematic conserved integrals found in the recent work are likewise shown to yield additional first-order generalized symmetries holding for a barotropic equation of state and an entropic equation of state. These symmetries produce an explicit transformation group acting on solutions of the fluid equations. Since these equations are well known to be equivalent to the equations of gas dynamics, all of the results obtained forn-dimensional radial fluid flow carry over to radial gas dynamics.

Efficient Information-Theoretic-Statistical (ITSM) Equation for Face Recognition Technique: Comparison with Statistical Technique and Information-Theoretic Technique

Spontaneous recognition of human faces is a challenging problem that has install important concern from signal processing researchers in Last years. This is owing to its many uses in various fields, including security and forensic analysis. Notwithstanding this interest, face recognition is yet one of the most challenging troubles. Up to this time, no way gives a good solution to all attitudes. In this paper we present a neoteric mathematical technicality for face recognition. which we call, (ITSM), is Accredit on our lately disseminated efficient information-theoretic-statistical equation (ITSM), which Merge three mathematically balanced equations. The first one is entropic equation (EE), the second one is histogram equation (HE), and the third one is the standard statistic (SSIM). (ITSM) Tested against versus (SSIM) and (ITSSIM) beneath Gaussian noise, so we got good results even beneath a large scale of PSNR. The face recognition with (ITSM) certified on both above measures of a test image and a database images. We performed the performance evaluation with (MATLAB) using part of the Famous (AT&T) gray Image Database that made up of (49) face images, from which we chose seven person and for each one we chose seven Perspectives (poses) with different facial emotions. The Target of this paper is to present an efficient technicality for face recognition that may work in real-time milieu. Through the implementation of our information, facial recognition has been proven with a method (ITSM) Hybrid (information - theoretic-statistical) that surpasses the known statistical technicality of face recognition (SSIM) and a technicality based on information theory known as (ISSIM).

Thermodynamic, economic analysis and optimization of a heat pump driven desalination system with open-air humidification dehumidification configurations

Abstract In this paper, the heat pump is coupled to a humidification dehumidification desalination system, with open-air configurations, to enhance the energy conversion efficiency. After establishing the energetic and entropic equations for all the thermal processes, the correlations between the desalination performance and the critical parameters, including the compression pressure ratio, pinch temperature difference of the condenser, terminal temperature difference of the evaporator, are revealed. Afterwards, the mass flow rate ratio and effectiveness during humidification and dehumidification are treated as the decision variables to optimize the energy conversion efficiency of the heat pump driven desalination system. The simulation results show that the actual top water production and gained-output-ratio of the desalination system reach 88.34 kgh−1 and 3.72 at the balance condition of the humidifier. It is also obtained that raising the compression pressure ratio and reducing the pinch temperature difference of the condenser and terminal temperature difference of the evaporator, can promote the desalination performance. Furthermore, based on the particle swarm optimization algorithm, the best desalination performance, with 151.03 kgh−1 for the water production, and 5.95 for the gained-output-ratio, is optimized within the prescribed range of the decision variables, while the corresponding cost of produced water arrives at 0.015$L−1 through the economic analysis.

Entropic Equation of the Condition of Simple Crystal Material

Entropic Equation of the Condition of Simple Crystal Material

An entropic equation to calculate contact angles of bulk water droplets on weakly-reactive solid surfaces

Room temperature contact angle (θ25) of a water droplet on a weakly-reactive solid surface is directly calculated from an entropic equation: S25 = 335.86–0.65θ25 (J. unit-mass−1 k−1), where S25 is the entropy of the air/water/solid system and the unit-mass is defined as the sum of 1 mol air, 1 mol water and 1 mol cation solid. Two parameters in the equation are optimized based on thermodynamic calculations of air/water/ice systems and experimental contact angle of water on biotite. This entropy to contact angle linear equation reproduces well experimental contact angles of water on graphite, copper, sapphire, quartz, and calcite, ranging from 9 to 82°. It suggested that (1) contact angle is a direct measure of the state function entropy, and (2) for all solids one (1) J. unit-mass−1 k−1 increment in S25 results in about two (∼2) degrees reduction in θ25. In addition, a new semi-empirical equation is established for calculation of contact angle at high temperatures, by considering the effect of steam-solid reactions. This temperature-dependence equation reproduces well experimental data in water/graphite, water/sapphire, and water/quartz systems from 25 to 272° C. It further demonstrated that under an adiabatic approximation the popular semi-empirical Young's equation is consistent with this entropic equation. This simple and practical entropic equation will advance a wide range of applications from adhesion, coatings, corrosion, protein adsorption, blood compatibility, to cell-surface interactions. It also opens a new field in physics to understand and characterize contact angles from state entropy.

Entropic equation of state and scaling functions near the critical point in uncorrelated scale-free networks

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions, which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in uncorrelated scale-free networks, where the node-degree distribution exponent λ appears to be a global variable and plays a crucial role, similar to the dimensionality d for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.

Microscopic expression of entransy

Boltzmann found that a proportional relation exists between the entropy and the logarithm of the microstate number in an approximate non-interaction particle system. The relation was expressed as the Boltzmanns entropic equation by Planck later. Boltzmanns work gives a microphysical interpretation of entropy. In this paper, a microscopic expression of entransy is introduced for an ideal gas system of monatomic molecules. The changes of the microstate number, the entropy and the entransy of the system are analyzed and discussed for an isolated ideal gas system of monatomic molecules going through the initial stage of unequilibriun thermal state to the thermal equilibrium state. It is found that the microstate number and the entropy always increase in the process, while the entransy decreases. The microstate number is a basic physical quantity which could measure the disorder degree of the system. The irreversibility of a thermal equilibrium process is attributed to the increase in microstate number. Entropy and entransy both are single value functions of the microstate number and they both could reflect the change of the state for the system. Therefore, both entropy and entransy could describe the irreversibility of thermal processes.

Branched-chain organic compounds. Part 11: Validation of a new method for determination of the potential energy of cohesion of an organic crystal and deduction of the heat capacity of the vapour

The cohesion energy of ethyl 3-cyano-3-(3,4-dimethyloxyphenyl)-2,2,4-trimethylpentanoate, as obtained from the change of kinetic and potential energies in the heat of sublimation of the crystal, E p,coh = −46.7 kJ mol−1 (78.6 °C), has been validated. A safe physicomathematic test based on the balance of entropy for the sublimation and Planck’s equation for changes of state, extended to entropy, was devised to ascertain the kinetic energies of the crystal and the gas molecule. Entropic equations were developed for the phase equilibrium to find precisely and with simplicity the vibrational energy of the crystal by using the vapour pressure exclusively and independently from the internal rotational and vibrational motion of the gas molecule. The heat capacity of the vapour was determined in this way, which in this case releases the solid allowing vibrational movement in the gas phase to meet the pressure of sublimation, C p (T)/J K−1 mol−1 = 1.268 T/K + 58.62 (71.1–86.1 °C). An independent variational method of deducing the vibrational entropy, energy, or heat capacity of the gas molecule from each other was compared with the equations and was shown to yield the quantities with high accuracy. Values of the Nernst–Lindemann functions are tabulated.

The composition‐dependent glass transition: Relations between temperature pressure, and composition

AbstractA new predictive relation between pressure and temperature changes on the glass‐transition boundary is derived for random solutions. The isobaric version of this relation is integrated to recover a previous theory for the compositional variation of glass‐transition temperatures. The isothermal form of the differential equation gives an equation for the compositional variation of glass‐transition pressures. An enthalpic definition of the transition boundary provides a relation between excess enthalpies of mixing for the glassy and liquid states for the isobaric and isothermal transitions. Similarly, a definition of the boundary in terms of the solution volume provides a relation between excess volumes of mixing for these two states for the isobaric and isothermal transitions. The primary entropic equation for the composition‐dependent isobaric transition gives two hierarchies of approximation, one of which is shown to be preferred for physical reasons. A parallel situation arises for the isothermal transition.

The effect of degree of polymerization on glass‐transition temperatures

AbstractFinite‐molecular‐mass homopolymers are modeled as binary random mixtures of high polymers and oligomers or chain ends, in proportions determined by the number‐average degree of polymerization. This leads directly to an entropic equation for the effect of molecular mass on Tq in terms of the glass‐transition temperatures and transition increments of heat capacity of these two components. Predictions of the theory are found to be in satisfactory agreement with calorimetric measurements of Tg over a wide range of molecular mass.

Entropic Equations of State and Their Application to Shock Wave Phenomena in Solids

The front of a shock wave in an ideal fluid is characterized by a discontinuous transition from the undisturbed state to a highly compressed state in which the entropy of the fluid has increased. The relations between pressure, density, propagation velocity, and particle velocity behind the shock front are represented by the equations for conservation of mass, momentum, and energy and by the equation of state of the fluid. The entropy change produced by the transition is third order in the compression for weak shocks. The propagation of shock waves through metals can be described by a hydrodynamic theory which assumes that the metal is an ideal fluid behind the shock front, and that the hydrostatic equation of state is applicable there. Three hydrostatic equations of state for Al, Cu, Fe, and Pb are compared with experimental data at low pressures and quantum mechanical calculations pressures up to several hundred megabars. With these equations of state the hydrodynamic theory is used to calculate explicitly the entropy increase across the shock front, the amount by which the pressure exceeds the adiabatic pressure for a given compression, and the temperature rise after the shock pressure has been relieved for the metals mentioned above.

Entropic Equations of State and Their Application to Shock Wave Phenomena

Entropic Equations of State and Their Application to Shock Wave Phenomena