The three isentropic exponents of dry steam

The isentropic change of an ideal gas is described by the well known relations pv^k=const, Tv^(k−1) =const and p^(1−k)T^k=const, where the exponent k is defined as the ratio of the constant pressure to the constant volume specific heat, k=c_p/c_v. The same relations are also used for real gases if small or differential isentropic changes are considered. A better examination of the differential isentropic change shows that for p, v, T systems, there are three different isentropic exponents corresponding to each pair formed out of the variables p, v, T. These three exponents noted k_T,p, k_T,v, k_p,v after the corresponding pair of variables used, are interconnected by one relation, and accordingly only two out of the three are independent. The analysis of the present paper leads to the conclusion that calculations encountered in real gas isentropic change, with the exponent k taken as the ratio of the local specific heat values may lead to incorrect results. The numerical values of these exponents for steam, have been calculated and are presented. It can be seen that the deviations obtained, in comparison to the use of conventional k=c_p/c_v values are considerable.     

Isentropic exponents of real gases and application for the air at temperatures from 150 K to 450 K

Summary Three real gas isentropic exponentsk _Tv,k _rv,k _pT are introduced, which when used in place of the classical isentropic exponentk=c _p/c in the ideal gas isentropic change equations, the latter may describe very accurately the isentropic change of real gases. The usual practice of employing exponentk may lead to considerably incorrect results even when the value ofk corresponds to the correct local value ofc _p/c _v of the real gas under examination. The numerical values of the new exponents are calculated in the case of real air for temperatures from 150 K to 450 K and pressures from 1 bar to 1000 bar. It is seen that at low temperatures and high pressures the values of the new exponents differ considerably from the values of the classical exponentk. Therefore, the error resulting by approximating, as is usually the case, the behaviour of real gases by the ideal gas isentropic change equations in a stepwise fashion with exponentk instead of the new exponents, is considerable. It follows that exponentk, which appears in various relations in thermodynamics, fluid mechanics, gasdynamics, heat transfer etc., should be suitably replaced by combinations of the three exponents. Related numerical examples, made in the case of real air, showed that the use ofk leads (in the temperature and pressure ranges examined) to a 5% error in the calculation of blowby rate in internal combustion enginers, high pressure compressors or steam turbines and to a 50% error in the calculation of the isentropic expansion or compression.Nomenclature A _ij,B _i,N _ij,O _ij,Q _ij Coefficients - c Velocity - c _p Specific heat under constant pressure - c _v Specific heat under constant volume - h Specific enthalpy - k Isentropic exponent,k=c _p/c _v - k _pT Real gas isentropic exponent corresponding to the pair of variablesp,T - k _pv Real gas isentropic exponent corresponding to the pair of variablesp, v - k _Tv Real gas isentropic exponent corresponding to the pair of variablesT,v - M Mach number,M=c/ - p Pressure - p _c Pressure at the critical point - R Constant of the air,R=287.22 J/kg K - s Specific entropy - T Temperature - T _c Temperature at the critical point - v Specific volume - v _c Specific volume at the critical point - z Compressibility factor - Sound velocity - T Temperature increment With 14 Figures     

Ideal gas relations for the description of the real gas isentropic changes

Using the best available relations describing the thermal and caloric behaviour of the media H₂O, air, NH₃ and of the refrigerants R12 and R22, numerous isentropic expansions starting at different initial points, have been computed. The results obtained were approximated by explicit relations having mathematical forms similar to those of the ideal gas but with different constants and exponents. The obtained accuracy is remarkable, being for the most cases better than 0.5% and in any case better than 3%. In this way the isentropic change, of the above mentioned media, can be computed by simple explicit relations having as independent variable the Mach number. Considering all the above media, the following general rules can be traced. The specific volume, reduced by the corresponding value of the stagnation point, up to a Mach number of less than 0.7, follows a parabolic law common to all gases considered. The reduced pressure, in the transonic region 0.7≦M≦1.3, has a nearly linear decrease, having a slope, common to all media, and equal to about ?0.605. The reduced nozzle cross-sectional area, for M≦1,2 has a common form given by the relation F^*/F=?0.034+M(2.04?M). The values of the constants and exponents used in the relations cannot be derived from the k _id =C_p/C_v values since they are all the three different isentropic exponents k_p,v, k_T,v and k_p,T involved and further since the true sound velocity α is given by the relation α=(zk_p,v RT)^1/2 and is not approximated by the ideal gas sound velocityα _id=(k _id RT)^1/2.     

Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G ^∗(iν). The experimental data are available in the frequency window ν∈[ν_min,ν_max] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor h( n) = \fracG"( n)G￠(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G ^∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G _k ,τ _k ,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).     

The use of theT *-integral to simulate subcritical crack growth taking into account the evolution of pores in the material

The formulation of the T^*-integral is proposed wherein this parameter (T _s ^* ) controls unambiguously the stress-strain state at the tip of both stationary and moving cracks in a medium with pores. It has been shown that under conditions of subcritical crack growth which is accompanied by processes of loosening of the material, the condition T _s ^* (ΔL)=const=J _1c ^v is met. Translated from Problemy Prochnosti, No. 3, pp. 5–18, May–June, 1997.     

The dispersion of3He quasiparticles in He II from neutron scattering

In an inelastic neutron scattering (INS) experiment on³He-⁴He mixtures one observes, besides the photon-roton mode which is barely modified by the admixture of³He, an additional excitation at lower energies which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data ofx ₃=1% and 4.5% mixtures at various pressures to extract the mean energy of the fermions. In the momentum range 9<q<17 nm^–1 (above 2k _F ) follows very closely the relation =A ₂ q ²+A ₄ q ⁴ at all concentrations, pressures and temperatures observed. In a 4.5% mixture (T _F 0.3 K), measurements were performed for temperatures in the range 0.07<T<0.9 K. We find bothA ₂ andA ₄ to be strongly temperature dependent. For the interpretation of thermodynamical properties, the single particle energy _k is parametrized as _k =_o+1/(2ms*) ·k ₂ · (1+k ²). Neglecting interactions between fermions, we calculate from the free-particle _k the scattering functionS(q, ) and the mean value of the fermion peak energy _q = S ₃(q, )d/S ₃(q, )d. We find that follows closely _q , deviating at most by 10%. A comparison to the measuredA ₂ andA ₄ directly yieldsms* (x ₃,p, T) and (x ₃,p, T). In the limitx ₃=0,p=0 andT=0, the density and concentration dependence of the inertial mass is in excellent agreement with values found by Sherlock and Edwards. The temperature dependence of the specific heat data from Greywall and Owers-Bradleyet al. are well represented by our model atT<0,5 K.     

Optical and structural properties of flash evaporated HgTe thin films

Thin films of HgTe were thermally flash evaporated onto glass and quartz substrates at room temperature. The structural investigations showed that stoichiometric and amorphous films were produced. The transmittance, T, and reflectance, R, of thin films of HgTe have been measured over the wavelength ranges 300–2500 nm. From analysis of the transmittance and reflectance results, the refractive index, n, and the extinction coefficient, k, has been studied. Analysis of the refractive index yields a high frequency dielectric constant, ɛ_∞, and the energy of the effective oscillator, E_o, the dispersion energy, E_d, the covalent value β and the M₋₁ and M₋₃ moments of the imaginary dielectric function of optical spectrum. Also, the dependence of the real part dielectric constant ɛ₁(hν) on its imaginary part ɛ₂(hν) of HgTe films can be used to determine the molecular relaxation time τ, the distribution parameter α^\ and the macroscopic (electronic) relaxation time τ_o. The graphical representations of surface and volume energy loss functions, dielectric constant, the optical conductivity as well as the relaxation time as a function of photon energy revealed three transitions at 0.63, 2.21 and 2.76 eV.     

A modular integration and multiresolution framework for image interpretation

In this paper, we give a generalized formulation for a vision problem in the framework of modular integration and multiresolution. The developed framework is used to solve the high-level vision problem of scene interpretation. The formulation essentially involves the concept of reductionism and multiresolution, where the given vision taskν is broken down into simpler subtasksν ₁,ν ₂, …,ν _m. Moreover, instead of solving the vision taskν ^Ω =ν at the finest resolution Θ, we solve the synergetically coupled vision subtasks at coarser resolutions (Ω −N) for Θ ≥N>0 and use the results obtained at resolution (Θ −N) to solveν ^{Ω −N+1}, the vision task at resolution (Θ −N+1). Image interpretation is a two-phased analysis problem where some salient features or objects in an image are identified by segmenting the image and the objects in the segmented image are interpreted based on their spatial relationships. We present a solution to the joint segmentation and interpretation problem in the proposed generalized framework. For the interpretation part we exploit the Markov Random Field (MRF) based image interpretation scheme developed by Modestino and Zhang. Experimental results on both indoor and outdoor images are presented to validate the proposed framework.     

Observation of Multiple Gap Structures Using NdFeAsO<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>F<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>–GaAs Tunneling Junction

We have carried out point contact tunneling measurements by contacting degenerated GaAs semiconductor to polycrystalline samples of NdFeAsO_1−x F _x with T _c=44−51±1.2. The obtained conductance curves have plural structures included in energy region of the superconducting gap. These structures are seen at almost the same bias positions on every measurement. And as temperature increases, the structures are smeared out. Thus, the structures are attributed to multiple gap structures. The gap values are Δ _S=6.3±0.3 meV, Δ _L=12.5±0.5 meV and 2Δ _S/k _B T _c=3.1±0.3, 2Δ _L/k _B T _c=6.2±0.7. Separately from these multiple gap structures, some fine structures are seen in outer energy region of the gap structures. We have calculated d² I/dV ² and T _c from using conventional s-wave Eliashberg equations by appropriately assuming α ² F(ω). The phonon positions of the calculated d² I/dV ² curve are in quite good agreement with that of experimental result. Moreover, the calculated T _c reproduces the experimental one.     

Electrical properties of (K0.5Na0.5)1? x Ag x NbO3 lead-free piezoelectric ceramics

(K_0.5Na_0.5)_1−x Ag _x NbO₃ lead-free piezoelectric ceramics have been fabricated by an ordinary ceramic technique. The results of XRD reveal that Ag⁺ diffuses into the K_0.5Na_0.5NbO₃ lattices to form a new solid solution with an orthorhombic perovskite structure and the solubility of Ag⁺ into A-sites of K_0.5Na_0.5NbO₃ is about 0.20. The ceramics can be well-sintered at 1,100–1,110 °C. The partial substitution of Ag⁺ for A-site ion (K_0.5Na_0.5)⁺ decreases slightly both paraelectric cubic-ferroelectric tetragonal (T _C) and ferroelectric tetragonal-ferroelectric orthorhombic phase transition temperatures (T _O−T). The ferroelectricity of the ceramics becomes weak at high Ag⁺ concentration. The ceramic with x = 0.10 possesses optimum electrical properties: d ₃₃ = 135 pC/N, k _P = 0.43, k _t = 0.46, ε _r = 470, tanδ = 3.39%, and T _C = 394 °C.     

An assessment of expressions for the apparent thermal conductivity of cellular materials

Diverse expressions for the thermal conductivity of cellular materials are reviewed. Most expressions address only the conductive contribution to heat transfer; some expressions also consider the radiative contribution. Convection is considered to be negligible for cell diameters less than 4 mm. The predicted results are compared with measured conductivities for materials ranging from fine-pore foams to coarse packaging materials. The dependencies of the predicted conductivities on the material parameters which are most open to intervention are presented graphically for the various models.Nomenclature a Absorption coefficient - C _itv(J mol^–1 K^–1) Specinc heat - E Emissivity - E _L Emissivity of hypothetical thin parallel layer - E _o Boundary surfaces emissivity - f Fraction of solid normal to heat flow - f _s Fraction of total solid in struts of cell - K(m^–1) Mean extinction coefficient - k(Wm^–1 K^–1) Effective thermal conductivity of foam - k _cd(Wm^–1 K^–1) Conductive contribution - k _cr(Wm^–1 K^–1) Convertive contribution - k _g(Wm^–1K^–1) Thermal conductivity of cell gas - k _r(Wm^–1 K^–1) Radiative contribution - k _s(Wm^–1 K^–1) Thermal conductivity of solid - L(m) Thickness of sample - L _g(m) Diameter of cell - L _s(m) Cell-wall thickness - n Number of cell layers - r Reflection coefficient - t Transmission coefficient - T(K) Absolute temperature - T _m(K) Mean temperature - T _N Fraction of energy passing through cell wall - T ₁(K) Temperature of hot plate - T ₂(K) Temperature of cold plate - V _g Volume fraction of gas - V _w Volume fraction of total solid in the windows - w Refractive index - (m) Effective molecular diameter - (Pa s) Gas viscosity - Structural angle with respect to rise direction - (Wm^–2 K^–4) Stefan constant     

Preliminary selection of instruments for automatic control and checking

Summary Having plotted for various instruments the curves of k_i=f₁() and k_r=f₂() for several values of (from the data of industrial or laboratory tests), it is possible to find k_i and k_r for any other values of. Similarly for pneumatic instruments we have k_i=f₁(P_s) and k_r=f₂(P_s). This facilitates the preliminary choice of instruments without the necessity of taking many response curves. The ratio _i/T_i can also be used for a mathematical analysis of the behavior of automatic control systems [13].     

Van der Waals chain-molecule fluid in self-consistent field approximation: Some thermal properties

The van der Waals equation for a monomer is used to derive the equation of state for a fluid consisting of chain molecules of equal length. The evolution of a part of the diagram of state pertaining to liquid-vapor equilibrium is treated for the case of an increase in the number of links in a molecule. The dependences on the number of links n are found for the following properties of polymer fluid: the critical temperatureT _c , the critical pressurep _c , the critical density p_c, the critical compressibilityz _c , the temperature of normal boiling, the Riedel parameter of similarity a, the acentric factor Ω, and the enthalpy of vapor formation δH_V, A comparison with the experimental data forn-alkanes and 1-alkanols reveals that the obtained dependences reflect qualitatively correctly the variation of the above-identified properties with an increase of the number of links in a molecule. For long chains(n ≪ 1), the scaling dependences are determined for the properties of a chain-molecule fluid:T _c ∽n ^−1/2,p _c ∽n ^−3/2ρ_c∽n ^−1/2,z _c∽n ⁻¹,α∽n, ω∽n ^2/3,ΔH _ν∽n.     

Non fermi liquid ground states in strongly correlated f-electron materials

Experimental efforts to characterize and develop an understanding of non Fermi liquid (NFL) behavior at low temperature in f-electron materials are reviewed for three f-electron systems: M_1–xU_xPd₃ (M = Sc, Y), U_1–xTh_xPd₂Al₃, and UCu_5–xPd_x. The emerging systematics of NFL behavior in f-electron systems, based on the present sample of nearly ten f-electron systems, is updated. Many of the f-electron systems exhibit the following temperature dependences of the electrical resistivity p, specific heat C, and magnetic susceptibility for T T₀, where T_o is a characteristic temperature: P(T) 1 –aT/T ₀, where a < 0 or > 0, C(T)/T (-1/T _o) In (T/bT ₀), and (T) 1 –c(T/T_o)^1/2. In several of the f-electron systems, the characteristic temperature T_o can be identified with the Kondo temperature T_k.     

Fluctuation-Induced Conductivity of Cu0.5Tl0.5Ba2Ca2Cu2M1O10−δ (M = Si, Sn, Ge) Superconductors

Fluctuation-induced conductivity of Cu_0.5Tl_0.5Ba₂Ca₂Cu₂M₁O_10−δ (M = Si, Sn, Ge) superconductors has been studied from the resistivity vs. temperature data. The logarithmic plots of excess conductivity (Δσ) vs. reduced temperatures [ε=(T−T _c ^mf )/T _c ^mf ] show two crossover temperatures with three exponents. A distinct crossover from two-dimensional to three-dimensional conductivity in accordance with the 2D, 3D Aslamazov–Larkin equations has been observed in all the samples. Another crossover from 2D to 0D fluctuations has also been witnessed. FIC data analysis has been found to be quite useful in explaining the superconducting properties of the samples. Si and Sn doped samples have shown almost similar characteristics, while in Ge doped sample diverse behavior is observed.     

Sound Velocity Measurements in the Low and the High Field Phases of the Nuclear-Ordered bcc Solid 3He in Magnetic Fields

We have measured the temperature and magnetic-field dependences of the sound velocity for one longitudinal and two transverse waves in the low field phase (LFP) and the high field phase (HFP) of nuclear spin ordered bcc solid ³He crystals with a single magnetic domain along the melting curve. From sound velocity measurements for various crystal orientations as a function of the sound propagation direction, we determined the elastic stiffness constants, c _ij (T,B). In the LFP with tetragonal symmetry for the nuclear spin structure, we extracted six nuclear spin elastic stiffness constants Δc _ij ^ℓ (T,0.06 T) from the temperature dependence of the sound velocity at 0.06 T and Δc _ij ^ℓ (0.5 mK,B) from the magnetic-field dependence of sound velocity at 0.5 mK. In the HFP with cubic symmetry for the nuclear spin structure, we extracted three Δc _ij ^h (T,0.50 T) at 0.50 T and Δc _ij ^h (0.5 mK,B) at 0.5 mK. At the first-order magnetic phase transition from the LFP to the HFP at the lower critical field B _c1, large jumps in sound velocities were observed for various crystal directions and we extracted three . Using the thermodynamic relation between Δc _ij and the change in the internal energy for the exchange interaction in this system, ΔU _ex(T,B), Δc _ij are related to the generalized second-order Grüneisen constants Γ _ij ^X ≡∂ ²ln X/∂ ε _i ∂ ε _j as Δc _ij (T,B)=Γ _ij ^X ΔU _ex(T,B), where X represents some physical quantity which depends on the molar volume and ε _j is the j-th component of a strain tensor. In the LFP, the Δc _ij ^ℓ (T,0.06 T) were proportional to T ⁴, and Δc _ij ^ℓ (0.5 mK,B) were proportional to B ². We extracted for the spin wave velocity in the LFP, s ^ℓ , from Δc _ij ^ℓ (T,0.06 T) and for the inverse susceptibility, 1/χ ^ℓ from Δc _ij ^ℓ (0.5 mK,B). In the HFP, Δc _ij ^h (T,0.50 T) were proportional to T ⁴ and Δc _ij ^h (0.5 mK,ΔB) were proportional to ΔB(≡B−B _c1). We obtained for the spin wave velocity in the HFP, s ^h , from Δc _ij ^h (T,0.50 T) and for B _c1 from Δc _ij ^h (0.5 mK,ΔB). The values obtained for and were compared with the Multiple Spin Exchange model (MSE) with three parameters by using analytic expressions for s ^ℓ and χ ^ℓ . The three-parameter MSE does not agree with the observed Δc _ij in the LFP.      

Tantalum influence on electrical properties of lead-free (K0.4425Na0.52Li0.0375)(Nb0.93?xTaxSb0.07) O3 piezoelectric ceramics

Lead-free (K_0.4425Na_0.52Li_0.0375)(Nb_0.93−x Sb_0.07Ta _x )O₃ (abbreviated as KNLNST _x ) piezoelectric ceramics with x = 0.045–0.075 have been prepared by an ordinary sintering technique with sintering temperature at 1,120 °C. The results of X-ray diffraction reveal that Ta⁵⁺ has diffused into the perovskite lattice to form a solid solution. The grain growth of the ceramics was inhibited by substituting Ta⁵⁺ for Nb⁵⁺. It has been shown that the substitution of Ta decreases Curie temperature T _C and orthorhombic-tetragonal phase transition temperature T _O-T. Besides, the dependence of the ceramics with different Ta content on the dielectric, piezoelectric and ferroelectric properties has been investigated. The results indicate that Ta substitution provides “soft” piezoelectric characteristics, owing to improvements in d ₃₃, k _p and ε _r and a decease in Q _m. For the ceramics with x = 0.06, the piezoelectric coefficient d ₃₃ becomes maximum at a value of 270 pC/N, while the other electrical properties remain reasonably high: dielectric constant ε _r = 1,577, planar mode electromechanical coupling factors k _p = 0.4, Curie temperature T _C = 252 °C and the remanent polarization P _r = 16.03 μC/cm². These results show that (K, Na, Li) (Nb, Sb)O₃ ceramics with small amount of Ta (x <8 mol%) are good lead-free piezoelectric ceramic.     

Density and deposition rates of amorphous CVD-Si3N4 including carbon

Amorphous Si₃N₄ containing uniformly distributed carbon was prepared by chemical vapour deposition [Am. CVD-(Si₃N₄-C)] using SiCl₄ vapour and NH₃, H₂ and C₃ H₈ gases at deposition temperatures (T _dep) of 1100 to 1300° C and at total gas pressures (P _tot) of 30 to 70 torr. The density of Am.CVD-(Si₃N₄-C) is between 2.80 and 3.00 g cm⁻³, depending upon the deposition conditions. Rate of growth in thickness increases with increasingT _dep andP _tot, and has the largest value of 0.6 mm h⁻¹ atT _dep=1300° C,P _tot=70 torr and propane gas flow rates [FR(C₃H₈)] of 0 to 20 cm³ min⁻. The activation energy of the formation decreases from 38 to 20 kcal mol⁻¹ with increasingP _tot andFR(C₃H₈).     

Low temperature synthesis and characterisation of lecontite, (NH4)Na(SO4)·2H20

Lecontite, (NH₄)Na(SO₄).2H₂O, was synthesised at room temperature in high purity compared to earlier work with a minor impurity of mascagnite, (NH₄)₂SO₄. Rietveld refinement of the XRD results confirmed the crystal structure and unit cell dimensions as published earlier. Raman and Infrared spectroscopy, in conjunction with factor group analysis, resulted in a complex pattern of overlapping sulphate, NH and OH modes. The NH modes υ₁ was observed around 2880 cm⁻¹, υ₂ around 1700 cm⁻¹ overlapping with water OH-bending modes, υ₃ around 3300 cm⁻¹ overlapping with water OH-stretching modes around 3023, 3185 and 3422 cm⁻¹, and υ₄ around 1432, 1447 and 1462 cm⁻¹. The sulphate group in the crystal structure displays a decrease in symmetry from T_d as evidenced by the activation of the ν₁ mode at 982 cm⁻¹ and the ν₂ mode around 452 cm⁻¹ in the Infrared spectrum. The υ₃ mode shows clear splitting in the infrared spectra with a strong band at 1064 cm⁻¹ accompanied by two shoulders at 1107 and 1139 cm⁻¹. The Raman spectra show three weak bands at 1068, 1109 and 1135 cm⁻¹ with a shoulder at 1155 cm⁻¹. Similar splitting was observed for the υ₄ mode around 611 and 632 cm⁻¹ in the Infrared and Raman spectra, respectively.