Thermal conductivity of air in the range 312 to 373 K and 0.1 to 24 MPa

We have used the transient hot-wire technique to make absolute measurements of the thermal conductivity of dry, CO₂-free air in the temperature range from 312 to 373 K and at pressures of up to 24 MPa. The precision of the data is typically ±0.1%, and the overall absolute uncertainty is thought to be less than 0.5%. The data may be expressed, within their uncertainty, by polynomials of second degree in the density. The values at zero-density agree with other reported data to within their combined uncertainties. The excess thermal conductivity as a function of density is found to be independent of the temperature in the experimental range. The excess values at the higher densities are lower than those reported in earlier work.Nomenclature Thermal conductivity, mW · m^–1 · K^–1 - Density, kg · m^–3 - C _p Specific heat capacity at constant pressure, J · kg^–1 · K^–1 - T Absolute temperature, K - q Heat input per unit wire length, W · m^–1 - t Time, s - K(=/C _p) Thermal diffusivity, m² · s^–1 - a Wire radius, m - Euler's constant (=0.5772 ) - p _c Critical pressure, MPa - T _c Critical temperature, K - _c Critical density, kg · m^–3 - R Gas constant (=8.314 J · mol^–1 · K^–1) - V _c Critical volume, m³ · mol^–1 - Z _c(=p _c V _c/RT _c) Critical compressibility factor     

Isochoric specific heat of sulfur hexafluoride at the critical point: Laboratory results and outline of a spacelab experiment for the d1-mission in 1985

The specific heat at constant volume c_v shows a weak singularity at the critical point. Renormalization group techniques have been applied, predicting a universal critical behavior which has to be experimentally confirmed for different systems. In this paper an experiment is presented to measure the specific heat of SF₆ along the critical isochore (_c=0.737 g·cm^–3), applying a continuous heating method. The results cover a temperature span of –1.5×10^–2< <1.70×10^–2 [=(T–T _c)/T _c] and were strongly affected by gravity effects that emerge in the sample of 1-mm hydrostatic height near the critical point. Using regression analysis, data were fitted with functions of the form c _v/R=A × ¦¦^– + B for the one-phase state and c _v/R=A × ¦¦^– + B for the twophase state. Within their error bounds the critical values (==0.098, A/A=1.83) represent the measurements for the temperature span 3.5×10^{–5< ¦¦<2.0×10 –3}, in good agreement with theoretical predictions. In order to exclude density profiles in the specimen, which are unavoidable in terrestrial experiments due to the high compressibility of fluids at the critical point and the gravity force, a space-qualified scanning ratio calorimeter has been constructed, which will permit long-term c_v measurements under microgravity (-g) conditions. The experiment will be part of the German Spacelab mission in October 1985. The significant features of the apparatus are briefly sketched.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

New equations for enthalpy of vaporization from the triple point to the critical point

Two new equations are proposed for the enthalpy of vaporization from the triple point to the critical point. One of these equations containing four parameters is exceptionally good for fitting the data. The other equation containing three parameters is quite adequate for fitting the data but it is exceptionally suited for interpolation when the data do not cover the entire range. These equations have been tested using the enthalpy of vaporization of water from the triple point to the critical point and are compared with other equations.Nomenclature T _c Critical temperature, K - T _t Triple point, K - T _x Any particular temperature, K - T _r Reduced temperature - P _r Reduced pressure - R Gas constant - P Vapor pressure - X (T _c–T)/T _c - Y (T _c–T)/T - X _x (T _c–T)/(T _c–T _x) - X _t (T _c–T)/(T _c–T _t) - H _vt Enthalpy of vaporization at the triple point, kJ · mol^–1 - H _vx Enthalpy of vaporization at any temperature x, kJ · mol^–1 - Z _v Compressibilty factor of the saturated vapor - Z ₁ Compressibilty factor of the saturated liquid Relative deviation = 100[H_v(obs)–H_v(cal)]/H_v(obsd) Standard deviation = { [H _v(obs)–H _v(cal)]²/(No. points — No. parameters)}^0.5     

Gas absorptivity in a complete spectrum

Necessary conditions are established for the validity of the Hottel formulas for the absorptivity relative to black radiation. The formulas are used in describing the absorption of a badly mixed medium and for nonblack incident radiation.Notation x ray path in mat - p, P partial and total pressure - P_eff effective broadening pressure - T, T₀ gas and wall temperatures, °K - T_*, T_i selected temperature values - T_c weighted-mean temperature - a₀ absorptivity of the gas for black radiation - a same for a flux with nonblack spectrum - emissivity - m, u, n, , power exponents - i _0j Planck function for the center of the band, cm · W/m² · sr - I_j incident flux intensity at the center of the band j, cm · W/m² · sr - I integrated incident flux intensity, W/m² · sr - A_j integral absorption (equivalent width) of band f, cm^–1 - _j mean absorption in the band - wave number, cm_–1 - ₀ position of the band center - _j width parameter - _effj effective width - _j total width of the band j, cm^–1 - D_j mean transmissivity in the band j - S integrated line intensity, cm–1/mat - d, b spacing between lines and their half-width, cm–1 - S_j integrated intensity of the band j - L Landenburg and Reiche functions - spectral absorption coefficient, mat_–1 - (T) dimensionless function - c_i dimensionless number - R_*, R_c general notation for parameters averaged over the band and for T_c - E Elsasser function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 802–808, May, 1971.     

The thermal conductivity of propane

This paper presents thermal conductivity measurements of propane over the temperature range of 192–320 K, at pressures to 70 MPa, and densities to 15 mol · L^–1, using a transient line-source instrument. The precision and reproducibility of the instrument are within ±0.5%. The measurements are estimated to be accurate to ±1.5%. A correlation of the present data, together with other available data in the range 110–580 K up to 70 MPa, including the anomalous critical region, is presented. This correlation of the over 800 data points is estimated to be accurate within ±7.5%.Nomenclature a _n, b_ij, b_n, c_n Parameters of regression model - C Euler's constant (=1.781) - P Pressure, MPa (kPa) - P _cr Critical pressure, MPa - Q ₁ Heat flux per unit length, W · m^–1 - t time, s - T Temperature, K - T _cr Critical temperature, K - T ₀ Equilibrium temperature, K - T _re Reference temperature, K - T _r Reduced temperature = T/T _cr - T _TP Triple-point temperature, K Greek symbols Thermal diffusivity, m² · s^–1 - T _i Temperature corrections, K - T Temperature difference, K - T _w Temperature rise of wire between time t ₁ and time t ₂, K - T ^* Reduced temperature difference (T–T _cr)/T_cr - _corr Thermal conductivity value from correlation, W · m^–1 · K^–1 - _cr Thermal conductivity anomaly, W · m^–1 · K^–1 - _e Excess thermal conductivity, W · m^–1 · K^–1 - ^* Reduced density difference - Thermal conductivity, W^–1 · m^–1 · K^–1, mW · m^–1 · K^–1 - _bg Background thermal conductivity, W · m^–1 · K^–1 - ₀ Zero-density thermal conductivity, W · m^–1 · K^–1 - Density, mol · L^–1 - _cr Critical density, mol · L^–1 - _re Reference density, mol · L^–1 - _r Reduced density Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Determination of the specular reflection coefficient of conduction electrons in Zn whiskers atT=4.2°K

The influence was studied of the transverse dimensions of Zn single crystals in the form of whiskers and thin platelets on their specific resistance atT=4.2°K. The thickness of the specimens measured ranged from 10 µm to 0.2 µm. With a decreasing thickness of the specimens the specific resistance increased considerably. Under the assumption that for a pure diffuse reflection of electrons on the specimen boundary the product ( ·d ) in a bulk specimen is equal to 1.8×10^–11 cm² for a crystallographic orientation corresponding to whiskers, and 2.2×10^–11 cm² for a crystallographic orientation corresponding to platelets, a specular reflection coefficientp approximately equal top=0.6 was calculated for both whiskers and platelets.     

A generalized equation for surface tension from the triple point to the critical point

A three-parameter generalized equation is proposed for surface tension from the triple point to the critical point. This equation not only fits the data well but also is good for interpolation between the normal boiling point and the critical point. This equation is also good for extrapolation to the triple point. This equation has been tested using the surface tension of water from the triple point to the critical point. The constants of this equation obtained using orthobaric surface tensions are given for a number of compounds. The isobaric surface tensions determined at a pressure of 1 atm do not differ significantly from the orthobaric surface tensions. Such data also have been used in obtaining equations from the triple to the critical point.Nomenclature T _c Critical temperature, K - T _t Triple point, K - T _m Melting point, K - T _r Reduced temperature, K - X (T _c-T)/T _c - Surface tension, dyne · cm^–1;10^–3N · m^–1 - _m Surface tension at the melting point - _f Surface tension at T _r=0.9 - _t Surface tension at the triple point - Relative deviation 100[ _obsd– _calcd]/ _obsd - Standard deviation [( _obsd– _calcd)²/(No. points—No. parameters)]^0.5     

Thermal conductivity of ethane from 290 to 600 K at pressures up to 700 bar,including the critical region

The paper presents thermal conductivity measurements of ethane over the temperature range of 290–600 K at pressures to 700 bar including the critical region with maximum uncertainty of 0.7 to 3% obtained with a transient line source instrument. A correlation of the data is presented and used to prepare tables of recommended values that are accurate to within 2.5% in the experimental range except near saturation, and in the critical region, where the anomalous thermal conductivity values are predicted to within 5%.Nomenclature a _k , b _ij , b _k , c _i Parameters of the regression model, k=0 to n, i=0 to m, j=0 to n - P Pressure, (MPa or bar) - Q _l Heat flux per unit length (mW · m^–1) - t Time, s - T Temperature, K - T _cr Critical temperature, K - T _r Reduced temperature = T/T _cr - T _w Temperature rise of wire between times t ₁ and t ₂ K - T ^* Reduced temperature difference (T–T _cr)/T _cr - Thermal conductivity, mW · m^–1 · K^–1 - ₁ Thermal conductivity at 1 bar, mW · m^–1 · K^–1 - _bg Background thermal conductivity, mW · m^–1 · K^–1 - _cr Thermal conductivity anomaly, mW · m^–1 · K^–1 - _e Excess thermal conductivity, mW · m^–1 · K^–1 - Density, g · cm^–3 - _cr Critical density, g · cm^–3 - _r Reduced density, = / _cr - ^* Reduced density difference =(- _cr)/ _cr     

The melting points of ultralong paraffins and their homologues

Because of the recent availability of the melting points of several ultralong normal paraffins, the melting behavior of normal paraffins has been investigated. Taking the melting point of polyethylene to represent the melting point of an ultralong paraffin, a new function has been established to represent the melting points of alkanes from the carbon number 32 onwards. Adopting the same value for the limiting melting point of an ultralong paraffin, equations are derived for the melting points of several homologous series.Nomenclature a A constant to be determined - b A constant to be determined - m Number of methylene groups in the molecule - n Number of carbon atoms in the molecule - n ^* Number of carbon atom above which Eq. (6) is applicable - T ₀ Temperature constant, K - T _c Critical temperature, K - T _c Critical temperature of an ultralong normal paraffin, K - T _b Normal boiling point, K - T _b Normal boiling point of an ultralong normal paraffin, K - T _m Melting point, K - T _m Melting point of an ultralong paraffin, K - Standard deviation {[(T _m (obsd)–T _m (calc)]²/(No. points–No. parameters)}^0.5     

Excess thermodynamic properties of mixtures of alkyl benzoates withn-heptane

The paper reportsh ^E values at 298.15 K andv ^E and values at various temperatures for binary mixtures of propyl or butyl benzoate andn-heptane. The excess Gibbs energy of viscous flow,g ^*E, and the thermodynamic activation properties were calculated from these values. The results are compared with those for similar mixtures and interpreted on the basis of the characteristic dipole-dipole interactions of alkyl esters.Nomenclature A _i Parameters in Eq. (2) - dg ^*E Gibbs free energy of viscous flow (J · mol^–l) - dg Activation free energy (kJ · mol^–1) - K Parameter in Eq. (2) - h Planck constant - h ^E Excess enthalpy (J · mol^–1) - h Activation enthalpy (kJ · mol^–1) - N Avogadro number - R Universal gas constant (J · K^–1 · mol^–1) - s Standard deviation - s Activation entropy (J · K^–1 · mol^–1) - T Temperature (K) - v Molar volume of pure component (m³ · mol^–1) - v ^E Excess volume (m³ · mol^–1) - x _i Mole fraction of componenti Greek Letters Expansion coefficient (K^–1) - Density (kg · m^–1 ) - Viscosity (mPa · s ) - Apparent excess viscosity (mPa · s)     

Determination of the vapor-liquid coexistence curve and the critical parameters for refrigerant 502

The vapor-liquid coexistence curve for refrigerant 502 (R 502) near the critical point has been determined by visual observation of the disappearance of the meniscus. Twenty-six saturated densities between 262 and 899 kg· m^–3 have been obtained within an experimental error in temperature and density of ± 10 mK and ± 0.5%, respectively. Using these results along the vapor-liquid coexistence curve, the critical parameters, i.e., the critical temperature T _c =355.37 ±0.01 K and the critical density _c =555±3kg · m^–3, have been determined based on the disappearance of the meniscus level as well as on the intensity of the critical opalescence. A critical pressure P _c =4.070±0.002 MPa has been calculated from the existing vapor-pressure correlation using the present T _c value. In addition, the critical exponent along the coexistence curve and the law of rectilinear diameter near the critical point are discussed.Paper presented at the Japan-United States Joint Seminar on Thermophysical Properties, October 24–26, 1983, Tokyo, Japan.     

Thermal conductivity of methane

This paper reports thermal conductivity data for methane measured in the temperature range 120–400 K and pressure range 25–700 bar with a maximum uncertainty of ± 1%. A simple correlation of these data accurate to within about 3% is obtained and used to prepare a table of recommended values.Nomenclature a _k ,b _ij ,b _k Parameters of the regression model, k= 0 to n; i =0 to m; j =0 to n - P Pressure (MPa or bar) - Q _kl Heat flux per unit length (mW · m^–1) - t time (s) - T Temperature (K) - T _cr Critical temperature (K) - T _r reduced temperature (= T/T _cr) - T _w Temperature rise of wire between times t ₁ and t ₂ (deg K) - T ^* Reduced temperature difference (TT _cr)/T _cr - Thermal conductivity (mW · m^–1 · K^–1) - ₁ Thermal conductivity at 1 bar (mW · m^–1 · K^–1) - _bg Background thermal conductivity (mW · m^–1 · K^–1) - _cr Anomalous thermal conductivity (mW · m^–1 · K^–1) - _e Excess thermal conductivity (mW · m^–1 · K^–1) - Density (g · cm^–3) - _cr Critical density (g · cm^–3) - _r Reduced density (= / _cr) - ^* Reduced density difference (– _cr )/ _cr      

Mean polarizabilities and second optical and density virial coefficients of CH3OH and CCl2F2 between 300 and 355 K

Mean dipole polarizabilities ₀(, T) as well as second optical (or refractive index) virial coefficients b _R(, T) and second density virial coefficients B(T) of gaseous CH₃OH and CCl₂F₂ have been determined by precise measurements of the refractive index n(, T, p) [543 nm 633 nm, 300 K T 355 K, p<0.25 bar (CH₃OH) and p<3 bar (CCl₂F₂)]. ₀ critically compared with the few data in literature. The b _R of these gases was measured for the first time with the cyclic-expansion method. The values of ¦B¦ and b _R=3160(25) cm³ · mol^–1 measured for CH₃OH are considerably greater than the values calculated by Buckingham's statistical-mechanical expressions for a Stockmayer interaction potential. This difference is discussed by assuming dimerization via H bonds, with result H ₂ ⁰ –(28 ... 33) kJ · mol^–1 and S ₂ ⁰ –(116 133) J · mol^–1 · K^–1 for the dimerization enthalpy and entropy for standard conditions, respectively. On the other hand, Buckingham's formulae can be used with success to estimate b _R and B of CCl₂F₂.Dedicated to Prof. Dr. F. Kohler on the occasion of his 65th birthday     

The Viscosity Anomaly Near the Lower Critical Consolute Point

Shear viscosity measurements for a critical mixture of 3-methylpyridine + heavy water near a lower critical consolute point are reported. The background contribution was determined from viscosity measurements of mixture at a noncritical composition. In the entire investigated temperature range T _c – T 15.6 K, the viscosity of the critical mixture exceeds the background contribution, and the critical enhancement is important. The increase of the viscosity near critical is found in the temperature range T _c–T 1.82 K. The critical exponent y = 0.0415 ± 0.002 and the wave number Q = (0.40 ± 0.07) nm^–1 are determined.     

Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow

Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature cp Specific heat of fluid, J · kg^–1 · K^–1 - d Diameter of tube, m - f Fanning friction factor, _w/(V²/2) - h Convective heat-transfer coefficient, q _w(T _w{T _b), W · m^–2 · K^–1 - k Thermal conductivity of fluid, W · m^–1 · K^–1 - j _H Heat-transfer j-factor, StPr _a ^2/3 - L _e Entrance length, m - Nu Nusselt number, hd/k - Pr _a Prandtl number based on apparent viscosity at the wall, c _p/k - q _w Heat flux at the wall, W · m^–2 - Re _a Reynolds number based on apparent viscosity at the wall, Vd/ - St Stanton number, Nu/(Re _a Pr _a) - T Temperature, K - T _b Bulk temperature of fluid, K - T _w Inside-wall temperature, K - V Average velocity, m · s^–1 - Ws Weissenberg number, V/d - x Axial coordinate, m Greek symbols g Shear rate, s^–1 - Apparent viscosity evaluated at the wall, P⁵ - ₀ Zero shear-rate viscosity, P⁵ - Apparent viscosity at infinite shear rate, P⁵ - Characteristic time of fluid, s - Density of fluid, kg · m^–3 - _w Wall shear stress, N · m^–2 Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Influence of Charge Doping on Thermal Diffusivity of Double Perovskite Sr2FeMoO6 Studied by Mirage Effect

Effects of charge doping on thermal diffusivity have been investigated in double perovskite ferromagnetic Sr_2–x La _x FeMoO₆ (0 x 0.4) by means of the mirage effect at 300 K ( the critical temperature T _c 420 K). Substitution of the La³⁺ ions for the Sr²⁺ ions significantly increases the value of the thermal diffusivity from 0.39 cm² · s^–1 at x = 0 to 0.54 cm² · s^–1 at x = 0.4. The increased thermal diffusivity is ascribed to the extra itinerant electrons on the Mo4d band.     

Measuring Turbidity in a Near-Critical, Liquid–Liquid System: A Precise, Automated Experiment

A ground based (1g) experiment is in progress that measures the turbidity of the density-matched, binary fluid mixture methanol–cyclohexane extremely close to its liquid–liquid critical point. By covering the range of reduced temperatures t (T–T _c)/T _c from 10^–8 to 10^–2, the turbidity measurements should allow the Green–Fisher critical exponent to be determined. This paper reports measurements showing ±0.1 % precision of the transmitted and reference intensities, and ±4K temperature control near the critical temperature of 320 K. Preliminary turbidity data show a nonzero consistent with theoretical predictions. No experiment has precisely determined a value of the critical exponent , yet its value is significant to theorists in critical phenomena. Relatively simple critical phenomena, as in the liquid–liquid system studied here, serve as model systems for more complex behavior near a critical point.     

Analysis of the supersonic flow of a viscous heat-conducting gas in the neighborhood of a backward step

Results are presented of numerical modelling of the supersonic flow of a viscous heat conducting gas in the neighborhood of a backward step for the Mach number M = 2.9 and the Reynolds number Re =9.5·10³–3.2·10⁴. Kinetically consistent difference schemes are used to perform the computations. The results obtained are compared with the data of full-scale experiments.Translated from Inzhenreno-Fizicheskii Zhurnal, Vol. 58, No. 4, pp. 675–681, April, 1990.     

Josephson Plasma in Various High-T c Cuprates

Josephson plasma in various high-T _c cuprates with and without magnetic field is studied by using the sphere resonance method. For Bi ₂ Sr ₂ CaCu ₂ O ₈₊, the plasma in a zero magnetic field exists at 5 cm ^–1 for a slightly overdoped sample (T _c = 85 K) and shifts to 11 cm ^–1 as the doping increases (T _c = 71 K). For SmLa _1–x Sr _x CuO _3.95 (T* phase), two peaks appear at 11 and 30 cm ^–1 in a zero magnetic field, and both peaks shift to lower frequencies as the magnetic field increases. These peaks are identified as the Josephson plasma of the intrinsic Josephson junction at the fluorite-type Sm ₂ O ₂ block layer and the rocksalt-type (La,Sr) ₂ O _2– block layer, respectively. This indicates that the T* phase can be regarded as the ···S/I/S/I/S/I/S/I/S··· (···superconductor/insulator1/superconductor/insulator2/superconductor···) -type Josephson junction array.