Second thermal conductivity virial coefficient

On the contrary, the second thermal conductivity virial coefficient originally derived for monatomic gases (5j "°") represents solely the contribution related to translational degrees of freedom for polyatomic gases (57 = A.,tr)- In order to describe the total initial density contribution to thermal conductivity, therefore, a term related to internal modes of motion has to be included. This can be conveniently done by applying the two-flux approach based on a suggestion of Eucken (Hanley et al. 1972 Maitland et al. 1987), whereby... 

For application to real gases, this theory has been modified (Enskog 1922 Hanley et al. 1972 Hanley Cohen 1976 Vogel etal. 1986 Ross etal. 1986). Although this has no rigorous theoretical basis, it does provide an alternative rqiresentation of the second viscosity virial coefficient and the translational part of the second thermal conductivity virial coefficient, which is particularly useful at reduced temperatures below T = 0.5, the lower limit of the coefficients in Table 5.1. On the basis that a real fluid differs from a hard sphere fluid mainly in the temperature dependence of the collision frequency, the pressure P of the hard-sphere fluid is replaced by the thermal pressure T(dP/dT)p of... 

Fig. 5.4. The reduced second thermal conductivity virial coefficient as a function of reduced temperature. Curves 1 - Rainwater-Friend theory (S = 1.04 and 6 = 1.25) 2 - Rainwater-Friend theory (3 = 1.02 and 0 = 1.15) 3 - MET-I (without 4 - MET-I (including...

Fig. 14.23. Second thermal conductivity virial coefficient for water vapor as a function of temperature.

Rainwater, J.C. Friend, D.G. (1987). Second viscosity and thermal-conductivity virial coefficients of gases Extension to low reduced temperatures. Phys. Rev., A 36, 4062-4066. 

Extensive tables and equations are given in ref. 1 for viscosity, surface tension, thermal conductivity, molar density, vapor pressure, and second virial coefficient as functions of temperature. 

It seems to me that we can scarcely progress in our understanding of the structural and kinetic effects of the H-bond without knowing the AG and AH terms involved, so I intend to discuss some methods of determining them. The references will provide simple examples of the methods mentioned. The most significant AG and AH values are those evaluated from equilibrium measurements in the gas phase—either by classical vapour density measurements, the second virial coefficient [1], or from, spectroscopic, specific heat or thermal conductance [2], or ultrasonic absorptions [3]. All these methods essentially measure departures from the ideal gas laws. The second virial coefficient provides a measure of the equilibrium constant for the formation of collision dimers in the vapour as was emphasized by Dr. Rowlinson in the discussion, this factor is particularly significant as only the monomer-dimer interaction contributes to it. 

How efficient is the described representation of the ArCC>2 potential To answer this question the above PES along with a few empirical potentials have been used to derive a number of properties, such as the ground vibrational state and dissociation energy of the complex, ground state rotational constants, the mean square torque, the interaction second virial coefficients, diffusion coefficients, mixture viscosities, thermal conductivities, the NMR relaxation cross sections, and many others [47]. Overall, the ab initio surface provided very good simulations of the empirical estimates of all studied properties. The only parameters that were not accurately reproduced were the interaction second virial coefficients. It is important that its performance proved comparable to the best empirical surface 3A of Bohac, Marshall and Miller [48], This fact must be greeted with satisfaction since no empirical adjustments were performed for the ab initio surface. 

The viscosity, thermal conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in terms of collision integrals defined [111] by... 

It is more usual with closed-shell atoms to consider potential models such as the exchange-Coulomb and Hartree-Fock dispersion potentials and to determine the parameters from dilute gas properties such as the second virial coefficient and the transport properties, viscosity and thermal conductivity, together with... 

Hellmann et al. [23, 177,178] have proposed ab initio force fields for several small molecules, such as helium, neon, or methane, based on the Tang and Toennies potential (9) and coulombic terms (14). With these force fields, gas phase properties like second virial coefficient, shear viscosity, thermal conductivity, or self-diffusion coefficient can be predicted extremely accurately. Typically, the generated data are within the experimental uncertainty. 

Comprisons between theory and experiment for the viscosity, thermal conductivity, equilibrium second virial coefficient, and the dielectric second virial coefficient are shown in Figures 3-6. One observes that a wide range of independent thermophysical properties have been fitted quite well. 

This theory covers the complete density range from dilute gas to solidification. However, the hard sphere model is inappropriate for a real gas at low and intermediate densities where specific effects of intermolecular forces are significant. It is therefore necessary to modify the theory this has been done in different ways. In Section 5.2, a method is described for determination of the second viscosity virial coefficient and the translational part of the thermal conductivity coefficient. Although this approach is not rigorous, it does provide a useful estimate for these coefficients - especially for low reduced temperatures. 

The first density correction for viscosity and for the translational part of the thermal conductivity is best predicted by the Rainwater-Friend model, for which values for the reduced second transport virial coefficients are given in Table 5.1. For computer codes the tabulated values can be approximated using the correlation... 

Theoretical expressions for the reduced viscosity and thermal conductivity second virial coefficients are presented in Section 5.3. An important contribution arises from the effect of the formation of dimers, even though the concentration of dimers is still small. For the evaluation of these transport property virial coefficients it was assumed that both the interaction potential between two monomers and between a monomer and a dimer is of the Lennard-Jones (12-6) form but with different potential parameters. The ratios of these parameters, which are characterized by the constants 8 and 6 defined in Section 5.3, are determined from a large selection of experimental data. According to Stogryn Hirschfelder (1959), the mole fraction of dimers in argon is 0.2% at 0.1 MPa and 200 K, while this fraction reduces to 0.04% when the temperature rises to 600 K. 

Values for the second virial coefficient of thermal conductivity, have been derived from experimental thermal conductivity data for steam. The temperature dependence is shown in Figure 14.23. It should be noted that the values below 100°C are less reliable because there are insufficient experimental data at these temperatures to determine the values of Bx with confidence. 

Chung-Lee-Starling expression for thermal conductivity of low pressure gases. The molar density, pj, can be calculated using and equation of state model (for example, the Peng-Robinson-Wong-Sandler equation of state) where the mixing rule for b is obtained as follows. The second virial coefficient must depend quadratically on the mole fraction ... 

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