Thermal Conductivity of Gas Mixture

Example 2.9 Estimation of thermal conductivity of gas mixtures at low density Estimate the thermal conductivity of the following gas mixture at 293 K and 1 atm using the data given in the following table ... 

The thermal conductivities of gas mixtures of ammonia with argon, neon, hydrogen, and methane are reported in [80] and [85]-[87]. 

The exact form of the expressions for the diffusional fluxes jj depends on the degree of sophistication used in representing the transport phenomena. A precise approach, including also the calculation of the thermal conductivity of gas mixtures, and based on the Chapman-Enskog kinetic theory, has been described by Dixon-Lewis [122]. However, simpler approaches involving the form j = —pDiAwijAy may also give satisfactory representation in many cases [119—121,123]. 

Example 2.7 Estimation of thermal conductivity of gas mixtures at low density... 

Intermolecular potential is directly related to the interaction of molecules of different gases, which affects the thermal conductivity of a given gas mixture. Caution should be observed when calculating the thermal conductivity of gas mixtures because a simple proportioning ( weighting ) of the components thermal conductivities can lead to considerable error if those conductivities are substantially different. 

For the thermal conductivities of gas mixtures at low pressure, two empirical methods and one corresponding-states scheme are presented by Reid er a/. (1987). Both empirical methods employ the Wassiljewa equation (Wassiljewa 1904)... 

Mason, E. A. Saxena, S. C. (1958). Approximate formula for the thermal conductivity of gas mixtures. Phys. Fluids, 1, 361-369. 

Fig. 4.3 Experimental setups for temperature-programmed desorption, reduction and oxidation, (a) The reactor is placed inside the furnace which is connected with temperature programmer. Detection of evolved gas(es) is performed by monitoring the variations in thermal conductivity of gas mixture, (b) The TPD apparatus equipped with mass spectrometer as a detector [5]...

Hirschfelder, J. O, Curtiss, C. F., and Bird, R. B., Molecular Theory of Gases and Liquids, John Wiley Sons, New York, 1954. Kestin, J., Knierim, K., Mason, E. A., Najafi, B., Ro, S. T., and Waldman, M., Equilibrium and Transport Properties of the Noble Gases and Their Mixtures at Low Density, Journal of Physical and Chemical Reference Data, Vol. 13, No. 1, 1984. Singh, K., Dham, A. K., and Gupta, S. C., Empirical Relationship for Higher Order Contributions to Thermal Conductivity of Gas Mixtures, Journal of Physics B, Atomic, Molecular, and Optical Physics 25,679-685,1992. 

The thermal conductivity of gas-phase deuterium is about 0.73 times that of gas-phase hydrogen. This thermal conductivity difference offers a convenient method for analysis of H2—D2 mixtures. Other physical properties of D2, T2, HD, DT, and HT are Hsted in the Hterature (60). 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

In general, the thermal conductivities of liquid mixtures, and gas mixtures, are not simple functions of composition and the thermal conductivity of the components. Bretsznajder (1971) discusses the methods that are available for estimating the thermal conductivities of mixtures from a knowledge of the thermal conductivity of the components. 

Figure 15.6 is a plot of the thermal conductivity of mixtures of helium and nitrogen obtained on an apparatus similar to that described in the next section. Characteristically, the thermal conductivity of most mixtures does not vary linearly with concentration. The slope of the curve at any point determines the value of A/c and, therefore, the detector response. Figure 15.6 also illustrates that the greater the difference between thermal conductivities of the adsorbate and carrier gas, the higher will be the slope and therefore the detector response. 

Gas thermal conductivity sensors are used to detect variations in the composition of mixtures of gases by monitoring changes in the thermal conductivity of the mixture. Such instruments are used (a) as detectors for gas chromatographs (Section... 

Consider one particular gas composition, e.g. 50 mole per cent H2. This is equivalent to (100/(100 + 800)) x 100 = 11.1 mass per cent H2. From Volume 6, Section 8.8.4, the thermal conductivity of the mixture kmjx can be considered as a simple weighted average, i.e ... 

Detectors vary in their response to the compounds being sensed, with respect both to the amount and to the class of compound. Since the thermal conductivity of a mixture of two gases (the carrier gas and the sample) is not necessarily a linear function of composition, absolute quantitative measurements with thermal-conductivity detectors can only be obtained after calibration with standard compounds. However, response to structurally similar compounds is quite uniform, and reliable, relative, quantitative data can be obtained with this detector. Ionization detectors give a signal that is related directly to the mass or the concentration of the components, and the response is uniform over a broad range of operating conditions these detectors are, therefore, ideally suited for quantitative work. 

Comparison of thermal conductivities of gas stream is done with gas mixture of known strength. It may show erroneous results due to the breakdown of suction blower, choking of sampling probe or conditioner, leaking connecting tube, and fault with electronic circuit of indicator and recorder or exhausting of the chemical standard solutions used for titration. 

One type of sample that cannot be analyzed with a TCD and helium carrier gas is hydrogen in a gas mixture. Hydrogen s thermal conductivity is so close to helium s that the peak shapes are often irregular—usually with a W-shape—and thus quantitative results are not possible [5]. The thermal conductivity of binary mixtures of helium and hydrogen is not a simple linear function. More discussion and some possible solutions to this problem can be found in Thompson s monograph [6]. 

It works by comparison of thermal conductivities of gas stream with gas mixture of known strength or by chemical titration with standard solutions. Concentrations of SO2, HCl, etc. can be seen on the digital indicator. 

The first term of equation (4.127) is an approximation to the translational contribution to the thermal conductivity of the mixture. It is obtained by making use of equations (4.122)-(4.125) for the thermal conductivity of a monatomic gas mixture. For this purpose approximate translational contributions to the thermal conductivity of each pure component X, tr and an interaction thermal conductivity for each unlike interaction Xqq are evaluated by the heuristic application of equation (4.125) for monatomic species to polyatomic gases. Thus, the technique requires the availability of experimental viscosity data for pure gases and the interaction viscosity for each binary system or estimates of them. As the discussion of Section 4.2 makes clear, the use of... 

The second term of equation (4.127) represents an approximation to the contribution of internal energy transport to the thermal conductivity of the mixture. The numerator of each term in the summation contains the difference between the total thermal conductivity of a pure gas and its translational part, estimated as discussed above. Thus, inasmuch as the latter quantity is approximate, the internal contribution to the thermal conductivity is merely an estimate. However, the combination of the first and second terms of equation (4.127), in the limit of any one mole fraction approaching unity, ensures that the total thermal conductivity of each pure component is reproduced. 

Thermal-Conductivity Analyzer. The thermal-conductivity analy2er operates on the principle that the loss of heat from a hot wire by gaseous conduction to a surface at a lower temperature varies with the thermal conductivity of the gas, and is virtually independent of pressure between 1.3 kPa (10 mm Hg) and 101 kPa (1 atm). This technique is frequently used in continuous monitors for tritium in binary gas mixtures for immediate detection of process change. 

The thermal conductivity of low pressure (1 atm or less) gas mixtures can be determined from the relation of Wassiljewa " " ... 

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