Thermal conductivity of a gas

Figure 24 The thermal conductivity of a gas as a function of pressure. (Data from Ref. 9.)...

What physical properties of gas molecules influence their ability to conduct heat A quantitative dependence of the thermal conductivity of a gas can be expressed in terms of the gas molecules specific heat, mass, and cross-sectional area. Specif-... 

Any gas may be used as the carrier as long as it does not react with the sample and/or stationary phase. However, other properties must be considered depending upon the type detector employed. With a thermal conductivity detector one uses a gas with high heat conductivity because thermal conductivity of a gas is inversely proportional to the square root of the molecular weight Thus, very low molecular weight gases are optimum. Helium is... 

These measure the change in thermal conductivity of a gas due to variations in pressure—usually in the range 0.75 torr (100 N/m2) to 7.5 x 10"4 torr (0.1 N/m2). At low pressures the relation between pressure and thermal conductivity of a gas is linear and can be predicted from the kinetic theory of gases. A coiled wire filament is heated by a current and forms one arm of a Wheatstone bridge network (Fig. 6.21). Any increase in vacuum will reduce the conduction of heat away from the filament and thus the temperature of the filament will rise so altering its electrical resistance. Temperature variations in the filament are monitored by means of a thermocouple placed at the centre of the coil. A similar filament which is maintained at standard conditions is inserted in another arm of the bridge as a reference. This type of sensor is often termed a Pirani gauge. 

The coefficients of transport properties considered here include the viscosity, diffusivity, and thermal conductivity of a gas. The transport coefficients vary with gas properties if the flow is laminar. When the flow is turbulent, the transport coefficients become strongly dependent on the turbulence structure. Here we only deal with the laminar transport coefficients the discussion of the turbulent transport coefficients is given in 5.2.4. 

Ke Apparent thermal conductivity of a gas-solid suspension flowing through an empty bed... 

The kinetic theory of gase.s predicts and the experiments confirm that the thermal conductivity of gases is proportional to the square root of the thermodynamic temperature T, and inversely proportional to the square root of the molar mass M. Therefore, the thermal conductivity of a gas increases with increasing temperature and decreasing molar mass. So it is not surprising that the iheniial conductivity of helium (Af 4) is much higher than those of air (M = 29) and argon M = 40). 

The thermal conductivity of a gas is the quantity which is measured in the Pirani gauge (page 125) and in the detector of a gas-phase chromatography column (page 171). The thermal conductivity is related to the heat capacity of the gas, which measures the amount of energy that can be absorbed per molecule to the velocity of the molecules, which is a measure of the number of collisions with the heated surface per unit time and pressure and to the pressure of the gas. 

For gas molecules, the heat capacity is a constant equal to C = (n/2)pkB where n is the number of degrees of freedom for molecule motion, p is the number density, and kB is the Boltzmann constant. The rms speed of molecules is given as v = V3kBTlm, whereas the mean free path depends on collision cross section and number density as = (pa)-1. When they are put together, one finds that the thermal conductivity of a gas is independent of p and therefore independent of the gas pressure. This is a classic result of kinetic theory. Note that this is valid only under the assumption that the mean free path is limited by inter-molecular collision. 

A simple and obvious modification of the above argument yields an expression for the thermal conductivity of a gas... 

This reflects the fact that the thermal conductivity of a gas obeying simple kinetic theory is independent of the pressure. The transition in thermal conductivity between asymptotes usually occurs between 0.1 and 100 mmHg, which includes the pressures characteristic of freeze drying processes. The pressure range over which the transition in thermal conductivity between asymptotes occurs is characteristic of the pore size distribution of the void spaces within the freeze-dried material [50]. A smaller pore dimension means that the gas must achieve a higher pressure in order for the mean free path of the gas to become comparable to the pore spacing and, hence, means that the transition between asymptotes will occur at higher pressures. 

In a stationary gas, all heat transfer is conductive. An example of this is the boundary layer immediately adjacent to a wall surface, such as a heat exchanger surface. The thermal conductivity of a gas is, in principle, independent of pressure but increases with rising tem-... 

Each of these thermal conductions mechanism is shown in Figure 13-3. Here, the thermal conduction through the air can be regarded as a transport phenomenon with kinetic energy driven by the collision of gas molecules in the air imder a temperature gradient. Therefore, the thermal conductivity of a gas depends on the mean free path of the gas, and the mean free path of a gas (If) enclosed in a narrow space can be given by equation (13-2), from the mean pore size (I,) and the mean free path of the gas in free space (Lg), and this can be transformed as in equation (13-3) (Takahama, 1995 Takita,... 

As for the pure gas case, the transport coefficients are related to individual expansion coefficients of the polynomial series. Thus, for the partial thermal conductivity of a gas mixture, one has... 

The thermal conductivity of a gas mixture which is measured directly is not the quantity X introduced in equation (4.79), because measurements are always performed in the absence of a net diffusive flux. In order to evaluate the measured thermal conductivity in the zero-density limit X, the multicomponent diffusion coefficients are employed (Ross et al. 1992) and then one obtains, in a consistent first-order approximation. 

The evaluation of the thermal conductivity of a gas mixture is rather more complicated and difficult than for the other two properties. The difficulty stems from equations (4.92)-(4.102), which make it clear that, in general, many more cross sections are involved for each binary interaction than for the viscosity or diffusion coefficient. This is a result of the presence of internal energy and its relaxation. Of course, if these cross sections could be evaluated from a pair potential, the additional difficulty would be rather minor, since the calculation of extra cross sections is a relatively small additional burden compared with the treatment of the collision dynamics. However, as has been pointed out before, the evaluation of the collision dynamics prevents such calculations from being performed routinely. As a result, the cross sections that enter the expressions for the thermal conductivity must be evaluated by other means for some of them this is extremely difficult, since there is little guidance from experiment or model calculations. 

Equations (4.92) to (4.102), which express the thermal conductivity of a gas mixture in terms of the cross sections of the Wang Chang-Uhlenbeck theory have been rewritten by Monchick et al. (1965) in an approximate form, in which so-called complex collisions have been neglected, as... 

Transport properties such as viscosity and thermal conductivity of a gas mixture are estimated based on the mixture rules. A simplified mixfure model developed based on fhe kinefic theory model is widely used (Bird et. al., 1960 Mills, 2001 Wilke, 1950). These formulae are given as follows ... 

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