Helium, specific heat

The coolant for the HTGR is helium. The helium is not corrosive has good heat properties, having a specific heat that is much greater than that of CO2 does not condense and can operate at any temperature has a negligible neutron absorption cross section and can be used in a direct cycle, driving a gas turbine with high efficiency. 

Figure 2.7 shows the specific heat of He and Cu for T< 1K. Down to 0.1K, the specific heat of both isotopes is larger than that of Cu. For example at 1.5 K (Tables 2.3 and 2.4), the specific heat of both isotopes is about 1.5 J/gK, whereas that of Cu is about 10 5 J/gK. This observation is very important in practical cryogenics for example, it means that the thermal time constant of an apparatus depends on the quantity of helium contained in it. 

The properties of the two helium isotopes in the liquid state are strongly influenced by quantum effects. In Fig. 2.8, the specific heat of 3He, calculated from the ideal gas Fermi model (Tp = 4.9 K) with the liquid 3He density, is compared with the experimental data. The inadequacy of this model is evident. A better fit, especially at the lower temperatures, is obtained by the Landau theory [25]. 

As we said, the material of the regenerator of a PTR must have a high specific heat to provide a good heat storage. Unfortunately, below 20 K, the specific heat of most regenerators rapidly decreases, whereas the heat capacity of helium increases and has a maximum at 10K (see Fig. 5.20). 

The recuperated Brayton cycle approaches Carnot efficiency in the ideal limit. As compressor and turbine work are reduced, the average temperatures for heat addition and rejection approach the cycle limit temperature. The limit is reached as compressor and turbine work (and cycle pressure ratio) approach zero and fluid mass flow per unit power output approaches infinity. It can be expected from this that practical recuperated Brayton cycles would operate at relatively low pressure ratios, but be very sensitive to pressure drop. With tire assumption of constant gas specific heat over the cycle temperature range, a good assumption for helium, the cycle efficiency of a recuperated Brayton cycle may be expressed ... 

Other properties of helium-4 show similar surprises. At the X point, the specific heat of the liquid increases to a large value as the temperature is decreased through this point. Once below the X point, the specific heat of helium II rapidly decreases to zero. The thermal conductivity of helium I, on the other hand, decreases with decreasing temperature. However, once the transition to helium II has been made, the thermal conductivity of the liquid can increase in value by as much as 106 that of helium I. 

The following table shows how the specific heat at constant pressure of liquid helium changes with temperature. Note the sharp increase over this temperature range ... 

Values given for gases apply to such substances as air, nitrogen, carbon dioxide, light hydrocarbon mixtures (no condensation), etc. Because of the very high thermal conductivities and specific heats of hydrogen and helium, gas... 

Fig. 6.4. Specific heat C/RT of 3He and of two diluted solution of 3He in 4He at saturated vapour pressure [10,11]. C is the specific heat for the total number of helium moles.

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