Heat capacity of helium

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). 

Figure 5.13 The Heat Capacity of Helium Near the Lambda Transition. The heat capacity appears to become infinite, as in a first-order phase transition, but it rises smoothiy instead of showing a spike at one point as does a first-order phase transition.

Homogeneous Liquids. The physical properties important in determining the suitability of a liquid for propellant application are the freezing point, vapor pressure, density, and viscosity. To a lesser extent, other physical properties are important such as the critical temperature and pressure, thermal conductivity, ability to dissolve nitrogen or helium (since gas pressurization is frequently used to expel propellants) and electrical conductivity. Also required are certain thermodynamic properties such as the heat of formation and the heat capacity of the material. The heat of formation is required for performing theoretical calculations on the candidate, and the heat capacity is desired for calculations related to regenerative cooling needs. 

We have directly measured the heat capacity of formaldehyde at temperatures close to that of liquid helium (about 2 10 3 cal g 1 grad-1 at 6 to 7°K) and we can say that the average heating of our sample by radiation itself (at the dose rate of about 50 rad sec-1) could not exceed 0.1°K, whereas the average increase of temperature caused by the heat of polymerization (Q 0.4eV, length of polymerization chain v 103) was not larger than about 0.5°K. 

Effect of Addition of Inert Diluents. The addition of inert gases to an explosive mixture will have two major effects. It will increase the heat capacity of the mixture, and depending upon the nature of the added gas, it will change the mixture thermal conductivity. Equation 26 shows that an increase in the heat capacity of the mixture will tend to increase the induction period. The addition of a high thermal conductivity gas such as helium will increase the limiting pressure. Rearranging Equation 18 shows that for a given vessel diameter, reactant concentration, and furnace temperature, the ratio... 

There have been other reports of heat capacity measurements of helium on carbon nanotubes [57-59]. Some of these resulted firom studies in which the main aim was to investigate the heat capacity of the carbon nanotubes themselves (helium was used as the exchange gas to help cool down the carbon nanotubes) [57, 59]. 

The heat capacities of films for two different coverages were determined for each one of the two substrates used [58]. In the highest coverages studied it was estimated that helium corresponded to 3 at. % (laser ablation sample) and 1.5 at. %... 

In this analysis the transition is defined as a step change in the heat capacity of the sample as a function of temperature. By far the most important transition that is generally considered to be second order is the glass transition, Tg. However, for completeness, other examples of second-order transitions include Curie point transitions where a ferromagnetic material becomes paramagnetic, the transition from an electrical superconductor to a normal conductor, and the transition in helium from being a normal liquid to being a superfluid at 2.2 K. 

The results listed in Table 6.1 were disappointing. It was clear that the heating capacity of the helium sample purge via the MS heated transfer line proved insufficient to compensate for the heat losses in the non-heated end-part of the MS capillary. 

In this study, the heat capacities of Ti, Zr, and Hf were measured using a vacuum calorimeter. The zirconium sample was placed in a copper capsule that was fitted with an external heater winding and a re-entrant thermometer as well as a small amount of helium gas to ensure heat transfer. The temperature was measured with a calibrated platinum resistance thermometer and measurements were taken from 20 to 200 K. The purity of the Zr was 99.5%, the major impurity being Na. 

The heat capaeity of zirconium was measured from 1.2 to 4.5 K. To samples thermally isolated from a helium bath, a known electrical energy input was applied and the temperature rise of the sample was measured. The heat rise in the experiment was corrected for the heat capacity of the measuring device. Typically, the correction for the measuring device was about 5% of the heat capacity of a 1 mole metal specimen. Four separate samples of zirconium were studied, of which two were studied in duplicate. Approximately 35 measurements were recorded for each of the six samples. The data were fitted to the function... 

The detection of molecules in a molecular beam by a bolometer is based on the bolometer s response to the total beam energy, including the center of mass translational energy (Zen, 1988). The bolometer consists of a liquid-helium-cooled thermocouple whose electrical response varies rapidly with the energy of the bolometer. The low temperature is necessary in order to reduce the heat capacity of the thermocouple, thereby increasing its sensitivity, as well as to minimize the thermal detector noise. 

The heat capacity of the samples was involved in the analysis of the results because the experiment was dynamic. This was eliminated by repeating each experiment with a heat sink of different thermal capacity. Thermal resistance was eliminated by making measurements in a helium atmosphere and then in a nitrogen atmosphere. Thus, to obtain conductivity values for one material four separate measurements were required. Apparatus of this type has also been used by Ott (26]. 

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