Helium heat capacity

We have seen in previous sections that the two-dimensional Ising model yields a syimnetrical heat capacity curve tliat is divergent, but with no discontinuity, and that the experimental heat capacity at the k-transition of helium is finite without a discontinuity. Thus, according to the Elirenfest-Pippard criterion these transitions might be called third-order. 

Lipa J A, Swanson D R, Nissen J A, Chui TCP and Israelsson U E 1996 Heat capacity and thermal relaxation of bulk helium very near the lambda point Phys. Rev. Lett. 76 944-7... 

Gaseous helium is commonly used as the working fluid ia closed-cycle cryogenic refrigerators because of chemical iaertness, nearly ideal behavior at all but the lowest temperatures, high heat capacity per unit mass, low viscosity, and high thermal conductivity. 

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 first heat capacity measurements were performed by Sorai and Seki on [Fe(phen)2(NCX)2] with X=S, Se [45,46]. A few other SCO compounds of Fe(II) [47], Fe(III) [48] and Mn(III) [49] have been studied quantitatively down to very low (liquid helium) temperatures. For a relatively quick but less precise estimate of AH, AS, the transition temperature and the occurrence of hysteresis, DSC measurements, although mostly accessible only down to liquid nitrogen temperatures, are useful and easy to perform [50]. 

Recently, the gas types nitrogen, carbon dioxide and helium were shown to have no influence on the reaction rate at 226 °C over 6h [32], Similarly, no difference between nitrogen and carbon dioxide at 210 °C over 24 h was observed [41], An early study [31] did show that the gas type influenced the reaction rate, but it has since been suggested that the different heat capacities and thermal conductivities of the gases affected the experimental temperatures [32],... 

The X transition in liquid helium shown in Figures 11.5 and 11.6 is a second-order transition. Most phase transitions that follow the Clapeyron equation exhibit a nonzero value of A5m and AYmi that is, they show a discontinuity in 5 and Fm. the first derivatives of the Gibbs free energy Gm- Thus, they are caHA A first-order transitions. In contrast, the X transition shows a zero value of A5m and AVm and exhibits discontinuities in the second derivatives of Gm, such as the heat capacity Cpm-... 

Heat capacity change, 269 Height equivalent to a theoretical plate. 8 Helium sparge, 188 Hemodialysis, 283 Heptane, 72,76. 173 Heptanoic acid, 260 1-Heptanol, 182, 183 Herbicides, analysis by RPC, 292 Herbicides, chromatography on polar sorbents, 103 Hesperidin, 293... 

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. 

Tip assemblies used for work at helium temperatures may be modified as shown in Fig. 12. The inclusion of the nichrome sections is necessary if temperature control is desired. Since both the heat capacity and the electrical resistivity of tungsten at helium temperatures are extremely low and its heat conductivity is very high, a rise in temperature from I K to about 1000°K corresponds to changes of a few milliamperes in the heating current if all-tungsten assemblies are used. The nichrome sections act as thermal barriers, since alloys do not lose their high-temperature thermal properties at 4°K, and permit fine control of temperature. For... 

The only coolant that car be used in such systems is liquid helium, which is expensive to produce and has a low heat capacity. 

The mysteries of the helium phase diagram further deepen at the strange A-line that divides the two liquid phases. In certain respects, this coexistence curve (dashed line) exhibits characteristics of a line of critical points, with divergences of heat capacity and other properties that are normally associated with critical-point limits (so-called second-order transitions, in Ehrenfest s classification). Sidebar 7.5 explains some aspects of the Ehrenfest classification of phase transitions and the distinctive features of A-transitions (such as the characteristic lambda-shaped heat-capacity curve that gives the transition its name) that defy classification as either first-order or second-order. Such anomalies suggest that microscopic understanding of phase behavior remains woefully incomplete, even for the simplest imaginable atomic components. 

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... 

Using this instrument in Figure 6.5, Handa (1986b) measured the heat input to a hydrate sample in the sample container S, relative to helium at ambient temperature and 5 kPa in reference cell R. The hydrate was externally prepared from ice in a rolling-rod mill, before a 4 g sample was loaded into the calorimeter at liquid nitrogen temperatures. For heat capacity measurements, a pressure greater than the hydrate dissociation pressure was maintained in the sample cell. By cycling... 

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

In cryogenic detectors, a simultaneous measurement of both ionization and thermal energy allows the discrimination of nuclear recoils from electrons produced in radioactive decays or otherwise. This discrimination, however, cannot tell if the nuclear recoil was caused by a WIMP or an ambient neutron. The detector, most often a germanium or silicon crystal, needs to be cooled at liquid helium temperature so that its low heat capacity converts a small deposited energy into a large temperature increase. Only relatively small crystals can be currently used in these cryogenic detectors, with relatively low detection rates. 

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