Heat capacity liquid helium

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]. 

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-... 

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. 

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. 

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. 

Differential scanning calorimetery (DSC) was used to measure heat capacity as a function of temperature. The DSC used in this study was a Perkin-Elmer model DSC-2. Liquid nitrogen was used as a heat sink and helium was used as the purge gas. Samples were usually about 30 mg, and a heating rate of 20°C/min was used for measuring Tgs and Tms. 

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. 

For the 11 substances, ammonia, 1,2-butanediol, 1,3-butanediol, carbon monoxide, 1,1-difluoroethane, ethane, heptane, hydrogen, hydrogen sulfide, methane, and propane, the liquid heat capacity CpL is calculated with Eq. (2) below. For all other compounds, Eq. (1) is used. For benzene, fluorine, and helium, two sets of constants are given for Eq. (1) that cover different temperature ranges, as shown in the table. 

The glass liquid helium cold finger used to freeze out reaction products was about 2 inches in diameter and had a 1 liter capacity. To minimize heat leakage it was surrounded by a liquid nitrogen heat shield. All surfaces in the Dewar system were silvered. After an experiment the cryo-... 

The authors stated that the measured values of the heat capacity were accurate to within + 1% below 100 K while the higher temperature data were accurate to about + 5%. The smoothed data were then used to calculate corresponding values of Cv and the contribution of the lattice vibrational component to Cv by substracting from the former value the electronic contribution. The electronic contribution was determined on the basis of previous measurements from the same laboratory at liquid helium temperatures [52EST/FRI]. The heat capacity data are in good agreement with the data obtained by Todd [50TOD] on a less pure sample of the metal. 

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 experimental measurements include susceptibility, magnetic moment, heat capacity (both calorimetric and AC magnetic methods) of the undiluted compounds, together with optical absorption and EPR on diluted crystals. The R ions form a close-packed hexagonal structure, in chains with two nn along the c-axis at +c, and six nnn on adjacent chains. A detailed study of Gd(OH)3 was carried out by Skjeltorp et al. (1973). At liquid-helium temperatures the inverse of the susceptibility is represented by a series... 

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