Alloys heat capacity

The tables in this section contain values of the enthalpy and Gibbs energy of formation, entropy, and heat capacity at 298.15 K (25°C). No values are given in these tables for metal alloys or other solid solutions, for fused salts, or for substances of undefined chemical composition. 

Specific Heats of Solid Mixtures.—The specific heat of a homogeneous solid mixture of solid components is not usually additively composed of the specific heats of the latter. W. Spring (1886) found that the total heat capacity of alloys of lead and tin was always greater than the sum of those of the components, but above the melting-point the two were equal. A. Bogojawlensky and N. Winogradoff (1908) find, however, that the heat capacities of the isomorphous mixtures ... 

Figure 8.22 Variation of the electronic heat capacity coefficient with composition for the alloys Rh-Pdand Pd-Ag [17]. Solid and dotted lines represent the electronic DoS for the 5s and 4d bands, respectively.

Constant conduction heat pipes, 13 227 Constant failure rate, 13 167 Constant-field scaling, of FETs, 22 253, 254 Constant-modulus alloys, 17 101 Constant of proportionality, 14 237 Constant pressure heat capacity, 24 656 Constant rate drying, 9 103-105 Constant rate period, 9 97 23 66-67 Constant retard ratio (CRR) mode, 24 103 Constant slope condition, 24 136-137 Constant stress test, 13 472 19 583 Constant-voltage scaling, of FETs, 22 253 Constant volume heat capacity, 24 656 Constant volume sampling system (CVS), 10 33... 

This competition between electrons and the heat carriers in the lattice (phonons) is the key factor in determining not only whether a material is a good heat conductor or not, but also the temperature dependence of thermal conductivity. In fact, Eq. (4.40) can be written for either thermal conduction via electrons, k, or thermal conduction via phonons, kp, where the mean free path corresponds to either electrons or phonons, respectively. For pure metals, kg/kp 30, so that electronic conduction dominates. This is because the mean free path for electrons is 10 to 100 times higher than that of phonons, which more than compensates for the fact that C <, is only 10% of the total heat capacity at normal temperatures. In disordered metallic mixtures, such as alloys, the disorder limits the mean free path of both the electrons and the phonons, such that the two modes of thermal conductivity are more similar, and kg/kp 3. Similarly, in semiconductors, the density of free electrons is so low that heat transport by phonon conduction dominates. 

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... 

Self-Test 6.7B An alloy of mass 25.0 g was heated to 88.6°C and then placed in a calorimeter that contained 61.2 g of water at 19.6°C. The temperature of the water rose to 21.3°C. What is the specific heat capacity of the alloy ... 

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. 

A substance, metallic in nature, is to be identified, and heat capacity is one of the clues to its identity. A block of the metal weighing 150g required 38.5 cal to raise its temperature from 22.8°C to 26.4°C. Calculate the specific heat capacity of the metal and determine if it is the correct alloy, which has a specific heat capacity of 0.0713 cal/g K. 

Fig. 10. Electronic contribution to the heat capacity divided by temperature vs. log Q T for a series of La doped alloys of CeR Sb]. The data has been corrected for a phonon contribution, using heat capacity data from LaRr Sb] and a nuclear quadrupo-lar contribution from 121 Sb and 123 Sb (Takeda and Ishikawa, 2001).

Clearly one obtains the best performance for a given time constant with a detector that has the lowest possible heat capacity. The heat capacity of a crystal varies like C oc (T/0 )3, where On is the Debye temperature. Diamond has the highest Debye temperature of any crystal, so FIRAS used an 8 mm diameter, 25 fim thick disk of diamond as a bolometer (Mather et al., 1993). Diamond is transparent, so a very thin layer of gold was applied to give a surface resistance close to the 377 ohms/square impedance of free space. On the back side of the diamond layer an impedance of 267 ohms/square gives a broadband absorbtion. Chromium was alloyed with the gold to stabilize the layer. The temperature of the bolometer was measured with a small silicon resistance thermometer. Running at T = 1.6 K, the FIRAS bolometers achieved an optical NEP of about 10 14 W/y/IIz. 

COMMENTS CONCERNING PARAMETERS OF THE SHORT-RANGE ORDER EVOLUTION DETERMINED FROM THE DATA ON KINETICS OF A HEAT-CAPACITY RELAXATION FOR Lu-H ALLOY... 

In heat installations with use of hydrides efficiency of their operation (efficiency, quantity of heat (or colds) and heat capacity) depends on amount of the hydrogen participating in reaction. The amount reserved an alloy of hydrogen is characterized by equilibrium R-S-Tdependence which today define empirically. Let s open the specified directions in more details. 

Figure 2, A, represents the experimental heat capacity data in the temperature range between 20° and 360° K. for H2 in Pd4H2—i.e., Pd4H2 minus the heat capacity of the palladium atoms in palladium black (7) and block palladium (5). In Figure 2, B, C, and D represent the similarly calculated experimental contributions for H2 in the other samples studied which had H/Pd ratios of 0.75, 0.25, and 0.125. Above 120° K. the results for palladium black are noticeably different from all of the others. This is apparently due to the fact that in palladium black, owing to the smallness of the particles, the lattice is somewhat more mobile. In Figure 3 all the experimental contributions of two hydrogen atoms to the heat capacity for alloys of compositions H/Pd = 0.75, 0.50, 0.25, and 0.125 are plotted between 35° and 85° K. (5). All the points lie on a single curve, within experimental error. Such a situation is difficult to conceive unless the hydrogens are similarly located with respect to each other in all samples.

The low temperature heat capacity is often used for the study of the band structure of metals and alloys since it yields direct information about the density of states. Neglecting magnetic contributions at low temperatures, the heat capacity of a solid consists of contributions owing to the lattice and, for metals, to the free electrons. For metals, the lattice contribution is masked by the electronic contribution, but the two can be separated. Derive the expression for the total heat capacity given the information in the preceding paragraph. 

The important characteristic for HHM efficiency is the alloy output, i.e. the heat capacity related to weight of hydride alloy. The value achieved for today on the average for a cycle makes 40-100 W/kg. At shortening of a cycle this value grows, but up to achievement of competitive (in comparison with other heat machines of similar type) value in 1000 W/kg [8] are necessary for increasing cardinally amount of active hydrogen, to increase effective heat conductivity of a hydride bed and to optimize operation of system a sorber-heat exchanger. Thus duration of a hill cycle is estimated 2-4 minutes. 

The above classification should not be taken too literally. For example, it is well known that new synthesis processes could also mean new alloys as mechanical alloying showed us. In the same way, tank design will need a better evaluation of the critical parameters such as heat capacities and heat conductivity of nanostructured metal hydrides. 

With the exception of liquid alloys and fused isomorphous mixtures the heat capacity of a mixture of liquids is usually larger than the sum of those of the components, e.g. with mixtures of alcohol with water, chloroform, carbon disulphide, and benzene. The 20 per cent solution of alcohol in water has a specific heat (1 046) greater than that of any other liquid below 100°.8 The heat capacities of mixtures of benzene and chloroform are the sum of those of the components. ... 

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