Silver heat capacity

P10.9 We have seen that the heat capacity of silver at low temperatures can be represented by the expression... 

The heat capacity of silver was taken from C. Kittel. Solid State Physics, Wiley, New York, 1956. The heat capacities of diamond were taken from J. E. Desnoyers. and J. A. Morrison. The Heat Capacity of Diamond between 12.8 and 222 °K . Phil. Mag.. 3, 42-48 (1958) and A. C. Victor, Heat Capacity of Diamond at High Temperatures . J. Chem. Phvs.. 36. 1903-1911(1962). 

Systems may be in chemical or mechanical equilibrium, and they may also exhibit thermal equilibrium. If a hot object is placed in contact with a colder mass of the same material inside an insulated container, heat flows from the hot object into the colder object until the temperatures of the two are equal. Heat lost by the warm object is equal to the amount gained by the cold object. The amount of heat needed to raise the temperature of an object a certain amount is equal to the amount which that object would lose in cooling by the same amount. The amount of heat needed to warm or the amount lost when cooling equals the product of the specific heat (or heat capacity) of the substance, the mass, and the change in temperature. For example, if a 50-gram (1.8-ounce) piece of silver at 70°C (158°F) is placed in 50 grams (1.8 ounces) of water at 15°C (59°F), the principle of thermal equilibrium can be used to calculate the final temperature of the water and silver ... 

One of the remarkable features of the FFB is its very high heat transfer rate. Because of extensive solids mixing in the FFB, the heat transfer rate between particles is several orders of magnitude higher than that of silver by conductive heat transfer. The high heat capacity and thermal conductivity... 

Essentially the characteristic temperature is a measure of the temperature at which the atomic heat capacity is changing from zero to 6 cal deg for silver (0 = 215 K) this occurs around 100 K, but for diamond (0 = 1860 K) with a much more rigid structure, the atomic heat capacity does not reach 5 cal deg i until 900 K. Those elements that resist compression and that have high melting points have high characteristic temperatures. Equations have been derived relating y/ u ) to the characteristic temperature 0. At room temperature diamond, with a characteristic temperature of 1860 K, has a root-mean-square amplitude of vibration, / u ) of 0.02 A, while copper and lead, with characteristic temperatures of 320 and 88 K, respectively, have values of 0.14 and 0.28 A for (u ). - Similar types of values are obtained for crystals with mixed atom (or ion) types. For example, average values of / u ) for Na+ and Cl in sodium chloride (0 = 281 K) are 0.14 A at 86 K and 0.23 A at 290 K. ° ... 

Use the empirical rule of Dulong and Petit stated in Problem 7 to estimate the specific heat capacities of vanadium, gallium, and silver. 

I7e. Heat Capacities at High Temperatures.—Although the theoretical treatment of heat capacities requires the limiting high temperature value to be 3/2, i.e., 5.96 cal. deg. g. atom , experimental determinations have shown that with increasing temperature Cv increases still further. The increase is, however, gradual for example, tfie heat capacity of silver is 5.85 cal. deg. g. atom at 300° K and about 6.5 cal. deg. g. atom at 1300° K. This increase is attributed mainly to the relatively free electrons of the metal behaving as an electron gas. By the use of the special form of quantum statistics, viz., Fermi-Dirac statistics, applicable to electrons, the relationship... 

The Debye characteristic temperature of silver is 212. Calculate the atomic heat capacity Cv of this metal at 20.0° K and 300° K. 

The heat capacity (C ) and heat conductivity (A) of crystals depend respectively on the vibrational density of states weighted by a Boltzmann s distribution factor and the anharmonic terms in the vibrational potential energy. C has been found to be in the range 0.100 to 0,117 cal./g./°C between 100—250 °C for crystals as widely varying in lattice geometry as mercuric fulminate, silver azide and lead azide 62). This is... 

Q.9.10 After reaching 327.5°C, a large section of the metal chunk melts, demonstrating tliat the metal chunk is a mixture of at least two different metals. A 0.8 kg dull silver chunk has a specific heat capacity of 0.13 kJ/kg-K. Can the specific heat capacity of the remaining chunk be determined without directly measuring it If yes, calculate it. 

Example 1-1 Ethylene oxide is produced by direct oxidation with air using a bed of catalyst particles (silver on a suitable carrier). Suppose that the stream enters the flow reactor at 200°C and contains 5 mole % ethylene and 95% air. If the exit temperature does not exceed 260°C, it is possible to convert 50% of the ethylene to the oxide, although 40% is also completely burned to carbon dioxide. How much heat must be removed from the reaction, per mole of ethylene fed, in order not to exceed the limiting temperature The average molal heat capacity of. ethylene may be taken as 18 Btu/(lb mole) (°R) between 25 and 200°C and as 19 Btu/(lb mole)(°R) between 25 and 260°C. Similar values for ethylene oxide are 20 and 21 Btu/(lb mole)(°R). The pressure is essentially atmospheric. 

The enthalpy of formation has been determined from vapour pressure and galvanic cell measurements. Each determination has been re-evaluated as discussed in Appendix A using the second and third laws, the selected heat capacity, the entropy of Ag2Se(cr), the selected properties of selenium, and the CODATA [89COX/WAG] values of silver. The results are summarised in Table V-62. 

Gronvold, F., Stolen, S., Semenov, Y., Heat capacity and thermodynamic properties of silver(I) selenide, oP-Ag2Se from 300 to 406 K and cl-Ag2Se from 406 to 900 K transitional behavior and formation properties, Thermochim. Acta, 399, (2003), 213-224. Cited on pages 298, 299. 

For crystals the lower limit of the integral is zero from the considerations just outlined. Equation (57) may be integrated if a relation between Cp and T is known. The available analytical relations are. however, complicated and of limited validity. Fortunately values of S may be obtained from measurements of heat capacity at different temperatures by graphical methods, A convenient method is one proposed by Lewis and Gibson17 which consists in plotting values of Cp/T against T and determining the area of the enclosed plot. Such a plot is shown in Fig. 7 for tine estimation of the entropy of metallic silver, from the work of Eucken, Clusius and Woitinek.18 Below the lowest... 

The third form (Fig. 7) differs only in detail from the second it was preferred for the experiments with liquid hydrogen, because it could be made of much smaller dimensions. The platinum wire was wound on the outside of the cylindrical silver vessel and covered, to avoid thermal losses, with silver foil which was soldered at the edges to give a better thermal contact this form has the advantage that the platinum wire docs not have to be introduced vacuum-tight into the inside of the silver vessel. In a small size and at low temperatures this form of calorimeter proved to be excellent. The heat capacity of the silver vessel could be calculated with good accuracy, but it was also directly determined by a series of... 

Grayish metal possesses a greenish-blue reflection tin- or silver-like when molten has a crystalline orthorhombic texture. mp 29.78. bp approx 2400 Cochran, Foster, J. Electrochem. Soc. 109, 144 (1962). Shows a tendency to remain in supercooled state. Contracts on melting (solid) 5.9037 d - 0iq) 6.0947 Richards, Boyer, J. Am. Chem. Soc. 43, 274 (1921). Heat capacity 0.09 cal/g/ C (0-24. solid). Latent heat of fusion 19.16 cal/g. Stable in dry air tarnishes in moist air or oxygen. Reacts with alkalies with evolution of hydrogen attacked by cold coned hydrochloric acid rendered passive by hot nitric acid readi -ly attacked by halogens. 

Silver-white, heavy, mobile, liquid metal slightly volatile at ordinary temp solid mercury is a tin-white, ductile, malleable mass which may be cut with a knife, mp —38.87" bp 356.72° dB 13.534, Heat capacity at constant pressure (25 ) 6.687 cal/moie deg. Vapor pressure (25°) 2 X ]0-3 mm heat of vaporization (25 ) 14.652 kcal/mole Busey,... 

Table 10.1 shows that silver has a specific heat capacity of 0.24 J/g °C. The metal is silver. 

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