Atomic heat capacity

ATOMIC HEAT. The product of the gram-atomic weight of an element and its specific heat The result is the atomic heat capacity per gram-atom. For many solid elements, the atomic heal capacity is very nearly the same, especially at higher temperatures and is approximately equal to 3R, where R is the gas constant (Law of Dulong and Petit). 

Some general rules exist, such as that the molal heat capacity (at constant pressure) of any monatomic gas is approximately 5 cal/deg mole, except at very low temperatures. The most useful rule (Kopp s rule) is that the. molal heat capacity of a solid substance is the sum of " its atomic heat capacities ivith the value about 6.2 for all atoms except the light ones, for which values used are... 

When the experimental or measured value of Cp for a particular liquid is not available, a fair approximation for Cp near room temperature can be obtained by Kopp s Rule, which states that the heat capacity of a liquid is approximately equal to the sum of the atomic heat capacities of its individual atoms. For the purpose of Kopp s Rule, these individual atomic heat capacities (molar basis) are given in Table 8.5. 

Table B.IO Atomic Heat Capacities for Kopp s Rule"...

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. ° ... 

TABLE 4.2 Values for Modified Kopp s Rule Atomic Heat Capacity at 20 C [cal/(g atom)(°C)]... 

In spite of the apparent agreement between the experimental data and the theoretical prediction based on the equipartition principle, there are nevertheless significant discrepancies. In the first place, the heat capacity of carbon, e.g., diamond, is only 1.45 cal. deg. g. atom at 293 K, and it increases with increasing temperature, attaining a value of 6.14 cal. deg. g. atom at 1080° K. Somewhat similar results have been obtained with boron, beryllium and silicon. Further, although the atomic heat capacities of most solid elements are about 6 caJ. deg. " g. atom at ordinary temperatures, and do not increase markedly as the temperature is raised, a striking decrease is always observed at sufficiently low temperatures. In fact, it appears that the heat capacities of all solids approach zero at 0° K. Such a variation of the heat capacity of a solid with temperature is not compatible with the simple equipartition principle, and so other interpretations have been proposed. ... 

The important conclusions, therefore, to be drawn from the Debye theory are that at low temperatures the atomic heat capacity of an element should be proportional to T, and that it should become zero at the absolute zero of temperature. In order for equation (17.4) to hold, it is necessary that the temperature should be less than about 9/10 this means that for most... 

The normal state of atomic oxygen is an inverted triplet consisting of tliree levels with j values of 2, 1 and 0. The frequency separation between the j — 2 (lowest) and the j 1 (second) levels is 157.4 cm, i and that between the j = 2 and the 7 = 0 (third) levels is 226 cm. Calculate the electronic partition function of atomic oxygen at 300 K and the corresponding contribution to the atomic heat capacity. 

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

Dulong and Petit s law. The atomic heat capacity (atomic weight times specific heat) of elementary substances is a constant whose average... 

Assume that upon the completion of crystallization at 40°C, we have a solution containing 100 g of water (MW =18) and the equilibrium solubility of sodium acetate (MW = 82), or 65.5 g of sodium acetate from the above table. Let the solid crystals at 40°C be a g of solid crystalline trihydrate of sodium acetate (MW = 136). For a thermod3mamic path, take crystallization at 20°C, but with the 40°C solubility, followed by heating the crystaUine solids and the solution to 40°C. Therefore, specific heats are needed for the solid and the solution. In the absence of data for the trihydrate of sodium acetate, Kopp s rule (Felder and Rousseau, 2000) is applied with atomic heat capacities in cal/mol-°C of 1.8 for C, 2.3 for H, 4.0 for 0, 9.8 for water of crystallization, and 6.2 for all other atoms in the four salts. Thus, for NaC2H302 3H2O,... 

In the absence of data for sodium acetate dissolved in water, Wenner s values for atomic heat capacities of dissolved solids, in cal/mol-°C, can be applied, with 2.8 for C, 4.3 for H, 6.0 for O, and 8 for all other atoms in the four salts. Thus, for NaCjHjOj,... 

The entropy of fusion L/T) of completely disordered intermetallic phases can generally be calculated by fractional addition from those of the components. For the completely ordered state the term — 19.146 (Afi log Afi-F A 2 log A 2) is to be added to the calculated entropy of fusion [1.216-218,221,222]. The molar heat capacity of the homogeneous alloy phases and intermetallic compounds, as calculated approximately from the atomic heat capacities of the components using Neumann-Kopps rule, is obeyed to within 3% in the temperature range 0-500 °C in the Ag—Au, Ag—Al, Ag—Al, and Ag—Mg alloy systems. The heat capacities of heterogeneous alloys may he calculated hy fractional addition from those of the components hy the empirical relation Cp = 4.1816(a-F lO- i r-F 105cr-2)J/(Kmol) to satisfactory accuracy. 

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