Heat Capacity of the Elements at

Heat Capacity of Selected Solids, 12-200 Heat Capacity of the Elements at 25 C, 4-135 Heat conductivity see Thermal conductivity Heat of Combustion, 5-70 Heat of dilution see Enthalpy of dilution Heat of formation see Enthalpy of formation Heat of fusion see Enthalpy of fusion Heat of solution see Enthalpy of solution Heat of vaporization see Enthalpy of vaporization Hebrew alphabet, 2-36 Helium see also Elements... 

The heat capacity, the heat required to raise 1 g-mole drrough one kelvin, can be calculated at temperatures generally above 300 K by two simple empirical rules. The first of these, Dulong and Petit s rule, was discovered in the course of calorimeU ic smdies of the heat capacities of the elements and shows drat the heat capacity has a value,... 

Kopp s law PHYS chem The law that for solids the molal heat capacity of a compound at room temperature and pressure approximately equals the sum of heat capacities of the elements in the compound. kaps, 16 ... 

Cpm - is the standard heat capacity of species j at constant pressure, and Ns is the number of species in the chemical reaction. Note that the standard molar heat capacities of the elements cancel in the summation. Equation 10.4-2 was given earlier as equation 3.2-19, and it was used to show that the pK of acetic acid goes through a maximum not far from room temperature. Equation 10.4-3 was given earlier as equation 3.2-16. 

The heat capacity of an element at a temperature equal to its characteristic temperature, calculated ... 

FIGURE 1 A thermal detector of optical radiation. The detector of area, A, is illuminated by optical power, P, and is enclosed in a chamber at temperature, T. Gt and Ct are the thermal conductance and heat capacity of the element, and the network, N, converts the temperature change to a signal voltage, vs. 

The high-temperature contribution of vibrational modes to the molar heat capacity of a solid at constant volume is R for each mode of vibrational motion. Hence, for an atomic solid, the molar heat capacity at constant volume is approximately 3/. (a) The specific heat capacity of a certain atomic solid is 0.392 J-K 1 -g. The chloride of this element (XC12) is 52.7% chlorine by mass. Identify the element, (b) This element crystallizes in a face-centered cubic unit cell and its atomic radius is 128 pm. What is the density of this atomic solid ... 

Approximate values can be calculated for solids, and liquids, by using a modified form of Kopp s law, which is given by Werner (1941). The heat capacity of a compound is taken as the sum of the heat capacities of the individual elements of which it is composed. The values attributed to each element, for liquids and solids, at room temperature, are given in Table 8.2 the method illustrated in Example 8.6. 

As already indicated, Tian s equation supposes (1) that the temperature of the external boundary of the thermoelectric element 8e, and consequently of the heat sink, remains constant and (2) that the temperature Oi of the inner cell is uniform at all times. The first condition is reasonably well satisfied when the heat capacity of the heat sink is large and when the rate of the heat flux is small enough to avoid the accumulation of heat at the external boundary. The second condition, however, is physically impossible to satisfy since any heat evolution necessarily produces heat flows and temperature gradients. It is only in the case of slow thermal phenomena that the second condition underlying Tian s equation is approximately valid, i.e., that temperature gradients within the inner cell are low enough to be neglected. The evolution of many thermal phenomena is indeed slow with respect to the time constant of heat-flow calorimeters (Table II) and, in numerous cases, it has been shown that the Tian equation is valid (16). 

In equations 7.27 and 7.28 m(BA), m(cot), m(crbl), and m(wr) are the masses of benzoic acid sample, cotton thread fuse, platinum crucible, and platinum fuse wire initially placed inside the bomb, respectively n(02) is the amount of substance of oxygen inside the bomb n(C02) is the amount of substance of carbon dioxide formed in the reaction Am(H20) is the difference between the mass of water initially present inside the calorimeter proper and that of the standard initial calorimetric system and cy (BA), cy(Pt),cy (cot), Cy(02), and Cy(C02)are the heat capacities at constant volume of benzoic acid, platinum, cotton, oxygen, and carbon dioxide, respectively. The terms e (H20) and f(sin) represent the effective heat capacities of the two-phase systems present inside the bomb in the initial state (liquid water+water vapor) and in the final state (final bomb solution + water vapor), respectively. In the case of the combustion of compounds containing the elements C, H, O, and N, at 298.15 K, these terms are given by [44]... 

Equation 38 shows that ASf°[ij, Tmij] is independent of temperature and requires extrapolation of Cp[n] only over the limited temperature range from Tmn to Tmij, and the extrapolated Cp[n] contribution would be partially cancelled by the last term in equation 36 for Tmn < Tm,j. The data base for the application of equation 37 is the measurable activity product at the melting temperature, Tmij, ASf°[ij, TJ] (as discussed earlier), Cps[ij], Cp[i or j], Cps[i or j], and AHm,orj. The advantages of method III are the explicit statement of the principal temperature dependence and the extrapolation of, at most, only the heat capacity of the liquid element. 

Some measure of the variety of information available from displacement parameters can be illustrated by studies of cubic crystals of the elements. For example, the specific heat of an element is related to these displacement parameters. The heat capacity of an element or compound denoted Cv if measured at constant volume, is the quantity of heat required to raise the temperature of the atomic (or molecular) weight in grams... 

The entropy at 298.15 was estimated by considering the additive entropy constants of Kelley (6) and Evans and Kubaschewski (7 ). The heat capacity was estimated in a similar manner by considering the heat capacities of the constituent elements and related compounds such as Mg, Og, MgO, P, 3 2 8 ... 

Tables for this defined reference state, including the heat capacity, the heat content relative to 298.15° K., the absolute entropy, and the free energy function at even 100° intervals from 298.15° to 3000° K. have b n assembled for the first 92 elements. These tables are arranged alphabetically beginning on page 36. The choice of 298.15° K. as the reference temperature is made because the low temperature heat capacities of many elements and compounds are not known. Most of the thermodynamic data now reported in the literature refer to 25° C., which, when combined with the recent international agreement on 273.15° K. for the ice point (319) gives a reference temperature of 298.15° K. The figure 298° K. quoted in the tables and text should be understood to be the reference temperature, 298.15° K. For those who prefer to use 0° K. as the reference temperature, we have included, for cases in which it is known, the heat content at 298.15° K. relative to 0° K.

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