Specific heat of solids

Table 6. Specific Heat of Solid Ammonium Carbamate...

C. Cp Specific heat at constant pressure for specific heat of solid Cg for specific heat of gas J/(kg-K) Btii/(lk-°F)... 

R = reflux ratio, g reflux/g product Tp = product temperature, °C Tp = saturated-feed temperature, °C Cp = specific heat of solid ciys-tals, cal/(g °C) and X = heat of fusion, cal/g. 

Heat transfer between gas and sohds is exceedingly hard to measure because it is so rapid. Although the coefficient is low, the available surface area and the relative specific heat of solid to gas are so large that temperature equilibration occurs almost instantaneously. Experiments on injection of argon plasmas into fluidized beds have shown quenching rates of up to fifty million degrees Kelvin per second. Thus, in a properly designed bed, gas to solids heat transfer is not normally a matter of concern. 

The specific heats of solids at low temperatures are appreciably less than at higher temperatures. A maximum specific heat has been observed in the case of iron at 740° and nickel at 320° (Lecher, 1908). Since these are the temperatures at which recalescence and loss of magnetic properties occur, the close relation of specific heat to molecular structure is evident. 

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 ... 

The problem has been largely worked at from both sides from the theoretical side the point of view has been almost exclusively that of the kinetic gas theory. It must be kept in mind, however, that it is possible that a purely mechanical theory may not be sufficient to cover the phenomena, as has recently appeared in the case of the specific heats of solids. 

This remarkable result has been verified by experimental measurements of specific heats at very low temperatures, viz., in liquid air and liquid hydrogen (cf. references in Chap. I.). It was formerly believed that the specific heats of solids approached small positive limiting values at the absolute zero, but the form of the curve at very low temperatures alters appreciably, and it may be inferred that the specific heat is vanishingly small at... 

Pollitzer (ZeiUchr. Elcktrochem., 17, 5, 1911 Berechmuig Chan. Affinitiiten nach Xernstschen Warmetheoi em, 1912) has carried out calculations with the new formula for the specific heats of solids ( 204), but this introduces nothing new in principle. 

The coffee-cup calorimeter can be used to measure the heat changes in reactions that are open to the atmosphere, qp, constant pressure reactions. We use this type of calorimeter to measure the specific heats of solids. We heat a known mass of a substance to a certain temperature and then add it to the calorimeter containing a known mass of water at a known temperature. The final temperature is then measured. We know that the heat lost by the added substance (the system) is equal to the heat gained by the surroundings (the water and calorimeter, although for simple coffee-cup calorimetry the heat gained by the calorimeter is small and often ignored) ... 

The specific heat of solid anhydrous Mg(N03)2 may be calculated from the equation ... 

A steam calorimeter was perfected by J. Joly (1886) and used for the accurate determination of specific heats of solids, liquids, and gases. In principle this apparatus consists of a balance, with the specimen hung from one pan and surrounded by an enclosure that can be flooded with steam. The mass of moisture condensing on the specimen, multiplied by the heat of vaporization of water, gives the quantity of heat imparted to the specimen. 

Cs, Cm Specific heat of solid and molten polymer (Section 5.1)... 

If the specific heat of the metal is known, an approximate atomic weight can be determined. This can be done using the relationship between the specific heat of solid metallic objects and their atomic weights observed by Pierre Dulong and Alexis Petit in 1819 it is known as the Law of Dulong and Petit. 

Equation (6.4) is the general one for vapor pressure, and it shows that the undetermined constant in In P, in Eq. (5.9), is just the chemical constant that we have already determined in Eq. (3.16) of Chap. VIII. The simplest experimental method of finding the chemical constants is based on Eq. (6.4) one measures the vapor pressure as a function of the temperature, finds the specific heats of solid and gas, so that one can calculate the term in the specific heats, and computes the quantity... 

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