Specific heat Appendix

An Excel macro is given in Appendix 7.2, and some results are shown in Figure 7.7. The macro is specific to the example reaction with v = - -l but can be generalized to other reactions. Components of the macro illustrate many of the previous examples. Specific heats and enthalpies are calculated analytically using the functional form of Equation (7.19) and the data in Tables 7.1 and 7.2. The main computational loop begins with the estimation of Kthermo using the methodology of Example (7.15). 

The specific heat capacity of nitrobenzene can be estimate using the methods given in Chapter 8. Take the other data required from Appendix C. 

From the steam tables in the Appendix, the latent heat of vaporisation of water at 312 K is 2410 kl/kg. Again from steam tables, the specific heat capacity of water vapour = 1.88 kJ/kg K and that of the solids will be taken as 2.18 kl/kg K. 

This is a three-part calculation. First you need to calculate the amount of heat required to raise the water s temperature from —273° to 0.00°C. Then you need to calculate the amount of heat required to transform the 1.00 gram of ice into liquid water. Third, you need to calculate the amount of heat required to raise the water s temperature from 0.00°C ro +100°C. From Table 8.1 you have that the specific heat of ice is 2.01 J/g °C. Note this calculation provides three significant figures (see Appendix B). 

Reference TDI contains an enthalpy table for ammonia at different pressures. Reference TD2 contains a series of tables in an appendix from which the specific heats of the reaction-gas mixture were calculated. Humidity charts were also useful. Reference TD3 is valuable for its steam tables, while Ref. TD4 contains both thermodynamic and chemical equilibria data for nitric acid. The final reference, Robertson and Crowe (Ref. TD5), contains formulae and tables for the sizing and choice of an air-feed compressor. 

C = Coefficient determined from an expression of the ratio of specific heats of the gas or vapour at standard conditions (see Appendix D). Use C = 315 if value is unknown. 

M = Molecular weight of the gas or vapour obtained from standard tables G = Specific gravity of the gas or vapour obtained from standard tables C = Coefficient determined from an expression of the ratio of specific heats of the gas or vapour at standard conditions obtained from standard tables, or if the ratio of specific heats value is known, see in Appendix D Ratio of specific heats k and coefficient C. Use C = 315 if value is unknown. 

Optical (Specific) Rotation Transfer an accurately weighed amount of sample, equivalent to about 100 mg of total tocoph-erols, into a separator, and dissolve it in 50 mL of ether. Add 20 mL of a 10% solution of potassium ferricyanide in a 1 125 sodium hydroxide solution, and shake for 3 min. Wash the ether solution with four 50-mL portions of water, discard the washings, and dry over anhydrous sodium sulfate. Evaporate the dried ether solution on a water bath under reduced pressure or in an atmosphere of nitrogen until about 7 or 8 mL remains, and then complete the evaporation, removing the last traces of ether without the application of heat. Immediately dissolve the residue in 5.0 mL of isooctane, and determine the optical rotation. Calculate the optical rotation [see Optical (Specific) Rotation, Appendix HB], using as c the concentration expressed as the number of grams of total tocopherols, as determined in the Assay (above), in 100 mL of the solution. 

We will now consider the amount of energy that can be stored because of changes in leaf temperature. For purposes of calculation, we will assume that a leaf has the high specific heat of water (4.18 kJ kg-1 °C 1 at 20° C Appendix I), where specific heat is the energy required to raise the temperature of unit mass by one degree. We will further assume that the leaf is 300 pm thick (e.g., Fig. 1-2) and has an overall density of700 kg m-3 (0.7 g cm-3) — a leaf is often 30% air by volume. Hence, the mass per unit leaf area in this case is... 

The constant-volume and constant-pressure specific heats are identical for incompressible substances (Fig. 1-10). Therefore, for solids and liquids the subscripts on c and Cp can be dropped and both. specific heals can be represented by a single symbol, c. That is, Cp = tv = c- This result could also be deduced from the physical definitions of constant-volume and constant-pressure specific heats. Specific heats of several common gases, liquids, and solids are given in the Appendix. 

The model uses material properties and models of these properties, such as thermal conductivity, permeability, diffusivity, specific heats, heat of pyrolysis, final sample radius and so on. The appendix gives an overview of the data used in the simulations. 

For more practice calculating and using specific heat, go to Supplemental Practice Problems in Appendix A. 

The specific heats obtained from Appendix E are as follows ... 

It is often more convenient to use the "specific" (per unit weight) values of thermodynamic properties, rather than "molar" (per mole) values. Specific values can be obtained by dividing molar values by the molecular weight per mole of repeat units, which are listed in the Appendix at the end of this book. For example, the specific heat capacity cp at constant pressure is the... 

Tb - bubble point of returned reflux, 55.1 T = tempemture of returned reflux, 25 Specific heats from Appendix 15, for (55.1 + 25)/2-40.05(104 )... 

For more about specific heat capacity and heat changes during changes of state see Appendix 10 on the website. 

The heat of vaporization of water at the normal boiling point, 373.2 K, is 40.66 kj/mol. The specific heat capacity of liquid water is 4.184 J g and of gaseous water is 2.02 J K g . Assume that these values are independent of temperature. What is the heat of vaporization of water at 298.2 K Does this result agree with Appendix 4 data ... 

Transient conduction conditions occur in polymer processing. Appendix A derives Eq. (A.14) for one-dimensional transient heat flow, which contains the thermal diffusivity a. This is the combination k/pCp of the thermal conductivity k, density p and specific heat Cp. For most polymer melts a is approximately equal to O.lmm s" (Fig. 5.3). For the melting of low-density polyethylene in an extruder, typical conditions are a barrel temperature of To = 220 °C, an initial polymer temperature Tp = 20 °C, and a melting process complete at T = 120 °C. Consequently, using Eq. (C.19), after a contact time t, the melt front is at a distance from the barrel given by... 

Since the enthalpy of the system is a sum of contributions of many molecules, the probability distribution of enthalpy Tf is a Gaussian function, with the width of the distribution naturally given by the mean-square deviation of enthalpy, or the fluctuation of enthalpy. The exact relationship between specific heat and enthalpy fluctuation is given in Appendix 2. A. 

Definitions of these response functions in terms of the mean-square fluctuations or correlations among appropriate thermodynamic quantities are given in Appendix 2.A. Thus, the increase of specific heat and compressibility is related to a rather sudden increase in these fluctuations as temperature is lowered below the fi eezing/ melting temperature of water/ice. Also, the increase in mean-square fluctuations in entropy and volume is accompanied by a decrease in correlations between these two quantities. The latter could happen if there is some degree of anti-correlation between the two fluctuations. That is, increase in volume leads to decrease in entropy and vice versa. 

APPENDIX 2.A MICROSCOPIC EXPRESSIONS OF SPECIFIC HEAT, ISOTHERMAL COMPRESSIBILITY,... 

The reversing heat capacity and the total heat-flow rate of an initially amorphous poly(3-hydroxybutyrate), PHB, are illustrated in Fig. 6.18 [21]. The quasi-isothermal study of the development of the crystallinity was made at 296 K, within the cold-crystallization range. The reversing specific heat capacity gives a measure of the crystallization kinetics by showing the drop of the heat capacity from the supercooled melt to the value of the solid as a function of time, while the total heat-Uow rate is a direct measure of the evolution of the latent heat of crystallization. From the heat of fusion, one expects a crystallinity of 64%, the total amount of solid material, however, when estimated from the specific heat capacity of PHB using the ATHAS Data Bank of Appendix 1, is 88%, an indication of a rigid-amorphous fraction of 24%. 

---