Specific Heat Values

Consider now a situation in which the bias limits in the temperature measurements are uncorrelated and are estimated as 0.5 °C, and the bias limit on the specific heat value is 0.5%. The estimated bias error of the mass flow meter system is specified as 0.25% of reading from 10 to 90% of full scale. According to the manufacturer, this is a fixed error estimate (it cannot be reduced by taking the average of multiple readings and is, thus, a true bias error), and B is taken as 0.0025 times the value of m. For AT = 20 °C, Eq. (2.9) gives ... 

Mean specific heat values are tabulated in various handbooks. If the values are for unit mass, calculated from some standard reference temperature, tr, then the change in enthalpy between temperatures i and t2 is given by ... 

Source Molecular weight, specific gravity, individual gas constant, and specific heat values were abstracted from, or based on, data in Table 24 of Mark s Standard Handbook for Mechanical Engineers (7th ed.). 

Use specific heat values of 250 J/K mole for butane and 36 J/K mole for oxygen and nitrogen. 

Polyacrylonitrile (C3H3N) bums to form vapor, carbon dioxide and nitrogen. The heat of formation of the polyacrylonitrile is +15.85 kcal/g mol (1 cal= 4.186 kJ). Use data from Tables 2.1 and 2.2 use specific heat values at 1000 K. 

Both kinetic and thermodynamic approaches have been used to measure and explain the abrupt change in properties as a polymer changes from a glassy to a leathery state. These involve the coefficient of expansion, the compressibility, the index of refraction, and the specific heat values. In the thermodynamic approach used by Gibbs and DiMarzio, the process is considered to be related to conformational entropy changes with temperature and is related to a second-order transition. There is also an abrupt change from the solid crystalline to the liquid state at the first-order transition or melting point Tm. 

The enthalpies of formation AfH°2n i5, absolute entropy 5 29g ]5 and specific heat values C°P i of component i can be found in tables. 

The specific heat of Si3N4 ceramics is in the temperature range 293 up to 1200 K [Cp (293 K) = 0.67 KJ (K kg)-1] nearly independent of the composition of the additives. The isobaric specific heat values agree well with the isochoric specific heat calculated by Debye s theory. Also the Dulong Petit s rule can applied as an approximation of the Cv values [25 J(K mol)-1] at temperatures >1100 K [371]. From the Cp values at around 100 K the amount of the amorphous grain boundary phase can be calculated [371]. 

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. 

This concept presumes that the calorific input of the fire may be partly absorbed by the endothermic changes of the mineral substances employed in the formulation of the mastic. Thus, for example, such latent heat as the heat of fusion, heat of vaporization, heat of sublimation, and heat of transition (the heat required to change a unit mass of a given substance from one crystalline structure to another) all can absorb considerable energy which would otherwise be used to raise the combustible substrate to an ignition point. The efficiency of these fire-resistant minerals can also be adjudged by their specific heat values. 

Some difference is noticed if you calculate the shell-side Q. This difference is mainly due to variations in the accuracies of the specific heat values obtained. For our purpose and for accuracy within 3%, however, the calculated tube-side heat is sufficient. 

The specific heat value Cp should reference the gas phase for a condensing fluid. 

Step 10. The air quantity flow is next calculated, knowing the values of DTA (step 2) and Q (step 4) and using a specific heat air constant of 0.24 Btu/lb °F. This air specific heat value is applicable to all cases. Equation (5.41) is now used to determine airflow WA ... 

This program is also used for condensing steam. A given Q fixes heat transfer. A 1500 Btu/h ft2 °F steam-condensing tube-side film coefficient is assumed. This condensing film coefficient is set by inputting a specific heat value of 0. 

Specific heat can be predicted fairly accurately by mathematical models through statistical mechanics and quantum theory. For solids, the Debye model gives a satisfactory representation of the specific heat with temperature. Difficulties, however, are encountered when the Debye theory is applied to alloys and compounds. Plastics and glasses are other classes of solids that fail to follow this theory. In such cases, only experimental test data will provide sufficiently reliable specific heat values. 

Table 11.1 Specific Heat Values for Some Common Substances 1 ... 

MDSC, by varying the furnace temperature sinusoidally, has been used to determine the specific heat of PA6 materials (similar measurements have been performed for polypropylene nanocomposites). The materials were heated from -80°C to 250°C at 2°C/min. The reversible signal recorded during the experiment is related to the specific heat of the sample. The specific heat values versus temperature for the different PA6-based formulations are given in Figure 19.3, showing no significant differences between different formulations. The peaks noted on the specific heat curves correspond to the transition from the solid to the liquid states. 

Table 6.25(a) Specific heat values of selected materials... 

The finite changes in the internal energy and enthalpy of an ideal gas during a process can be expressed approximately by using specific heat values at the average temperature as... 

You may be tempted to think lhat the cold water should be heated to 70 C in the limiting case of maximum heat transfer. But this will require the temperature of the. hot water to drop to -170 C (below 10°C), which is impossible. Therefore, heat transfer in a heat exchanger reaches Its maximum value when (he fluid with the smaller heat capacity rate (or the smaller mass flow rate when both fluids have the same specific heat value) experiences the maximum temperature change. This example explains why vie use in the evaluation of instead of... 

Source Specific heat values are obtained pflrnarily from the property routines prepared by The National Institute of Standards and Technology (NIST), Gaithersburg, MD. 

Specific heat data are based on the specific heat values of a water and ice at CfC anc are determined from Sieoei s formulas - 3.35 X (Water content + 0.S4, above freezing, zee... 

Edmister (1948) published a generalized plot showing the isothermal pressure correction for real gases as a function of the reduced pressure and temperature. His chart, converted to SI units, is shown as Eigure 3.2. Edmister s chart was based on hydrocarbons but can be used for other materials to give an indication of the likely error if the ideal gas specific heat values are used without corrections. 

Since specific heat under constant pressure and at constant volume differs little in condensed systems, the data in Fig. 51 indicate satisfactory agreement with theory the theoretical specific heat value at a constant volume at high temperatures is 24.94 20.02 — 1.25 J g K (i.e. 3R divided byt he ratio Mjn where M is molecular weight and ft is the number of atoms in the molecule). The value is very close to the actual specific heat of silica glass above about 1000 "C (cf. Fig. 51). 

The decomposition of ozone has been of great interest to those concerned with combustion, because of the apparent simplicity of the reaction and the fact that there is only one product gas, oxygen. Lewis and von Elbe (13) developed a theory of flame propagation in ozone-oxygen mixtures on the basis of their burning velocity studies. They (13) derived high-temperature specific heat values for oxygen from their explosion data. 

Unexpected but often abrupt changes in the properties of aqueous interfacial systems with temperature constitute one of the unique characteristics of vicinal water. Attention has already been drawn to the anomalies observed by Etzler in the specific heat values of vicinal water. Evidence of abrupt changes in the properties of both pure water and aqueous solutions have been studied in the past, but it was not until 1968 that it became clear that although unusual changes in some aqueous properties do indeed occur, they are associated only with interfacial water and not bulk water or bulk aqueous solutions (see Drost-Hansen, 1965, 1968, 1969). 

Two different approaches need to be considered. In the first one the thermodynamic parameters are calculated on the basis of spectroscopic and specific heat data of monomer and its polymer. The estimation of entropy from specific heat values is based on the assumption that at 0 °K the entropy of the perfect crystal equals zero. Since polymers are never perfectly crystalline this method is based on a rough approximation. 

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