Composite specific heat capacity

For matches between process and refrigeration, A Tmin = 10°C. Draw the process grand composite curve and set the targets for the utilities. Below the pinch use of higher temperature, cold utilities should be maximized. For boiler feedwater, the specific heat capacity is 4.2 kJ kg K-1 and the latent heat of vaporization is 2238 kJ-kg1. 

The temperature profile of a planetary atmosphere depends both on the composition and some simple thermodynamics. The temperature decreases with altitude at a rate called the lapse rate. As a parcel of air rises, the pressure falls as we have seen, which means that the volume will increase as a result of an adiabatic expansion. The change in enthalpy H coupled with the definition of the specific heat capacity... 

The thermal properties (i.e., density, specific heat capacity, and thermal conductivity) have a particularly strong influence on the curing behavior. The exothermal peak temperature is one example It can differ significantly between a composite mold with low thermal mass and a metal mold [35], A more thorough discussion of pros and cons of different mold materials can be found in Morena [37]. 

The heat capacity of the reacting fluid depends on both the composition and the temperature. This situation occurs in gas-phase reactions, where the species heat capacities vary with temperature. In this case, the specific heat capacities of the individual species are usually expressed in the form... 

For gas-phase reactions, the heat capacity of the reacting fluid depends on both composition and temperature. Also, the specific heat capacity of the injection stream is usually different from that of the inlet stream. To accoimt for the effect of composition and temperature, molar-based specific heat capacities are used. The molar-based and the mass-based specific heat capacities are related by... 

Figure 18.11. Predicted specific heat capacity of amorphous random copolymers of styrene and oxytrimethylene at room temperature, as a function of the composition. 

Liquid specific heat capacity for fatty acids, triacylglycerols, and vegetable oils was estimated based on their fatty acid composition (Morad et al. 2000). A Rowlinson-Bondi equation was used to estimate specific heat (Cp) for pure fatty acid. The liquid specific heat capacities of oils were estimated by using mixture properties corresponding to the fatty acid composition and a correction factor, which accounts for the TAG form. The Rowlinson-Bondi equation used is as follows ... 

Morad, N.A., Mustafa Kamal, A.A., Panau, F. and Yew, T.W. (2000) Lipid specific heat capacity estimation for fatty acids, triacylglycerols, and vegetable oils based on their fatty acid composition. J. Am. Oil Chem. Soc., 77, 1001-1005. 

The specific heat capacity - temperature dependence for four different types of nickel have been determined and the effects of the method of manufacture, the heat treatment and the chemical composition have been ascertained. The results, together with those obtained by previous investigators were reviewed and an attempt was made to evaluate the most probable C , versus T curve for nickel in the temperature range 100 to 600°C. 

The partial specific heat capacity of the folded state is typically on the order of 0.3 cal K g at 25° with a linear temperature dependence of 0.001 to 0.002 cal K g The partial specific heat capacity of the unfolded state is approximately 0.5 cal K g and varies in a nonlinear fashion with temperature, reaching a plateau above about 70°. It can be calculated from the amino acid composition of the protein if there is no residual structure. " In practice, the baseline above the transition contains contributions from effects other than the heat capacity of the unfolded protein (e.g., chemical modification of the unfolded chain and aggregation" ) so that the experimental measurement of the absolute heat capacity of the unfolded chain can be unreliable. Thus, although it might be expected that DSC should be an ideal method to determine differences in heat capacities, in practice the measurement obtained from a difference between the extrapolated baselines is not used. 

The heat effects accompanying a crystallization operation may be determined by making heat balances over the system, although many calculations may be necessary, involving knowledge of specific heat capacities, heats of crystallization, heats of dilution, heats of vaporization, and so on. Much of the calculation burden can be eased, however, by the use of a graphical technique in which enthalpy data, solubilities and phase equilibria are represented on an enthalpy-composition H x) diagram, sometimes known as a Merkel chart. 

The true specific heat capacity of a material is defined as the quantity of heat required to raise the temperature of a specified mass by a specified temperature. For composites, it can be estimated based on the rale of mixture. Considering again that the material is composed of two phases - undecomposed and decomposed materials - the total heat, H, required to raise the temperature by AT of the material with the mass M should be equal to the sum of the heat required to raise the temperature of all its phases to the same level, as shown in Eq. (4.30) [12] ... 

As mentioned, many experimental results have shown that the specific heat for composites increases sHghtly with temperature before decomposition. In some previous models, the specific heat was described as a Hnear function. Theoretically, however, the specific heat capacity for materials wiU change as a function of temperature, as on the micro level, heat is the vibration of the atoms in the lattice. Einstein (1906) and Debye (1912) individually developed models for estimating the contribution of atom vibration to the specific heat capacity of a sohd. The dimensionless heat capacity is defined according to Eq. (4.32) and Eq. (4.33) and illustrated in Figure 4.12 [25] ... 

Cp is the specific heat capacity of the decomposed material. As the polymer matrix almost decomposed into gases, most mass of the material after decomposition is composed of fibers. As a result, Cp, is approximately equal to the specific heat capacity of the fibers (as the mass fraction of the remaining gases in the composition is negligible compared to that of the fibers) ... 

Figure 4.22 Effective specific heat capacity from different thermal loading programs for powdery GFRP composites curves at constant heating rates from DSC and modeling, and modeling curve based on ISO fire curve [30]. (With permission from SAGE.)...

The true specific heat capacity of a composite material was obtained by the mle of mixture and the mass fraction of each phase was determined by the decomposition and mass transfer model. The true specific heat capacity of resin or fiber was derived based on the Einstein or Debye model. The effective specific heat capacity was obtained by assembhng the trae specific heat capacity with the decomposition heat that was also described by the decomposition model. The modeling approach for effective specific heat capacity is useful in capturing the endothermic decomposition of resin and was further verified by a comparison to DSC curves. 

The specific heat capacity of a mixture (composite material) is determined by the properties of the different phases and their mass fraction, while the effective specific heat capacity includes the energy needed for additional chemical or physical changes. Consequently, the decomposition heat can be considered to be a part of the effective specific heat capacity as introduced in Chapter 4. The effects due to pyrolysis gases on the specific heat capacity are negligible, as most gases can escape from the material, and thus the mass fraction of the remaining gases is very small. The thermal conductivity of a mixture is determined by the properties of the different phases and their volume fraction. Consequently, the effect due to pyrolysis... 

The same trend is observed for the specific heat capacity. The intensity of the change in specific heat capacity (A is associated with T. Specific heat capacity of control PU is 1392 J/kg-K. Specific heat capacity of the PU composite increased by 5.8 % when 2% FR is added. However, specific heat capacity of FR-filled PU composites decreased by 3.5% and 14% when 4% and 6% FR respectively are added. A significant drop in specific heat capacity (A C ) is observed when more flame retardant is introduced to PU composites, therefore gradual and Unear reduction ocoured according to addition of FR (Sarier Onder 2007). 

TABLES TheT and specific heat capacity of control PU and FR-fiUed PU composites... 

This large volume of data shows that the apparent reversing specific heat capacity increases with comonomer content. This is seen best immediately above the glass transition temperature, as displayed in the insert in Fig. 7.37. The amount of irreversible crystals, which are identified as the normally grown folded-chain crystals, decreases with increasing comonomer composition, as expected (see Figs. 7.37 and 7.38 and compare to Fig. 7.35). 

Influence of miscibility on thermal conductivity and diffusivity was studied (Agari 1993, Agari and Ueda 1994). In the blend of low molecular weight PS with coumarone-indene resin, which showed miscibility over all blend compositions, the thermal conductivity was approximately linearly dependent on composition (Agari 1993). Thermal conductivity, thermal diffusivity, and heat capacity of PMMA/PC blends were studied with respect to temperature and blend composition. The specific heat capacity of the two-phase 50/50 blend was larger than that of the one-phase blend. The thermal diffusivity and the conductivity of the 50/50 blend slightly decreased with the increase of temperature up to 450-460 K (LCST) and then decreased abruptly with increase of temperature (Agari et al. 1997). 

The above Eq. 6.4 has two heat loss constants that can be converted into single heat loss constant by using the thermal mass relationship between the copper and composite. For a body of uniform composition, thermal mass, C , can be approximated by Cfh = m Cp, where m is the mass of the body and Cp is the isobaric specific heat capacity of the material averaged over temperature range in question. Thus, the equivalent thermal mass for a copper plate to aerogel composite for a constant cross-sectional area (Axz) will be as follows ... 

Equation 6.5 shows the equivalent thickness of a copper plate that will have the same thermal mass as the aerogel composite. Table 6.1 shows the specific heat capacities of the materials used in the experiment. The specific heat capacity for the aerogel composite is estimated using the mle of mixmre as shown where x is the weight fraction of the aerogels and y is the weight fraction of FMWNT. Where there... 

The specific heat capacity of a composite material denoted Cp and expressed in J.kg K is only related to the mass fractions, Wp, of each component k and hence it is given by the simple equation ... 

The heat transfer of oven processes is based on the same principle as the autoclave convection heating. The heat transfer medium, normally air, is different than for an autoclave, where it is usually compressed nitrogen. However, the specific heat capacity of air is lower than compressed nitrogen which makes it slower to react. This means that the effect and risk of exothermic reaction can only be restricted by ramping up the temperature very slowly and with very accurate control. Figure 14.4 shows an example of convection oven used for composite curing. 

Test method for compositional analysis hy thermogravimetry Test method for determining specific heat capacity by differential scanning calorimety... 

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