Specific enthalpy curve

The thermal energy requirements to achieve melting can be estimated from the specific enthalpy curves shown in Fig. 5.1. The area under any given curve represents the thermal energy needed to heat or melt one unit mass of that polymer from room to any higher temperature. 

Fig. 5.1 Specific enthalpy curves for some common polymers.

Figure 17. The specific enthalpy curve, /i(7) the specific enthalpy curves for the fully amorphous and crystalline states and the percentage crystallinity curve, all based on the specific heat...

The area under a curve of C /q versus Tg or i/q versus the specific enthalpy i may be used to solve for the area Ai required to obtain a given outlet temperature or to obtain the outlet temperature given Ai. Three points generally suffice to determine the area under the curve within 10 percent. 

The specific enthalpies of aqueous solutions and gaseous mixtures of ammonia and water are shown on the two curves on this figure. 

The specific enthalpy of a species H — 0 PV) also increases with increasing emper-ature. If a species is heated at constant pressure and H is plotted versus T. the slope of the resulting curve is the heat capacity at constant pressure of the species. Cp[T). or = ( f / r)consiant p- It follows that if a gas undergoes a change in temperature from T- to Tz. with or without a concurrent change in pressure. 

It follows from this that, under the assumptions made, the specific enthalpy hi, of the flowing condensate is independent of the film thickness. The equation further shows that the enthalpy of vaporization Ahv in the equations for Nusselt s film condensation theory has to be replaced by the enthalpy difference Ah. If we additionally consider that the temperature profile in the condensate film is slightly curved, then according to Rohsenow [4.10] in place of (4.27), we obtain for Ah the more exact value... 

Gray (39) developed a program which accepts the DSC sample and baseline data, matches the isothermal, performs cumulative and total area integrations in units of cal/g, corrects the temperature for thermal lag, and tabulates and plots ordinate values in specific-heat units as well as cumulative area in enthalpy units. The analog data from the DSC instrument are digitized and transferred to paper tape with the use of the Perkin-Eimer ADS VI Analytical Data System for Thermal Analysis. The data are digitized every two seconds or every 0.133°. A computer plotter then plots the DSC curve and also the cumulative peak area in specific enthalpy units, cal/g. 

The relationship between observed enthalpy-volume relaxations and thermal treatment of slightly oriented industrial PVC films was investigated. Differential scanning calorimetry at 20 -C per minute and specific volume analysis (density gradient column) were used to study the effects of annealing near and below Tg. Nonlinear effects in the volume relaxation at relatively long times and temperatures close to the glass transition produce deviations in the specific heat curves at temperatures far above Tg in addition to the normal overshoot effects. 

Enthalpy measurements have been measured by both Dennison et al. (1966a) (373-1762 K in the solid phase) and Stankus et al. (1995/1996) (400-1802 in the solid phase). The measurements of Stankus et al. were selected because of the much high purity samples available. The results were shown only in the form of an equation which had to be increased to higher order in order to accommodate both the values of the specific heat at 298.15 K and the slope of the specific heat curve. 

Figure 1. Schematic variation of the enthalpy H and specific heat capacity Cp with temperature T for transitions (at T ) that are (a) strongly first-order, (b) weakly first-order with pretransitional fluctuation behavior, (c) mean-field second-order (CP indicates the critical point on the enthalpy curve for the Landau second-order transition temperature Tc=T ), (d) and (e) are critical fluctuation dominated second-order transitions with a diverging (d) or large but finite (e) specific heat capacity at the critical temperature T =T . For the first-order transitions the latent heats AWl correspond with the steps in H(T) at T=T . 5W represent the fluctuation induced enthalpy change associated with the phase transition.

Early attempts at applying finite element analysis to solidification problems focused only on heat conduction. The most important phenomena taken into account are the release of latent heat due to phase change. If this is incorporated in the governing equations as a variation in the specific heat of material, it is evident that there occurs a jump at the phase-change temperature in the specific heat curve. This is analogous to the peak of a Dirac delta function. In order that this peak is not missed in the analysis, an alternate averaging procedure on the smoother enthalpy-temperature curve was suggested [60]. 

This is a specific value and comes from the definition of the fictive temperature as being the temperature of the frozen glassy state at which a material is in equilibrium (see Section 1.5.6). The calculation is taken from the enthalpy curve and is the intersection of tangents taken from above and below the Tg. The same value can be obtained by drawing tangents to the integral of the heat flow trace. 

To use a thermodynamic graph, locate the fluid s initial state on the graph. (For a saturated fluid, this point lies either on the saturated liquid or on the saturated vapor curve, at a pressure py) Read the enthalpy hy volume v, and entropy from the graph. If thermodynamic tables are used, interpolate these values from the tables. Calculate the specific internal energy in the initial state , with Eq. (6.3.23). 

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