Isobars heating

Fig. 28. Rankine cycle for superheat, where ( ) represents adiabatic (isentropic) compression ( ), isobaric heating ( ), vaporization (x x x x), superheating turbine expansion and (-----), heat rejection. To convert kPa to psi, multiply by 0.145. To convert kj to kcal, divide by 4.184.

Diagrams of isobaric heat capacity (C and thermal conductivity for carbon dioxide covering pressures from 0 to 13,800 kPa (0—2,000 psi) and 311 to 1088 K have been prepared. Viscosities at pressures of 100—10,000 kPa (1—100 atm) and temperatures from 311 to 1088 K have been plotted (9). 

The following tables of properties of carbon dioxide are available enthalpy, entropy, and heat capacity at 0 and 5 MPa (0 and 50 atm, respectively) from 273 to 1273 K pressure—volume product (PV), enthalpy, and isobaric heat capacity (C from 373 to 1273 K at pressures from 5 to 140 MPa (50-1,400 atm) (14). 

Fig. 6 shows both the actual cycle (shown in dashed lines) and the idealised cycle, which consists of two isosteres and two isobars. Heat flows in J/kg adsorbent q) are shown as shaded arrows. For most purposes, analysis of the ideal cycle gives an adequate estimate of the COP and cooling or heating per kg of adsorbent. An accurate calculation of the path of the actual cycle needs information on the dead volume of the whole system and of the heat transfer characteristics of the condenser and evaporator. General trends are more apparent from an analysis of the idealised cycle. 

The heat input per unit mass of adsorbent in the isobaric heating phase where the concentration varies is given by ... 

Equation (2.18) is another example of a line integral, demonstrating that 6q is not an exact differential. To calculate q, one must know the heat capacity as a function of temperature. If one graphs C against T as shown in Figure 2.8, the area under the curve is q. The dependence of C upon T is determined by the path followed. The calculation of q thus requires that we specify the path. Heat is often calculated for an isobaric or an isochoric process in which the heat capacity is represented as Cp or Cy, respectively. If molar quantities are involved, the heat capacities are C/)m or CY.m. Isobaric heat capacities are more... 

The linearity of van t Hoff plots, such as Figure 3.14, depends on the degree to which the isobaric heat capacity of the system (Cp) remains constant between the... 

Another heat capacity is Cp, the heat capacity measured at constant pressure (which is also called the isobaric heat capacity). The values of Cp and Cv will differ, by perhaps as much as 5-10 per cent. We will look at Cp in more depth in the next section. 

Table 5.24 lists selected data concerning entropy and isobaric heat capacity, covering andradite, grossular, pyrope, and almandine terms, compared with results of calculations based on the Kieffer model (Ottonello et al., 1996). 

Table 5.36 Thermodynamic properties of pure pyroxene components in their various structural forms according to Saxena (1989) (1), Berman (1988) (2), and Holland and Powell (1990) (3) database. = standard state entropy of pure component at 7) = 298.15 K and Py = bar (J/mole) Hjp p = enthalpy of formation from elements at same standard state conditions. Isobaric heat capacity function Cp is... 

Figure 8J (A) Isobaric thermal expansion, (B) its first r-derivative, (C) isothermal compressibility, and (D) isobaric heat capacity of H2O within the critical region, based on the equation of state of Levelt Sengers et al. (1983). From Johnson and Norton (1991), American Journal of Science, 291, 541-648. Reprinted with permission of American Journal of Science.

Draw an isobaric heating process on a T s diagram for a nonazeotropic mixture from a compressed liquid state to a superheated vapor state. Does the temperature remain the same in the boiling region ... 

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