Isobaric compression

Figure 2-31. P-V process diagrams (a) isothermal expansion (b) isobaric compression.

The schematic Ericsson cycle is shown in Fig. 4.27. The p-v and T-s diagrams of the cycle are shown in Fig. 4.28. The cycle consists of two isothermal processes and two isobaric processes. The four processes of the Ericsson cycle are isothermal compression process 1-2 (compressor), isobaric compression heating process 2-3 (heater), isothermal expansion process 3-4 (turbine), and isobaric expansion cooling process 4-1 (cooler). 

NMR success motivated other spectroscopic studies to measure the hydrate phase directly. This work represented an experimental departure, because previously only the fluid phases (vapor and liquid(s)) were measured, and any experimental error was incorporated in the solid-phase model of van der Waals and Platteeuw, However, with modem solid-phase measurements, the errors in the van der Waals and Platteeuw model could be clarified and corrected. Raman spectroscopy and diffraction (X-ray and neutron, supplemented by Rietveld analysis ) have been successful the first method to measure the relative occupation of single guest cages, and the second to extend the work to hydrate isothermal, adiabatic, and isobaric compressibilities. As shown in Section 4, these measurements combine with spectroscopic hydrate phase measurements to enable improvements of the model. 

Isobaric compression of ice Ih at 165 other phases (e.g., ices II and III) [40] and neither liquid nor amorphous ice can be formed in pure ice experiments. This is the main problem in understanding the relationship between the ice Ih melting line, at 7 > 250K, and the amorphization line, at 7 77K. One way to avoid the transformation of ice Ih to other crystalline forms is to use emulsified ice [13]. In this emulsion, water is mixed with different solutes and cooled at low temperature. The resulting ice emul slon consists of ice Ih domains confined in droplets with radius of 1-10 )U.m. Such small volumes suppress the transformation of ice Ih to other crystalline forms upon isothermal compression and the melting and amorphization lines obtained upon isobaric compression of emulsified ice Ih can be traced at all temperatures [37]. 

The expansibilities, compressibilities, and surface tensions of the mixtures are intensive properties, so they should be expressed not in terms of excess quantities but just as deviations from the linear dependence on the (mole fraction) composition. Data for the isobaric expansibilities and the adiabatic compressibilities of binary mixtures of water with many cosolvents on the list are available in [56]. The isobaric compressibilities can then be calculated from such data by Equation 3.3, using also the molar volumes of the mixtures, V = x V- + XcK -i- V. ... 

An ideal diatomic gas in an amount of v = 1 mole is under a pressure = 250 kPa and occupies volume Vj = 10 L. The gas is heated to Tj = 400 K and further isothennicaUy expanded to initial pressure. After that, the gas returns to its initial state by isobaric compression. Define the cycle thermal efficiency e. 

Two other important quantities are the isobaric expansivity ( coefficient of themial expansion ) and the isothermal compressibility k, defined as... 

The adjectives isobaric and isothennaT and the corresponding subscripts are frequently omitted, but it is important to distinguish between the isothemial compressibility and the adiabatic compressibility. ... 

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.

Vapor-Compression Cycles The most widely used refrigeration principle is vapor compression. Isothermal processes are realized through isobaric evaporation and condensation in the tubes. Standard vapor compression refrigeration cycle (counterclockwise Ranldne cycle) is marked in Fig. ll-72<7) by I, 2, 3, 4. 

Although the T-s diagram is veiy useful for thermodynamic analysis, the pressure enthalpy diagram is used much more in refrigeration practice due to the fact that both evaporation and condensation are isobaric processes so that heat exchanged is equal to enthalpy difference A( = Ah. For the ideal, isentropic compression, the work could be also presented as enthalpy difference AW = Ah. The vapor compression cycle (Ranldne) is presented in Fig. H-73 in p-h coordinates. 

Refrigerating capacity is the product of mass flow rate of refrigerant m and refrigerating effect R which is (for isobaric evaporation) R = hevaporator outlet evaporator mJef Powei P required foi the coiTipressiou, necessary for the motor selection, is the product of mass flow rate m and work of compression W. The latter is, for the isentropic compression, W = hjisehatge suction- Both of thoso chai acteristics could be calculated for the ideal (without losses) and for the ac tual compressor. ideaUy, the mass flow rate is equal to the product of the compressor displacement per unit time and the gas density p m = p. 

The Brayton cycle in its ideal form consists of two isobaric processes and two isentropic processes. The two isobaric processes consist of the combustor system of the gas turbine and the gas side of the HRSG. The two isentropic processes represent the compression (Compressor) and the expansion (Turbine Expander) processes in the gas turbine. Figure 2-1 shows the Ideal Brayton Cycle. 

In an isothermal process, heat must be added during an expansion and removed during a compression to keep the temperature constant. We will describe this more fully as we now calculate the heat added or removed in isobaric, isochoric, and isothermal processes. 

Both the compression and expansion are isobaric processes hence, the total work is given by... 

Typical values of the isobaric expansivity and the isothermal compressibility are given in Table 1.2. The difference between the heat capacities at constant volume and constant pressure is generally negligible for solids at low temperatures where the thermal expansivity becomes very small, but the difference increases with temperature see for example the data for AI2O3 in Figure 1.2. 

Table 1.2 The isobaric expansivity and isothermal compressibility of selected compounds at 300 K.

The effect of temperature on the equation of state is introduced through the iso-baric thermal expansivity. It is generally assumed that isobaric expansivity and iso-baric compressibility work independently of each order and the volume as a function of T and p is then expressed as... 

A (reversible) Joule cycle consists of the following four steps isobaric increase in volume, adiabatic expansion, isobaric decrease in volume, and adiabatic compression. Helium gas, with the equation of state... 

We may first assume that isothermal compressibility fiy and isobaric thermal expansion coefficient a are independent, respectively, of T and P. Equations 1.91 and 1.99, integrated on T and P, respectively, give... 

Table 5.48 summarizes thermal expansion and compressibility data for amphibole end-members according to the databases of Holland and Powell (1990) and Saxena et al. (1993). Isobaric thermal expansion (a, K ) and isothermal compressibility (jS, bar ) may be retrieved from the listed coefhcients by applying the polynomial expansions... 

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