Thermodynamics, Heat Transfer, And Fluid Flow. V.1. Thermodynamics, страница 10

The point where the three lines meet is called the triplepoint. The triple point is the only point at which all three phases can exist in equilibrium. Thepoint where the vaporization line ends is called the critical point. At temperatures and pressuresgreater than those at the critical point, no substance can exist as a liquid no matter how great apressure is exerted upon it.Figure 9 P-T Diagram for WaterHT-01Page 42Rev.

0ThermodynamicsPROPERTY DIAGRAMS AND STEAM TABLESPressure-Specific Volume (P-ν) DiagramA P-ν diagram is another commontype of property diagram. Figure10 is the P-ν diagram for purewater. A P-ν diagram can beconstructed for any pure substance.A P-ν diagram is different from aP-T diagram in one particularlyimportant way. There are regionson a P-ν diagram in which twophases exist together.In theliquid-vapor region in Figure 10,water and steam exist together.For example, at point A, waterwith a specific volume (νf), givenby point B, exists together withsteam with a specific volume (νg),given by point C.

The dotted linesFigure 10 P-v Diagram for Wateron Figure 10 are lines of constanttemperature. The quality of themixture at any point in the liquid-vapor region can be found because the specific volumes ofwater, steam, and the mixture are all known. The quality can be found using the followingrelationship.ν = xνg + (1 - x)νfxννfννfνgνfν=specific volume of the mixture (ft3/lbm)x=quality of the mixture (no units)νg=specific volume of the vapor (ft3/lbm)νf=specific volume of the liquid (ft3/lbm)νfg=specific volume change of vaporization (ft3/lbm) or vfg = vg - vfν fgwhere:Rev.

0Page 43HT-01PROPERTY DIAGRAMS AND STEAM TABLESThermodynamicsPressure-Enthalpy (P-h) DiagramA P-h diagram exhibits the samefeatures as a P-ν diagram. Figure11 is the P-h diagram for purewater. A P-h diagram can beconstructed for any pure substance.Like the P-ν diagram, there areregions on a P-h diagram in whichtwo phases exist together. In theliquid-vapor region in Figure 11,water and steam exist together.For example, at point A, waterwith an enthalpy (hf), given bypoint B, exists together with steamwith an enthalpy (hg), given bypoint C.The quality of themixture at any point in theliquid-vapor region can be foundusing the following relationship.Figure 11 P-h Diagram for Waterh = xhg + (1 - x)hfxhhfhfgwhere:HT-01h=specific enthalpy of the mixture (Btu/lbm)x=quality of the mixture (no units)hg=specific enthalpy of the saturated vapor (Btu/lbm)hf=specific enthalpy of the saturated liquid (Btu/lbm)hfg=specific enthalpy change of vaporization (Btu/lbm) or hfg = hg - hfPage 44Rev.

0ThermodynamicsPROPERTY DIAGRAMS AND STEAM TABLESEnthalpy-Temperature (h-T) DiagramAn h-T diagram exhibits the same features as on the previous property diagrams. Figure 12 isthe h-T diagram for pure water. An h-T diagram can be constructed for any pure substance. Asin the previous property diagrams, there are regions on the h-T diagram in which two phasesexist together.

The region between the saturated liquid line and the saturated vapor linerepresents the area of two phases existing at the same time. The vertical distance between thetwo saturation lines represents the latent heat of vaporization. If pure water existed at point Aon the saturated liquid line and an amount of heat was added equal to the latent heat ofvaporization, then the water would change phase from a saturated liquid to a saturated vapor(point B), while maintaining a constant temperature.

As shown in Figure 12, operation outsidethe saturation lines results in a subcooled liquid or superheated steam.Figure 12h-T Diagram for WaterThe quality of the mixture at any point in the liquid-vapor region can be found using the samerelationship as shown for the P-h diagram.xRev. 0h hfhfgPage 45HT-01PROPERTY DIAGRAMS AND STEAM TABLESThermodynamicsTemperature-Entropy (T-s) DiagramA T-s diagram is the type of diagram most frequently used to analyze energy transfer systemcycles. This is because the work done by or on the system and the heat added to or removedfrom the system can be visualized on the T-s diagram.

By the definition of entropy, the heattransferred to or from a system equals the area under the T-s curve of the process. Figure 13 isthe T-s diagram for pure water. A T-s diagram can be constructed for any pure substance. Itexhibits the same features as P-υ diagrams.Figure 13 T-s Diagram for WaterIn the liquid-vapor region in Figure 13, water and steam exist together.

For example, at pointA, water with an entropy (sf) given by point B, exists together with steam with an entropy (sg)given by point C. The quality of the mixture at any point in the liquid-vapor region can be foundusing the following relationship.s = xsg + (1 - x)sfxHT-01ssfsfgPage 46Rev. 0ThermodynamicsPROPERTY DIAGRAMS AND STEAM TABLESwhere:s=specific entropy of the mixture (Btu/lbm-°R)x=quality of the mixture (no units)sg=specific entropy of the saturated vapor (Btu/lbm-°R)sf=specific entropy of the saturated liquid(Btu/lbm-°R)sfg=specific entropy change of vaporization (Btu/lbm-°R) or sfg = sg - sfEnthalpy-Entropy (h-s) or Mollier DiagramThe Mollier diagram, shown in Figure A-1 of Appendix A, is a chart on which enthalpy (h)versus entropy (s) is plotted.

It is sometimes known as the h-s diagram and has an entirelydifferent shape from the T-s diagrams. The chart contains a series of constant temperature lines,a series of constant pressure lines, a series of constant moisture or quality lines, and a series ofconstant superheat lines. The Mollier diagram is used only when quality is greater than 50% andfor superheated steam.Steam TablesSteam tables consist of two sets of tables of the energy transfer properties of water and steam:saturated steam tables and superheated steam tables. Portions of the tables are shown in FigureA-2 of Appendix A.

Both sets of tables are tabulations of pressure (P), temperature (T), specificvolume (ν), specific enthalpy (h), and specific entropy (s). The following notation is used insteam tables. Some tables use v for ν (specific volume) because there is little possibility ofconfusing it with velocity.Rev. 0T=temperature (°F)P=pressure (psi)ν=specific volume (ft3/lbm)νf=specific volume of saturated liquid (ft3/lbm)νg=specific volume of saturated vapor (ft3/lbm)Page 47HT-01PROPERTY DIAGRAMS AND STEAM TABLESThermodynamicsνfg=specific volume change of vaporization (ft3/lbm)h=specific enthalpy (Btu/lbm)hf=specific enthalpy of saturated liquid (Btu/lbm)hg=specific enthalpy of saturated vapor (Btu/lbm)hfg=specific enthalpy change of vaporization (Btu/lbm)s=specific entropy (Btu/lbm-°R)sf=specific entropy of saturated liquid (Btu/lbm-°R)sg=specific entropy of saturated vapor (Btu/lbm-°R)sfg=specific entropy change of vaporization (Btu/lbm-°R)Sh=number of degrees of superheat (°F)The saturated steam tables give the energy transfer properties of saturated water and saturatedsteam for temperatures from 32 to 705.47°F (the critical temperature) and for the correspondingpressure from 0.08849 to 3208.2 psi.

Normally, the saturated steam tables are divided into twoparts: temperature tables, which list the properties according to saturation temperature (Tsat); andpressure tables, which list them according to saturation pressure (Psat). Figure A-2 shows aportion of a typical saturated steam temperature table and a portion of a typical saturated steampressure table. The values of enthalpy and entropy given in these tables are measured relativeto the properties of saturated liquid at 32°F. Hence, the enthalpy (hf) of saturated liquid and theentropy (sf) of saturated liquid have values of approximately zero at 32°F.Most practical applications using the saturated steam tables involve steam-water mixtures.

Thekey property of such mixtures is steam quality (x), defined as the mass of steam present per unitmass of steam-water mixture, or steam moisture content (y), defined as the mass of water presentper unit mass of steam-water mixture. The following relationships exist between the quality ofa liquid-vapor mixture and the specific volumes, enthalpies, or entropies of both phases and ofthe mixture itself. These relationships are used with the saturated steam tables.HT-01Page 48Rev.

0ThermodynamicsνxhxsxPROPERTY DIAGRAMS AND STEAM TABLESxν gν(1x) ν fνfν fgxhgh(1x) hfhfhfgxsgs(1x) sfsfsfgIn order to solve problems in Thermodynamics, information concerning the "state" of thesubstance studied must be obtained. Usually, two properties (for example, v, p, T, h, s) of thesubstance must be known in order to determine the other needed properties. These otherproperties are usually obtained utilizing either the Mollier diagram (if the substance is steam) orthe saturated and superheated steam tables, as shown in the Figures A-1 and A-2.The following two examples illustrate the use of the Mollier diagram and the steam tables.Example 1: Use of Mollier Chart.Superheated steam at 700 psia and 680°F is expanded at constant entropy to 140 psia.What is the change in enthalpy?Solution:Use the Mollier Chart.

Locate point 1 at the intersection of the 700 psia and the 680°Fline. Read h = 1333 Btu/lbm.Follow the entropy line downward vertically to the 140 psia line and read h = 1178Btu/lbm.∆ h = 1178 - 1333 = -155 Btu/lbmRev. 0Page 49HT-01PROPERTY DIAGRAMS AND STEAM TABLESThermodynamicsExample 2: Use of steam tablesWhat are the specific volume, enthalpy, and entropy of steam having a quality of 90%at 400 psia?Solution:From the steam tables at 400 psia:νf = 0.01934νg = 1.14162hf = 424.2hfg = 780.4sf = 0.6217sfg = 0.8630ν= νf + x (νfg)ν= 0.01934 + (0.9)(1.14162) = 1.0468 lbm/ft3h= hf + x(hfg)h= 424.2 + (0.90)(780.4) = 1126.56 Btu/lbms= sf + x(sfg)s= 0.6217 + (0.9)(0.8630) = 1.3984 Btu/lbm-°RIf the substance is not water vapor, the "state" of the substance is usually obtained through theuse of T-s (temperature-entropy) and h-s (enthalpy-entropy) diagrams, available in mostthermodynamics texts for common substances.

The use of such diagrams is demonstrated by thefollowing two examples.Example 3: Use of the h-s diagramMercury is used in a nuclear facility. What is the enthalpy of the mercury if its pressureis 100 psia and its quality is 70%?Solution:From the mercury diagram, Figure A-3 of Appendix A, locate the pressure of 100 psia.Follow that line until reaching a quality of 70%. The intersection of the two lines givesan enthalpy that is equal to h = 115 Btu/lbm.HT-01Page 50Rev.

0ThermodynamicsPROPERTY DIAGRAMS AND STEAM TABLESExample 4: Use of the T-s diagramCarbon dioxide is used in a particular process in which the pressure is 100 psia and thetemperature is 100°F. What is the enthalpy value of the gas?Solution:From the carbon dioxide diagram, Figure A-4 of Appendix A, locate the pressure of 100psia. Follow that line until reaching a temperature of 100°F. The intersection of the twolines gives an enthalpy that is equal to h = 316 Btu/lbm.Once the various states have been fixed for the particular process the substance has passedthrough (for example, going from a saturated liquid state to a compressed liquid state across apump), energy exchanges may be determined as was shown in Example 1.