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Phases of a pure substance

Phase change processes of pure substances

Compressed liquid, Saturated liquid, Saturated vapor, Superheated vapor Saturated temperature and Satuated pressure

Property diagrams for phase change processes

The T-v diagram, The P-v diagram, The P-T diagram, The P-v-T diagram

Property tables

Enthalpy

Saturated liquid, Saturated vapor, Saturated liquid vapor mixture, Superheated vapor, compressed liquid

Reference state and Reference values

The ideal gas equation of state

Is water vapor an ideal gas?

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- 1. PROPERTIES OF PURE SUBSTANCES Lecture 6 Keith Vaugh BEng (AERO) MEngReference text: Chapter 4 - Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 KEITH VAUGH
- 2. }KEITH VAUGH
- 3. OBJECTIVESIntroduce the concept of a pure substance. } KEITH VAUGH
- 4. OBJECTIVESIntroduce the concept of a pure substance.Discuss the physics of phase-change processes. } KEITH VAUGH
- 5. OBJECTIVESIntroduce the concept of a pure substance.Discuss the physics of phase-change processes. }Illustrate the P-v, T-v, and P-T propertydiagrams and P-v-T surfaces of puresubstances. KEITH VAUGH
- 6. OBJECTIVESIntroduce the concept of a pure substance.Discuss the physics of phase-change processes. }Illustrate the P-v, T-v, and P-T propertydiagrams and P-v-T surfaces of puresubstances.Demonstrate the procedures for determiningthermodynamic properties of pure substancesfrom tables of property data. KEITH VAUGH
- 7. OBJECTIVESIntroduce the concept of a pure substance.Discuss the physics of phase-change processes. }Illustrate the P-v, T-v, and P-T propertydiagrams and P-v-T surfaces of puresubstances.Demonstrate the procedures for determiningthermodynamic properties of pure substancesfrom tables of property data.Describe the hypothetical substance “ideal gas”and the ideal-gas equation of state. KEITH VAUGH
- 8. }KEITH VAUGH
- 9. Apply the ideal-gas equation of state in the solutionof typical problems. } KEITH VAUGH
- 10. Apply the ideal-gas equation of state in the solutionof typical problems.Introduce the compressibility factor, which accounts }for the deviation of real gases from ideal-gasbehaviour. KEITH VAUGH
- 11. Apply the ideal-gas equation of state in the solutionof typical problems.Introduce the compressibility factor, which accounts }for the deviation of real gases from ideal-gasbehaviour.Present some of the best-known equations of state. KEITH VAUGH
- 12. PURE SUBSTANCE Pure substance A substance that has a ﬁxed chemical composition throughout. Air is a mixture of several gases, but it is considered to be a } pure substance.Nitrogen and gaseous air are pure A mixture of liquid and gaseous water issubstances. a pure substance, but a mixture of liquid and gaseous air is not. KEITH VAUGH
- 13. KEITH VAUGH
- 14. The arrangement of atoms in different phases: (a) molecules are at relatively ﬁxed positions in a solid, (b) groups of molecules move about each other in the liquid phase, and (c) molecules move about at random in the gas phase. KEITH VAUGH
- 15. PHASE CHANGE PROCESSES OF PURE SUBSTANCES } KEITH VAUGH
- 16. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) } KEITH VAUGH
- 17. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. } KEITH VAUGH
- 18. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } KEITH VAUGH
- 19. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } A liquid that is about to vaporise. KEITH VAUGH
- 20. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } A liquid that is about to vaporise. Saturated vapour KEITH VAUGH
- 21. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } A liquid that is about to vaporise. Saturated vapour A vapour that is about to condense. KEITH VAUGH
- 22. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } A liquid that is about to vaporise. Saturated vapour A vapour that is about to condense. Saturated liquid–vapour mixture KEITH VAUGH
- 23. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } A liquid that is about to vaporise. Saturated vapour A vapour that is about to condense. Saturated liquid–vapour mixture The state at which the liquid and vapour phases coexist in equilibrium. KEITH VAUGH
- 24. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } A liquid that is about to vaporise. Saturated vapour A vapour that is about to condense. Saturated liquid–vapour mixture The state at which the liquid and vapour phases coexist in equilibrium. Superheated vapour KEITH VAUGH
- 25. PHASE CHANGE PROCESSES OF PURE SUBSTANCES Compressed liquid (sub-cooled liquid) A substance that it is not about to vaporise. Saturated liquid } A liquid that is about to vaporise. Saturated vapour A vapour that is about to condense. Saturated liquid–vapour mixture The state at which the liquid and vapour phases coexist in equilibrium. Superheated vapour A vapour that is not about to condense (i.e., not a saturated vapour). KEITH VAUGH
- 26. KEITH VAUGH
- 27. At 1 atm and20°C, waterexists in theliquid phase(compressedliquid). KEITH VAUGH
- 28. At 1 atm and At 1 atm pressure20°C, water and 100°C, waterexists in the exists as a liquidliquid phase that is ready to(compressed vaporiseliquid). (saturated liquid). KEITH VAUGH
- 29. At 1 atm and At 1 atm pressure As more heat is20°C, water and 100°C, water transferred, partexists in the exists as a liquid of the saturatedliquid phase that is ready to liquid vaporises(compressed vaporise (saturatedliquid). (saturated liquid–vapour liquid). mixture). KEITH VAUGH
- 30. At 1 atm and At 1 atm pressure As more heat is At 1 atm pressure,20°C, water and 100°C, water transferred, part the temperatureexists in the exists as a liquid of the saturated remains constant atliquid phase that is ready to liquid vaporises 100°C until the last(compressed vaporise (saturated drop of liquid isliquid). (saturated liquid–vapour vaporised liquid). mixture). (saturated vapour). KEITH VAUGH
- 31. At 1 atm and At 1 atm pressure As more heat is At 1 atm pressure, As more heat is20°C, water and 100°C, water transferred, part the temperature transferred, theexists in the exists as a liquid of the saturated remains constant at temperature of theliquid phase that is ready to liquid vaporises 100°C until the last vapour starts to rise(compressed vaporise (saturated drop of liquid is (superheatedliquid). (saturated liquid–vapour vaporised vapour). liquid). mixture). (saturated vapour). KEITH VAUGH
- 32. KEITH VAUGH
- 33. If the entire process between state 1and 5 described in the ﬁgure isreversed by cooling the water whilemaintaining the pressure at the samevalue, the water will go back to state 1,retracing the same path, and in sodoing, the amount of heat released willexactly match the amount of heatadded during the heating process. T-v diagram for the heating process of water at constant pressure. KEITH VAUGH
- 34. SATURATED TEMPERATUREAND SATURATED PRESSURE The temperature at which water starts boiling depends on the pressure; therefore, if the pressure is ﬁxed, so is the boiling temperature. } Water boils at 100°C at 1 atm pressure. Saturation temperature Tsat The temperature at which a pure substance changes phase at a given pressure. Saturation pressure Psat The pressure at which a pure substance changes phase at a given temperature. KEITH VAUGH
- 35. The liquid–vapour saturation curve of apure substance (numerical values arefor water). KEITH VAUGH
- 36. KEITH VAUGH
- 37. Latent heat KEITH VAUGH
- 38. Latent heatThe amount of energy absorbed or released during a phase-change process. KEITH VAUGH
- 39. Latent heatThe amount of energy absorbed or released during a phase-change process.Latent heat of fusion KEITH VAUGH
- 40. Latent heatThe amount of energy absorbed or released during a phase-change process.Latent heat of fusionThe amount of energy absorbed during melting. It is equivalent to the amount ofenergy released during freezing. KEITH VAUGH
- 41. Latent heatThe amount of energy absorbed or released during a phase-change process.Latent heat of fusionThe amount of energy absorbed during melting. It is equivalent to the amount ofenergy released during freezing.Latent heat of vaporisation KEITH VAUGH
- 42. Latent heatThe amount of energy absorbed or released during a phase-change process.Latent heat of fusionThe amount of energy absorbed during melting. It is equivalent to the amount ofenergy released during freezing.Latent heat of vaporisationThe amount of energy absorbed during vaporisation and it is equivalent to theenergy released during condensation. KEITH VAUGH
- 43. Latent heatThe amount of energy absorbed or released during a phase-change process.Latent heat of fusionThe amount of energy absorbed during melting. It is equivalent to the amount ofenergy released during freezing.Latent heat of vaporisationThe amount of energy absorbed during vaporisation and it is equivalent to theenergy released during condensation.The magnitudes of the latent heats depend on the temperature or pressure at whichthe phase change occurs. KEITH VAUGH
- 44. Latent heatThe amount of energy absorbed or released during a phase-change process.Latent heat of fusionThe amount of energy absorbed during melting. It is equivalent to the amount ofenergy released during freezing.Latent heat of vaporisationThe amount of energy absorbed during vaporisation and it is equivalent to theenergy released during condensation.The magnitudes of the latent heats depend on the temperature or pressure at whichthe phase change occurs.At 1 atm pressure, the latent heat of fusion of water is 333.7 kJ/kg and the latentheat of vaporisation is 2256.5 kJ/kg. KEITH VAUGH
- 45. Latent heatThe amount of energy absorbed or released during a phase-change process.Latent heat of fusionThe amount of energy absorbed during melting. It is equivalent to the amount ofenergy released during freezing.Latent heat of vaporisationThe amount of energy absorbed during vaporisation and it is equivalent to theenergy released during condensation.The magnitudes of the latent heats depend on the temperature or pressure at whichthe phase change occurs.At 1 atm pressure, the latent heat of fusion of water is 333.7 kJ/kg and the latentheat of vaporisation is 2256.5 kJ/kg.The atmospheric pressure, and thus the boiling temperature of water, decreaseswith elevation. KEITH VAUGH
- 46. Some Consequences of Tsat and Psat DependenceThe variation of the temperature offruits and vegetables with pressureduring vacuum cooling from 25°Cto 0°C. KEITH VAUGH
- 47. Some Consequences of Tsat and Psat DependenceThe variation of the temperature offruits and vegetables with pressureduring vacuum cooling from 25°Cto 0°C. KEITH VAUGH
- 48. Some Consequences of Tsat and Psat DependenceThe variation of the temperature of In 1775, ice was made byfruits and vegetables with pressure evacuating the air spaceduring vacuum cooling from 25°C in a water tank.to 0°C. KEITH VAUGH
- 49. PROPERTY DIAGRAMS FORPHASE-CHANGE PROCESSES The variations of properties during phase-change processes are best studied and understood with the help of property diagrams such as the T-v, P-v, and P-T diagrams for pure substances. } Recall T-v diagram for the heating process of water at constant pressure. KEITH VAUGH
- 50. KEITH VAUGH
- 51. T-v diagram for a pure substance KEITH VAUGH
- 52. T-v diagram for a pure substance KEITH VAUGH
- 53. T-v diagram for a pure substance KEITH VAUGH
- 54. T-v diagram for a pure substance KEITH VAUGH
- 55. T-v diagram for a pure substance KEITH VAUGH
- 56. T-v diagram for a pure substance KEITH VAUGH
- 57. T-v diagram for a pure substance KEITH VAUGH
- 58. T-v diagram for a pure substance KEITH VAUGH
- 59. T-v diagram for a pure substance KEITH VAUGH
- 60. KEITH VAUGH
- 61. Critical pointThe point at which the saturatedliquid and saturated vapour statesare identical.At supercritical pressures (P > Pcr), there isno distinct phase-change (boiling) process. KEITH VAUGH
- 62. KEITH VAUGH
- 63. T-v diagram of constant-pressurephase-change processes of a puresubstance at various pressures(numerical values are for water). KEITH VAUGH
- 64. KEITH VAUGH
- 65. P-v diagram of a pure substance KEITH VAUGH
- 66. The pressure in a P-v diagram of a pure substancepiston–cylinder devicecan be reduced byreducing the weight ofthe piston. KEITH VAUGH
- 67. Extending the diagrams to include the Solid Phase }P-v diagram of a substance that contracts on freezing KEITH VAUGH
- 68. KEITH VAUGH
- 69. P-v diagram of a substance thatexpands on freezing (such aswater) KEITH VAUGH
- 70. P-v diagram of a substance that At triple-point pressureexpands on freezing (such as and temperature, awater) substance exists in three phases of equilibrium KEITH VAUGH
- 71. Sublimation: Passing from the solidphase directly into the vapour phase.P-T diagram of pure substance KEITH VAUGH
- 72. Sublimation: Passing from the solidphase directly into the vapour phase.P-T diagram of pure substance KEITH VAUGH
- 73. Sublimation: Passing from the solidphase directly into the vapour phase.P-T diagram of pure substance At low pressures (below the triple-point value), solids evaporate without melting ﬁrst (sublimation) KEITH VAUGH
- 74. The P-v-T surfaces present a great deal of information at once, but in athermodynamic analysis it is more convenient to work with two-dimensionaldiagrams, such as the P-v and T-v diagrams.P-v-T surface of a substance thatcontracts on freezing KEITH VAUGH
- 75. The P-v-T surfaces present a great deal of information at once, but in athermodynamic analysis it is more convenient to work with two-dimensionaldiagrams, such as the P-v and T-v diagrams.P-v-T surface of a substance thatcontracts on freezing KEITH VAUGH
- 76. The P-v-T surfaces present a great deal of information at once, but in athermodynamic analysis it is more convenient to work with two-dimensionaldiagrams, such as the P-v and T-v diagrams.P-v-T surface of a substance that P-v-T surface of a substance thatcontracts on freezing expands on freezing (like water) KEITH VAUGH
- 77. PROPERTY TABLESFor most substances, the relationships amongthermodynamic properties are too complex to beexpressed by simple equations. }Properties are frequently presented in the form oftables.Some thermodynamic properties can be measuredeasily, but others cannot and are calculated by usingthe relations between them and measurableproperties.The results of these measurements and calculationsare presented in tables in a convenient format. KEITH VAUGH
- 78. The combination u+Pv isfrequently encountered in theanalysis of control volumes KEITH VAUGH
- 79. The combination u+Pv is frequently encountered in the analysis of control volumesEnthalpy—A Combination Property h = u + Pv ( kg) kJ H = U + PV ( kJ ) KEITH VAUGH
- 80. The combination u+Pv is frequently encountered in the analysis of control volumesEnthalpy—A Combination Property h = u + Pv ( kg) kJ H = U + PV ( kJ ) The product pressure × volume has energy units KEITH VAUGH
- 81. Saturated liquid and saturated vapour statesA partial list of Table A-4 page 994 KEITH VAUGH
- 82. Saturated liquid and saturated vapour states v f = specific volume of saturated liquid vg = specific volume of saturated vapor v fg = difference between v f and vg (that is v fg = vg − v f )A partial list of Table A-4 page 994 KEITH VAUGH
- 83. Saturated liquid and saturated vapour states v f = specific volume of saturated liquid vg = specific volume of saturated vapor v fg = difference between v f and vg (that is v fg = vg − v f ) Enthalpy of vaporisation, hfg (Latent heat of vaporisation) The amount of energy needed to vaporise a unit mass of saturated liquid at a given temperature or pressure.A partial list of Table A-4 page 994Table A–4: Saturation properties of water under temperature, page 994Table A–5: Saturation properties of water under pressure, page 996 KEITH VAUGH
- 84. P-v diagram of saturated liquid andsaturated vapour states of water KEITH VAUGH
- 85. P-v diagram of saturated liquid andsaturated vapour states of water KEITH VAUGH
- 86. P-v diagram of saturated liquid and T-v diagram of saturated liquid andsaturated vapour states of water saturated vapour states of water KEITH VAUGH
- 87. Saturated liquid - vapour mixtureThe relative amounts of liquid andvapour phases in a saturated mixtureare speciﬁed by the quality x. KEITH VAUGH
- 88. Saturated liquid - vapour mixture mvapor The ratio of the mass of Quality, x = vapour to the total mass mtotal of the mixtureThe relative amounts of liquid andvapour phases in a saturated mixtureare speciﬁed by the quality x. KEITH VAUGH
- 89. Saturated liquid - vapour mixture mvapor The ratio of the mass of Quality, x = vapour to the total mass mtotal of the mixture mtotal = mliquid + mvapor = m f + mgThe relative amounts of liquid andvapour phases in a saturated mixtureare speciﬁed by the quality x. KEITH VAUGH
- 90. Saturated liquid - vapour mixture mvapor The ratio of the mass of Quality, x = vapour to the total mass mtotal of the mixture mtotal = mliquid + mvapor = m f + mg Temperature and pressure are depended properties for a mixtureThe relative amounts of liquid andvapour phases in a saturated mixtureare speciﬁed by the quality x. KEITH VAUGH
- 91. Saturated liquid - vapour mixture mvapor The ratio of the mass of Quality, x = vapour to the total mass mtotal of the mixture mtotal = mliquid + mvapor = m f + mg Temperature and pressure are depended properties for a mixtureThe relative amounts of liquid and A two-phase system can bevapour phases in a saturated mixture treated as a homogenousare speciﬁed by the quality x. mixture for convenience KEITH VAUGH
- 92. KEITH VAUGH
- 93. Quality is related to the horizontaldistances on P-v and T-v diagrams KEITH VAUGH
- 94. vavg = v f + xv fg ( kg) m3Quality is related to the horizontaldistances on P-v and T-v diagrams KEITH VAUGH
- 95. vavg = v f + xv fg ( kg) m3 mg x= mtQuality is related to the horizontaldistances on P-v and T-v diagrams KEITH VAUGH
- 96. vavg = v f + xv fg ( kg) m3 mg vavg − v f x= x= mt v fgQuality is related to the horizontaldistances on P-v and T-v diagrams KEITH VAUGH
- 97. vavg = v f + xv fg ( kg) m3 mg vavg − v f x= x= mt v fg uavg = u f + xu fg ( kg) kJ havg = h f + xh fg ( kg) kJQuality is related to the horizontaldistances on P-v and T-v diagrams KEITH VAUGH
- 98. vavg = v f + xv fg ( kg) m3 mg vavg − v f x= x= mt v fg uavg = u f + xu fg ( kg) kJ havg = h f + xh fg ( kg) kJ y → v,u, or h yavg = y f + xy fgQuality is related to the horizontal y f ≤ yavg ≤ ygdistances on P-v and T-v diagrams KEITH VAUGH
- 99. vavg = v f + xv fg ( kg) m3 mg vavg − v f x= x= mt v fg uavg = u f + xu fg ( kg) kJ havg = h f + xh fg ( kg) kJ y → v,u, or h yavg = y f + xy fgThe v value of a saturated liquid–vapour y f ≤ yavg ≤ ygmixture lies between the vf and vg valuesat the speciﬁed T or P. KEITH VAUGH
- 100. Superheated VapourIn the region to the right of the saturatedvapor line and at temperatures above thecritical point temperature, a substanceexists as superheated vapour.In this region, temperature and pressureare independent properties. KEITH VAUGH
- 101. Superheated VapourIn the region to the right of the saturated }vapor line and at temperatures above thecritical point temperature, a substanceexists as superheated vapour.In this region, temperature and pressureare independent properties. A partial listing of Table A-6 page 998 KEITH VAUGH
- 102. Superheated VapourIn the region to the right of the saturated }vapor line and at temperatures above thecritical point temperature, a substanceexists as superheated vapour.In this region, temperature and pressureare independent properties.Compared to saturated vapour, superheated A partial listing of Table A-6vapour is characterised by page 998Lower pressures ( P < Psat at a given T )Higher temperatures (T < Tsat at a given P ) (Higher specific volumes v < vg at a given P or T )Higher specific energies ( u < u at a given P or T ) gHigher enthalpies ( h < h at a given P or T ) g KEITH VAUGH
- 103. Compressed LiquidCompressed liquid is characterised byHigher pressures ( P > Psat at a given T )Lower temperatures (T < Tsat at a given P ) (Lower specific volumes v < vg at a given P or T )Lower specific energies ( u < u at a given P or T ) gLower enthalpies ( h < h at a given P or T ) g KEITH VAUGH
- 104. Compressed LiquidCompressed liquid is characterised byHigher pressures ( P > Psat at a given T )Lower temperatures (T < Tsat at a given P ) (Lower specific volumes v < vg at a given P or T )Lower specific energies ( u < u at a given P or T ) gLower enthalpies ( h < h at a given P or T ) gThe compressed liquid properties depend ontemperatures more so that they do on pressure Given: P and T v ≅ v f @T A compressed liquid may be u ≅ u f @T approximated as a saturatedliquid at a given temperature h ≅ h f @T KEITH VAUGH
- 105. Compressed LiquidCompressed liquid is characterised byHigher pressures ( P > Psat at a given T )Lower temperatures (T < Tsat at a given P ) (Lower specific volumes v < vg at a given P or T )Lower specific energies ( u < u at a given P or T ) gLower enthalpies ( h < h at a given P or T ) gThe compressed liquid properties depend ontemperatures more so that they do on pressure Given: P and T A more accurate relation for h v ≅ v f @T h ≅ h f @T + v f @T ( P − Psat @T ) A compressed liquid may be u ≅ u f @T approximated as a saturatedliquid at a given temperature h ≅ h f @T KEITH VAUGH
- 106. REFERENCE STATE AND REFERENCE VALUES } KEITH VAUGH
- 107. REFERENCE STATE AND REFERENCE VALUES The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties. } KEITH VAUGH
- 108. REFERENCE STATE AND REFERENCE VALUES The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties. } KEITH VAUGH
- 109. REFERENCE STATE AND REFERENCE VALUES The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties. } However, those relations give the changes in properties, not the values of properties at speciﬁed states. KEITH VAUGH
- 110. REFERENCE STATE AND REFERENCE VALUES The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties. } However, those relations give the changes in properties, not the values of properties at speciﬁed states. KEITH VAUGH
- 111. REFERENCE STATE AND REFERENCE VALUES The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties. } However, those relations give the changes in properties, not the values of properties at speciﬁed states. Therefore, we need to choose a convenient reference state and assign a value of zero for a convenient property or properties at that state. KEITH VAUGH
- 112. REFERENCE STATE AND REFERENCE VALUES The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties. } However, those relations give the changes in properties, not the values of properties at speciﬁed states. Therefore, we need to choose a convenient reference state and assign a value of zero for a convenient property or properties at that state. KEITH VAUGH
- 113. REFERENCE STATE AND REFERENCE VALUES The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between properties. } However, those relations give the changes in properties, not the values of properties at speciﬁed states. Therefore, we need to choose a convenient reference state and assign a value of zero for a convenient property or properties at that state. The reference state for water is 0.01°C and for R-134a is -40°C in tables. KEITH VAUGH
- 114. { KEITH VAUGH
- 115. { KEITH VAUGH
- 116. { Some properties may have negative values as a result of the reference state chosen. KEITH VAUGH
- 117. { Some properties may have negative values as a result of the reference state chosen. KEITH VAUGH
- 118. { Some properties may have negative values as a result of the reference state chosen. Sometimes different tables list different values for some properties at the same state as a result of using a different reference state. KEITH VAUGH
- 119. { Some properties may have negative values as a result of the reference state chosen. Sometimes different tables list different values for some properties at the same state as a result of using a different reference state. KEITH VAUGH
- 120. { Some properties may have negative values as a result of the reference state chosen. Sometimes different tables list different values for some properties at the same state as a result of using a different reference state. However, In thermodynamics we are concerned with the changes in properties, and the reference state chosen is of no consequence in calculations. KEITH VAUGH
- 121. Refer to pages, 1003 and 1006 KEITH VAUGH
- 122. IDEAL GAS EQUATION OF STATEEquation of stateAny equation that relates the pressure, temperature, andspeciﬁc volume of a substance. }The simplest and best-known equation of state for substancesin the gas phase is the ideal-gas equation of state. Thisequation predicts the P-v-T behaviour of a gas quiteaccurately within some properly selected region. KEITH VAUGH
- 123. IDEAL GAS EQUATION OF STATEEquation of stateAny equation that relates the pressure, temperature, andspeciﬁc volume of a substance. }The simplest and best-known equation of state for substancesin the gas phase is the ideal-gas equation of state. Thisequation predicts the P-v-T behaviour of a gas quiteaccurately within some properly selected region. ⎛ T ⎞ Ideal Gas P = R ⎜ ⎟ → Pv = RT ⎝ v ⎠ equ. of state KEITH VAUGH
- 124. IDEAL GAS EQUATION OF STATEEquation of stateAny equation that relates the pressure, temperature, andspeciﬁc volume of a substance. }The simplest and best-known equation of state for substancesin the gas phase is the ideal-gas equation of state. Thisequation predicts the P-v-T behaviour of a gas quiteaccurately within some properly selected region. ⎛ T ⎞ Ideal Gas P = R ⎜ ⎟ → Pv = RT ⎝ v ⎠ equ. of state R: gas constant Ru R= M ( kJ kg 3 ⋅ K or kPa ⋅ m kg ⋅ K ) M: molar mass (kg/kmol) Ru: universal gas constant KEITH VAUGH
- 125. Mass = Molar mass × Mole number m = MN ( kg ) KEITH VAUGH
- 126. Mass = Molar mass × Mole number m = MN ( kg ) V = mv → PV = mRT Various expressions of mR = ( MN ) R = NRu → PV = NRuT ideal gas V = Nv → Pv = RuT equation Properties per unit mole are denoted with a bar on the top. KEITH VAUGH
- 127. Mass = Molar mass × Mole number m = MN ( kg ) V = mv → PV = mRT Various expressions of mR = ( MN ) R = NRu → PV = NRuT ideal gas V = Nv → Pv = RuT equation Properties per unit mole are denoted withIdeal gas equation at two states for a ﬁxed mass a bar on the top. P1V1 P2V2 = T1 T2 KEITH VAUGH
- 128. Mass = Molar mass × Mole number m = MN ( kg ) V = mv → PV = mRT Various expressions of mR = ( MN ) R = NRu → PV = NRuT ideal gas V = Nv → Pv = RuT equation Properties per unit mole are denoted withIdeal gas equation at two states for a ﬁxed mass a bar on the top. P1V1 P2V2 = T1 T2Real gases behave as an ideal gas at low densities(i.e., low pressure, high temperature). KEITH VAUGH
- 129. Is water vapour an Ideal Gas? KEITH VAUGH
- 130. Is water vapour an Ideal Gas?At pressures below 10 kPa, water vapourcan be treated as an ideal gas, regardlessof its temperature, with negligible error(less than 0.1 percent). KEITH VAUGH
- 131. Is water vapour an Ideal Gas?At pressures below 10 kPa, water vapourcan be treated as an ideal gas, regardlessof its temperature, with negligible error(less than 0.1 percent).At higher pressures, however, the idealgas assumption yields unacceptableerrors, particularly in the vicinity of thecritical point and the saturated vapourline. KEITH VAUGH
- 132. Is water vapour an Ideal Gas?At pressures below 10 kPa, water vapourcan be treated as an ideal gas, regardlessof its temperature, with negligible error(less than 0.1 percent).At higher pressures, however, the idealgas assumption yields unacceptableerrors, particularly in the vicinity of thecritical point and the saturated vapourline. KEITH VAUGH
- 133. Is water vapour an Ideal Gas?At pressures below 10 kPa, water vapourcan be treated as an ideal gas, regardlessof its temperature, with negligible error(less than 0.1 percent).At higher pressures, however, the idealgas assumption yields unacceptableerrors, particularly in the vicinity of thecritical point and the saturated vapourline.In air-conditioning applications, thewater vapour in the air can be treated asan ideal gas. Why?In steam power plant applications,however, the pressures involved areusually very high; therefore, ideal-gasrelations should not be used. KEITH VAUGH
- 134. Pure substancePhases of a pure substancePhase change processes of pure substances Compressed liquid, Saturated liquid, Saturated vapour, Superheated vapour Saturated temperature and Saturated pressureProperty diagrams for phase change processes The T-v diagram, The P-v diagram, The P-T diagram, The P-v-T diagramProperty tables Enthalpy Saturated liquid, Saturated vapour, Saturated liquid vapour mixture, Superheated vapour, compressed liquid Reference state and Reference valuesThe ideal gas equation of state Is water vapour an ideal gas? KEITH VAUGH

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