CHAPTER 3 Properties of Pure Substances 純質的性質

3.1 Pure Substance 純質  A substance that has a fixed chemical composition throughout is called a Pure Substance.  Pure Substance: - N 2, O 2, gaseous Air -A mixture of liquid and gaseous water is a pure substance, but a mixture of liquid and gaseous Air is not.  A substance that has a fixed chemical composition throughout is called a Pure Substance.  Pure Substance: - N 2, O 2, gaseous Air -A mixture of liquid and gaseous water is a pure substance, but a mixture of liquid and gaseous Air is not.

3.2 Phases of a Pure Substance 純質的相  Solid 固體 : -The molecules in a solid are kept at their positions by the large springlike intermolecular forces. -The attractive and repulsive forces between the molecules tend to maintain them at relatively constant distances from each other.  Liquid 液體 : Groups of molecules move about each other.  Gas 氣體 : Molecules move about at random.  Solid 固體 : -The molecules in a solid are kept at their positions by the large springlike intermolecular forces. -The attractive and repulsive forces between the molecules tend to maintain them at relatively constant distances from each other.  Liquid 液體 : Groups of molecules move about each other.  Gas 氣體 : Molecules move about at random.

3.3 Phase-Change Processes of Pure Substance 純質的相變化過程  Compressed liquid 壓縮液體 or a subcooled liquid 過冷液體 : A liquid that is not about to vaporize. 汽化  Saturated liquid 飽和液體 : A liquid that is about to vaporize.  Saturated vapor 飽和蒸汽 : A vapor that is about to condense.  Saturated liquid-vapor mixture 飽和液汽混 合物 : the liquid and vapor phases coexist in equilibrium.  Superheated vapor 過熱汽體 : A vapor that is not about to condense  Compressed liquid 壓縮液體 or a subcooled liquid 過冷液體 : A liquid that is not about to vaporize. 汽化  Saturated liquid 飽和液體 : A liquid that is about to vaporize.  Saturated vapor 飽和蒸汽 : A vapor that is about to condense.  Saturated liquid-vapor mixture 飽和液汽混 合物 : the liquid and vapor phases coexist in equilibrium.  Superheated vapor 過熱汽體 : A vapor that is not about to condense

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-1 FIGURE 3-11 T-v diagram for the heating process of water at constant pressure.

3.3 Phase-Change Processes of Pure Substance  Saturated temperature 飽和溫度, T sat : At a given pressure, the temperature at which a pure substance changes phase.  Saturated pressure 飽和壓力, P sat : At a given temperature, the pressure at which a pure substance changes phase.  Latent heat 潛熱 : the amount of energy absorbed or released during a phase-change process.  Latent heat of fusion 熔解潛熱 : the amount of energy absorbed during melting.  Latent heat of vaporization 蒸發潛熱 : the amount of energy absorbed during vaporization.  Saturated temperature 飽和溫度, T sat : At a given pressure, the temperature at which a pure substance changes phase.  Saturated pressure 飽和壓力, P sat : At a given temperature, the pressure at which a pure substance changes phase.  Latent heat 潛熱 : the amount of energy absorbed or released during a phase-change process.  Latent heat of fusion 熔解潛熱 : the amount of energy absorbed during melting.  Latent heat of vaporization 蒸發潛熱 : the amount of energy absorbed during vaporization.

3.4 Property Diagrams for Phase- Change Processes  The T-v diagram: -Critical point: the point at which the saturated liquid and saturated vapor states are identical. -Saturated liquid line: -Saturated vapor line: -Compressed liquid region: -Superheated vapor region: -Saturated liquid-vapor mixture region:  The T-v diagram: -Critical point: the point at which the saturated liquid and saturated vapor states are identical. -Saturated liquid line: -Saturated vapor line: -Compressed liquid region: -Superheated vapor region: -Saturated liquid-vapor mixture region:

3.4 Property Diagrams for Phase- Change Processes  The critical-point properties of water: - P cr = 22.09MPa - T cr = C - v cr = m 3 /kg  The critical-point properties of helium: - P cr = 0.23MPa - T cr = C - v cr = m 3 /kg  The critical-point properties of water: - P cr = 22.09MPa - T cr = C - v cr = m 3 /kg  The critical-point properties of helium: - P cr = 0.23MPa - T cr = C - v cr = m 3 /kg

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-2 FIGURE 3-16 T-v diagram of constant- pressure phase-change processes of a pure substance at various pressures (numerical values are for water).

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-3 FIGURE 3-18 T-v diagram of a pure substance.

3.4 Property Diagrams for Phase- Change Processes  The P-v diagram: - The triple line 三相線 : three phases of a pure substance coexist in equilibrium, these triple-phase states forms a line. - The triple point 三相點 : the triple line appears as a point on the P-T diagrams. For water, 0.01C & kPa -Sublimation 昇華 : Passing from the solid phase directly into the vapor phase.  The P-T diagram(phase diagram 相圖 ):  The P-v-T surface:  The P-v diagram: - The triple line 三相線 : three phases of a pure substance coexist in equilibrium, these triple-phase states forms a line. - The triple point 三相點 : the triple line appears as a point on the P-T diagrams. For water, 0.01C & kPa -Sublimation 昇華 : Passing from the solid phase directly into the vapor phase.  The P-T diagram(phase diagram 相圖 ):  The P-v-T surface:

FIGURE 3-19 P-v diagram of a pure substance. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-4 臨界點

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-5 FIGURE 3-21 P-v diagram of a substance that contracts on freezing.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-6 FIGURE 3-22 P-v diagram of a substance that expands on freezing (such as water).

EVALUATING THERMODYNAMIC PROPERTIES The P-V-T Surface for Water

Description of thermodynamic state f( P 1,P 2,P 3 ) = 0 P1P1 P2P2 P3P3

Experimental basis One independent property for each way that the energy of the system can be varied independently.

Experimental basis The number of independent properties that uniquely describes the state of the system is the number of relevant work interactions plus one. one.

Simple, compressible systems In simple chemical systems, there is only one way to alter E, or U, by work via a quasistatic process. p, V

Simple chemical systems Work interaction Heat interaction Surroundings System Interactions = 2 Properties Needed = 3

Simple compressible systems f(p,V,T) = 0 f(p,V,T) = 0 p = p(V,T) V = V(p,T)

State and Equilibrium  A simple compressible system: The state of a simple compressible system is completely specified by two independent, intensive properties. -two properties specified be independent to fix the state. -Once the two properties are fixed, all the other properties become dependent properties.  A simple compressible system: The state of a simple compressible system is completely specified by two independent, intensive properties. -two properties specified be independent to fix the state. -Once the two properties are fixed, all the other properties become dependent properties.

State Equations f(p,V,T) = 0 p(V,T) = p v(p,T) = V T(p,V) = T f(U,V,T) = 0 U = U(V,T) V = V (U, T) T = T(U,V)

The p-V-T surface for water...

The P-v-T surface for water Ice cube and pure water vapor Solid-vapor equilibrium.

At a total constant pressure.... p Water vapor and liquid water Ice cube and water vapor p p Add heat

The p-V-T surface for water Solid in equilibrium with vapor (0 o C) Solid in equilibrium with vapor and liquid (0 o C) Liquid and vapor in equilibrium ( 0 < T < 100 o C) Saturated Vapor (T = 100 o C) Superheated Vapor (T > 100 o C)

The P-v-T Surface for Water Vapor T P V Liquid Solid Critical Point

The p-T plane for water, Phase diagram Liquid Vapor- Liquid Critical Point Vapor Triple PointpT Solid

Water Liquid-vapor dome (two-phase) v Triple line (solid- liquid-vapor line) p Critical point Triple point TcTc

Water v p TcTc T = T sat p = p sat p pcpcpcpc Vapor-liquid equilibrium at p and T.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-7 FIGURE 3-25 P-T diagram of pure substances.

FIGURE 3-26 P-v-T surface of a substance that contracts on freezing. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-8

FIGURE 3-27 P-v-T surface of a substance that expands on freezing (like water). Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-9

3.5 Property Tables  Table A-4: Saturated water-Temperature table  Table A-5: Saturated water-Pressure table  Table A-6: Superheated water  Enthalpy, H H= U + PV (kj) h= u + Pv (kj/kg)  Entropy, S  Table A-4: Saturated water-Temperature table  Table A-5: Saturated water-Pressure table  Table A-6: Superheated water  Enthalpy, H H= U + PV (kj) h= u + Pv (kj/kg)  Entropy, S

FIGURE 3-30 A partial list of Table A–4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-10

FIGURE 3-40 A partial listing of Table A–6. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-11

Quality... 質

Liquid-vapor equilibrium Liquid at P,T Surroundings Vapor at P,T

Quality

The two-phase region for water p Saturated Liquid V Saturated Vapor Critical Point

Quality defined Quality, x, allows location of states inside the vapor-liquid region. p V

Water v p TcTc T = T sat p = p sat p pcpcpcpc Vapor-liquid equilibrium at p and T. Specific volume of the liquid at p and T Specific volume of the gas at p and T

Quality

Internal energy 內能 in the vapor-liquid region

Key concepts and terms Critical point P - v - T surface Quality Saturation pressure Saturation temperature State equation State surface The State Principle Triple point

ADDITIONAL ASPECTS OF THE P-V-T SURFACE FOR WATER

The P-v-T surface for water Liquid Vapor- Liquid Critical Point Vapor T P V Liquid Solid Critical Point Vapor Triple Point P T Solid

Water

At the critical point for water

Compressed liquids

3.6 The Ideal-Gas Equation of State 理想氣體方程式  Equation of state 狀態方程式 : Any equation that relates the pressure, temperature, and specific volume of a substance.  Gas: The vapor phase of a substance  Vapor: A gas that is not far from a state of condensation  Equation of state 狀態方程式 : Any equation that relates the pressure, temperature, and specific volume of a substance.  Gas: The vapor phase of a substance  Vapor: A gas that is not far from a state of condensation

Definition of gas...

Fluids 流體 and gases 氣體 A liquid will take the shape of its container but exhibits a free surface. A liquid will take the shape of its container but exhibits a free surface. A gas will fill its container completely and does not exhibit a free surface. A gas will fill its container completely and does not exhibit a free surface.

What is gas?

The ideal gas...

P-V-T relation for ideal gases T1T1T1T1 T2T2T2T2 T3T3T3T3 p

The ideal gas equation of state This implies: (1) very little molecular interaction (p = 0), (2) molecules are point masses, i.e., zero volume.

The universal gas constant 萬有氣體常數 M = Molecular weight 分子量, kg/kmol or lbm/lbmol.

The ideal gas state surface Ideal Gas State Surfacep V T

The perfect gas

3.7 Compressibility Factor 壓縮因子 - A Measure of Derivation from Ideal-Gas Behavior  Compressibility Factor, Z Z = Pv/RT Z = v actual /v ideal  Ideal gas: Z = 1  Real gases: Z > 1 Z = 1 Z < 1  Compressibility Factor, Z Z = Pv/RT Z = v actual /v ideal  Ideal gas: Z = 1  Real gases: Z > 1 Z = 1 Z < 1

Real gases...

Real Gases P 1 Z T1T1 T2T2 T3T3 T 1 < T 2 < T 3 Ideal Gas

The virial form for compressibility

3.8 Other Equations of State  Van der Waals Equation of state:  Beattie-Bridgeman Equation of state:  Benedict-Webb-Rubin Equation of state:  Virial Equation of state:  Van der Waals Equation of state:  Beattie-Bridgeman Equation of state:  Benedict-Webb-Rubin Equation of state:  Virial Equation of state:

Key concepts and terms FluidGas Ideal gas Perfect gas Compressibility factor Compressibility chart Local equilibrium Reduced pressure Reduced temperature Thermodynamic pressure Virial equation of state