CHAPTER 3 Properties of Pure Substances 純質的性質. 3.1 Pure Substance 純質 A substance that...

CHAPTER

3

Properties of Pure Substances純質的性質

3.1 Pure Substance純質

3.1 Pure Substance純質

A substance that has a fixed chemical composition throughout is called a Pure Substance.

Pure Substance: - N2, O2, 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: - N2, O2, 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

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

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

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2-1

FIGURE 3-11T-v diagram for the heating process of water at constant pressure.

3.3 Phase-Change Processes of Pure Substance

3.3 Phase-Change Processes of Pure Substance

Saturated temperature 飽和溫度 , Tsat: At a given pressure, the temperature at which a pure substance changes phase.

Saturated pressure 飽和壓力 , Psat: 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 , Tsat: At a given pressure, the temperature at which a pure substance changes phase.

Saturated pressure 飽和壓力 , Psat: 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

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

3.4 Property Diagrams for Phase-Change Processes

The critical-point properties of water: - Pcr= 22.09MPa - Tcr= 374.14C - vcr= 0.003155 m3 /kg

The critical-point properties of helium: - Pcr= 0.23MPa - Tcr= -267.85C - vcr= 0.01444 m3/kg

The critical-point properties of water: - Pcr= 22.09MPa - Tcr= 374.14C - vcr= 0.003155 m3 /kg

The critical-point properties of helium: - Pcr= 0.23MPa - Tcr= -267.85C - vcr= 0.01444 m3/kg

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2-2

FIGURE 3-16T-v diagram of constant-pressurephase-change processes of a puresubstance at various pressures(numerical values are for water).

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2-3

FIGURE 3-18T-v diagram of a pure substance.

3.4 Property Diagrams for Phase-Change Processes

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 & 0.06113 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 & 0.06113 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 3-19P-v diagram of a pure substance.

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2-4

臨界點

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2-5

FIGURE 3-21P-v diagram of a substance thatcontracts on freezing.

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2-6

FIGURE 3-22P-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(f(PP11,P,P22,P,P3 3 ) = 0) = 0

P1

P2

P3

Experimental basis

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

Experimental basis

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

Simple, compressible systems

In simple chemical systems, there is only In simple chemical systems, there is only oneone way to alter E, or U, by way to alter E, or U, by workwork via a via a quasistatic process.quasistatic process.

p, Vp, V

Simple chemical systems

Work interactionWork interaction

Heat interactionHeat interaction SurroundingsSurroundings

SystemSystem

externalF

Q

Interactions = 2Interactions = 2Properties Needed = 3Properties Needed = 3

Simple compressible systems

f(p,V,T) = 0f(p,V,T) = 0

p = p(V,T)p = p(V,T)

V = V(p,T)V = V(p,T)

State and Equilibrium 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) = 0f(U,V,T) = 0

U = U(V,T)U = U(V,T)

V = V (U, T)V = V (U, T)

T = T(U,V)T = T(U,V)

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

The P-v-T surface for water

Ice cube Ice cube andandpure water vaporpure water vapor

Solid-vapor equilibrium.Solid-vapor equilibrium.

At a total constant pressure....At a total constant pressure....p

Water vaporWater vaporWater vaporWater vaporand and

liquid waterliquid water

Ice cube Ice cube andand

water vaporwater vapor

p

p

Add heatAdd heat

The p-V-T surface for water

• Solid in equilibrium with vapor (0 oC)• Solid in equilibrium with vapor and

liquid (0 oC)• Liquid and vapor in equilibrium

( 0 < T < 100 oC)• Saturated Vapor (T = 100 oC)• Superheated Vapor (T > 100 oC)

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- LiquidVapor- Liquid

Critical PointCritical Point

Vapor

Triple Point

p p

T T

Solid

Water

Liquid-vapor Liquid-vapor dome (two-phase)dome (two-phase)

vTriple line (solid-Triple line (solid-liquid-vapor line)liquid-vapor line)

p

Critical pointCritical point

Triple pointTriple point

Tc

Water

v

p Tc

T = TT = Tsatsat

p = pp = psatsat

pp

ppcc

Vapor-liquidVapor-liquidequilibrium atequilibrium atp and Tp and T..

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2-7

FIGURE 3-25P-T diagram of pure substances.

FIGURE 3-26P-v-T surface of a substance that contracts on freezing.

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2-8

FIGURE 3-27P-v-T surface of a substance that expands on freezing (like water).

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2-9

3.5 Property Tables3.5 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 3-30A partial list of Table A–4.

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2-10

FIGURE 3-40A partial listing of Table A–6.

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2-11

Quality... 質

Liquid-vapor equilibrium

Liquid at P,TLiquid at P,T Surroundings

Vapor at P,TVapor at P,TVapor at P,T

Quality

vaporliquid

vapor

mm

mx

The two-phase region for water

pp

Saturated LiquidSaturated Liquid V

Saturated VaporSaturated Vapor

Critical PointCritical Pointgl VVV

gl vvv

lgfg vvv

Quality defined

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

gl vvv

gf vvv

pp

Vgvfv v

Water

v

p Tc

T = TT = Tsatsat

p = pp = psatsat

pp

ppcc

Vapor-liquidVapor-liquidequilibrium atequilibrium atp and Tp and T..

lv gvSpecific volume ofSpecific volume ofthe liquid at p and Tthe liquid at p and T

Specific volume ofSpecific volume ofthe gas at p and Tthe gas at p and T

Quality

vaporliquid

vapor

mm

mx

fgg

fgf

vxxvv

xvvv

1

Internal energy 內能 in the vapor-liquid region

fgg

fgf

uxxuu

xuuu

)1(

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

Temp

(deg C)

Pressure, P

(bars)

Sat Liq, vf x 1000

(m3/kg)

Sat Vapor vg

(m3/kg)

Interanl Engery, uf

(kJ/kg)

Internal Energy, ug

(kJ/kg)

15

0.017

1.001

77.93

62.99

2396.1

20 0.023 1.002 57.79 83.95 2402.9

50 100

0.124 1.014

1.012 1.043

12.03 1.673

209.3 418.9

2443.5 2506.5

At the critical point for water

CT

barp

kgkJuu

oc

c

gf

14.374

9.220

/6.2029

Compressed liquids

v v f

u u f

3.6 The Ideal-Gas Equation of State理想氣體方程式

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 containerbut exhibits a free surface.

A liquid will take the shape of its containerbut exhibits a free surface.

A gas will fill its containercompletely and does notexhibit a free surface.

A gas will fill its containercompletely and does notexhibit a free surface.

What is gas?

gasgas

containergas

PT

VV

,

The ideal gas...

P-V-T relation for ideal gases

TT11

TT22

TT33

pp

T

vp

RT

vp

p

lim0

The ideal gas equation of state

TRvp 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

Rlbmollbfft

KkmolkJ

RMR

/1545

/314.8

M = Molecular weightM = Molecular weight 分子量分子量 , , kg/kmol or lbm/lbmol.kg/kmol or lbm/lbmol.

The ideal gas state surface

Ideal Gas State Surfacepp

VTT

The perfect gas

1

.

RT

Pv

Rvcpc

constvc

3.7 Compressibility Factor 壓縮因子 - A Measure of Derivation from Ideal-Gas

Behavior

3.7 Compressibility Factor 壓縮因子 - A Measure of Derivation from Ideal-Gas

Behavior Compressibility Factor, Z Z = Pv/RT Z = vactual/videal

Ideal gas: Z = 1 Real gases: Z > 1 Z = 1 Z < 1

Compressibility Factor, Z Z = Pv/RT Z = vactual/videal

Ideal gas: Z = 1 Real gases: Z > 1 Z = 1 Z < 1

Real gases...

Real Gases

P

1

Z

T1

T2

T3

T1 < T2 < T3Ideal Gas

TR

vp

The virial form for compressibility

....3

)(2

)()(1

v

TD

v

TC

v

TBZ

TRZvp

3.8 Other Equations of State3.8 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

FluidFluid

GasGas

Ideal gasIdeal gas

Perfect gasPerfect gas

Compressibility factorCompressibility factor

Compressibility chartCompressibility chart

Local equilibriumLocal equilibrium

Reduced pressureReduced pressure

Reduced temperatureReduced temperature

Thermodynamic pressureThermodynamic pressure

Virial equation of stateVirial equation of state