Chapter 2

Properties of Pure Substances

Ability to acquire and explain the basic

concepts in thermodynamics

Course Learning OutcomesThe student should be able to:

• Define saturated liquid, saturated vapor, saturated liquid-vapor mixture,

compressed liquid, superheated vapor, critical points, and triple point.

• Sketch a P-v, T-v, and P-T diagrams and identify the phase regions of pure

substances on the diagrams.substances on the diagrams.

• Obtain thermodynamic properties of pure substances from property tables.

• Show the state of pure substance on a P-v and T-v diagram with respect to

saturation lines.

• Show the isobaric, isochoric and isothermal processes on a P-v and T-v

diagram with respect to saturation lines.

• Solve problems related to properties and processes of pure substance

2.1 Pure substance

2.2 Equilibrium phases of pure substance

2.3 Phase change processes of pure substance2.3 Phase change processes of pure substance

2.4 Property diagrams for phase change processes

2.5 Property tables

2.6 The ideal gas equation of state

2.1 Pure Substance� Pure substance - A substance that has a fixed chemical

composition throughout

� Examples of pure substances:

1. Water (solid, liquid, and vapor phases)

2. Mixture of liquid water and water vapor

3. CO2

4. N2

5. Mixtures of gases, such as air, as long as there is no

change of phase

6. He

� Air is a mixture of several gases, but it is considered to be a

pure substance.

Nitrogen and gaseous air are pure substances.

6

A mixture of liquid and gaseous water is a pure substance, but a

mixture of liquid and gaseous air is not.

2.2 Equilibrium phases of pure substance

Phase is identified as having a distinct molecular arrangement that is

homogeneous throughout and separated from the others by easily

identifiable boundary surfaces.

The arrangement of atoms in different phases:

(a) solid phase - molecules are at relatively fixed positions

(b) liquid phase - groups of molecules move about each other in the

molecules

(c) gas phase - move about at random

Equilibrium phases of pure substance

Phase equilibrium: Phase equilibrium: Phase equilibrium: Phase equilibrium: If a system involves two phases and when the mass of each phase reaches an equilibrium level and stays there.

State PostulateState PostulateState PostulateState Postulate

8

State PostulateState PostulateState PostulateState PostulateThe state postulate for a simple, pure substance states that the equilibrium state can be determined by specifying any two independent intensive properties.

2.3 Phase-change processes of pure

substance

Saturated vapor

Saturated liquid

- Water exists in

the liquid phase

- compressed

liquid or

subcooled liquid:

A substance that

it is not about to

vaporize.

- Water exists as a

liquid that is ready

to vaporize

- saturated liquid:

A liquid that is

about to vaporize..

- As more heat is

transferred, part of

the saturated liquid

vaporizes

-saturated liquid-

vapor mixture

- At 1 atm

pressure, the

temperature

remains constant

at 100°C until the

last drop of liquid

is vaporized

- saturated vapor

- As more heat is

transferred, the

temperature of

the vapor starts

to rise

- superheated

vapor

If the entire process between state 1 and 5 described in the figure is reversed by cooling the water (maintain the pressure at the same value), the water will go back to state 1, retracing the same path, and in so doing, the amount of heat released amount of heat released amount of heat released amount of heat released (during the cooling process) will exactly match the amount of (during the cooling process) will exactly match the amount of (during the cooling process) will exactly match the amount of (during the cooling process) will exactly match the amount of heat addedheat addedheat addedheat added during the heating process.

T-v diagram for the heating process of water at constant pressure

• Saturation temperature Saturation temperature Saturation temperature Saturation temperature TTTTsatsatsatsat: The temperature at which a pure substance changes phase at a given pressure.

• Saturation pressure Saturation pressure Saturation pressure Saturation pressure PPPPsatsatsatsat: The pressure at which a pure substance changes phase at a given temperature.

11

Example: For water (pure substance)

At a pressure of 101.325 kPa, Tsat is 99.97°C.

At a temperature of 99.97°C, Psat is 101.325 kPa.

• 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.

1212

The liquid-vapor saturation curve of a pure substance

(water). Cengel 6th Ed pg 116

Example 2.1Example 2.1Example 2.1Example 2.1

Determine the saturation pressure, Psat for water at temperature of

i) 25°Cii) 225°C.

13

Determine the saturation temperature, Tsat for water at pressure of

i) 1.23 kPaii) 500 kPa.

� Latent heatLatent heatLatent heatLatent heat: The amount of energy absorbed or released during a phase-change process.

� Latent heat of fusionLatent heat of fusionLatent heat of fusionLatent heat of fusion: The amount of energy absorbed during melting (equivalent to the amount of energy released during freezing). released during freezing).

� Latent heat of vaporization: Latent heat of vaporization: Latent heat of vaporization: Latent heat of vaporization: The amount of energy absorbed during vaporization (equivalent to the energy released during condensation)

14

� The magnitudes of the latent heats depend on the temperature or pressure at which the phase change occurs.

� At 1 atm pressure, the latent heat of fusion of water is 333.7 kJ/kg and the latent heat of vaporization is 2256.5 kJ/kg.

� Atmospheric pressure and boiling temperature of water decrease with water decrease with increases of elevation.

15

The variations of properties during phase-change processes are best studied using property diagrams for

pure substances.

T-v Diagram

P-vDiagram

P-TDiagram

The T-v Diagram

17T-v diagram of constant-pressure phase-change processes of water (pure

substance) at various pressures. Cengel 6th Ed pg 119.

At supercritical pressures (P >Pcr), there is no a distinct phase-change process.

18

Critical pointCritical pointCritical pointCritical point: The point at which the saturated liquidsaturated liquidsaturated liquidsaturated liquid and saturated vaporsaturated vaporsaturated vaporsaturated vaporstates are identical

19

The P-v Diagram

20P-v diagram of a pure substance.

The pressure in a piston-cylinder

device can be reduced by

reducing the weight of the

piston.

At triple-point pressure and

temperature, a substance exists in

three phases in equilibrium.

For water, Ttp = 0.01°C Ptp = 0.6117

kPa

21

P-v diagram of a substance that contracts on freezing.

P-v diagram of a substance that expands on freezing (such as

water).

Phase Diagram

The P-T Diagram

22

P < Ptp: Sublimation (Evaporation directly without melting first)

P > Ptp: Melting -> Evaporation

P > Ptp

23

Sublimation

P < Ptp

2.5 Property Tables

• For most substances, the relationships among thermodynamic properties

are too complex to be expressed by simple equations.

• Therefore, properties are frequently presented in the form of tables.

• Some thermodynamic properties can be measured easily, but others

cannot and are calculated by using the relations between them and

measurable properties. measurable properties.

• The results of these measurements and calculations are presented in

tables in a convenient format.

Table A–4: Saturation properties of water under temperature. Pg 916-917

Table A–5: Saturation properties of water under pressure. Pg 918-919

Table A–6: Superheated properties of water. Pg 920-923

Table A–7: Compressed liquid water. Pg 924

Enthalpy - A Combination Property

The product pressure × volume has

energy units.or

25

The combination u + Pv is frequently encountered in

the analysis of control volumes.

Saturated Liquid and Saturated Vapor States

Table A–4: Saturation properties of water under temperature. Pg 916

Table A–5: Saturation properties of water under pressure. Pg 918

A partial list of Table A–4.

26

Enthalpy of vaporization, hfg (Latent heat of

vaporization): The amount of energy needed

to vaporize a unit mass of saturated liquid at a

given temperature or pressure.

The subscript fgfgfgfg used in Tables A–4 and A–5 refers to the difference between the saturated vapor value and the saturated liquid value region. That is,

u u ufg g f= −

27

h h h

s s s

fg g f

fg g f

= −

= −

A rigid tank contains 50 kg of saturated liquid water at 90°C. Determine the pressure in the tank and the volume of the tank.

Example Example Example Example 3.23.23.23.2

28

A piston-cylinder device contains 0.06 m3 of saturated water vapor at 350 kPa pressure. Determine the temperature and the mass of the vapor inside the cylinder.


29

A mass of 200 g of saturated liquid water is completely vaporized at a constant pressure of 100 kPa. Determinea) The volume changeb) The amount of energy transferred to the water


30

• During vaporization process, a substance exists as part liquid and part vapor � mixture of saturated liquid and saturated vapor

31

The relative amounts of liquid and vapor phases in a saturated mixture are specified by the quality xquality xquality xquality x.

vapor g gmass m mx

mass m m m= = =

+

• Quality, Quality, Quality, Quality, x : The ratio of the mass of vapor to the total mass of the mixture.

• Quality is between 0 and 1 Quality is between 0 and 1 Quality is between 0 and 1 Quality is between 0 and 1 �� 0: sat. liquid, 1: sat. vapor.0: sat. liquid, 1: sat. vapor.0: sat. liquid, 1: sat. vapor.0: sat. liquid, 1: sat. vapor.

total t f g

xmass m m m

= = =+

32

We note

, ,

f g

f g

t avg f f f g g g

V V V

m m m

V m v V m v V m v

= +

= +

= = =

Substituting mf = mt – mg, dividing (1) by mt

and substituting mg/mt = x yields A two-phase system can be treated as a

t

(1)f f g gmv m v m v= +mtvavg

33

(1 )avg f gv x v xv= − +

and substituting mg/mt = x yields

avg f fgv v xv= +

avg f

fg

v vx

v

−=

A two-phase system can be treated as a

homogeneous mixture for convenience.

where vfg = vg - vf

Then

y v, u, or h.• The previous relationships can be summarized in a

single equation as:

• This application is called the Lever Rule

34

The v value of a saturated liquid–vapor

mixture lies between the vf and vg values at

the specified T or P.

avg f

fg

v vx

v

−=

Example 3.4

A rigid tank contains 10 kg of water at 90°C. If 8 kg of the water is in the liquid

form and the rest is in the vapor form, determine:

a) The pressure in the tank

b) The volume of the tank

35


An 80-L vessel contains 4 kg of refrigerant-134a at a pressure of 160 kPa. Determine:

a) The temperatureb) The qualityc) The enthalpy of the refrigerantd) The occupied by the vapor phase

36

Table ATable ATable ATable A––––6666: Superheated properties of water. Pg 920

• In the region to the right of the saturated vapor line and at temperatures above the critical point temperature, a substance exists as superheated vapor.

• In this region, temperature and pressure are independent properties.

ExerciseExerciseExerciseExerciseExerciseExerciseExerciseExercise

Identify:a) Saturated vapor lineb) Critical pointc) Superheated vapor region!

What is the phase of this region?

P or T

v

Compared to saturated vapor, superheated vapor is characterized by

A partial listing of Table A–6.

At a specified P, superheated vapor exists

at a higher h than the saturated vapor.


Determine the internal energy of water at 200 kPa and 300°C.

Example Example Example Example 3.73.73.73.7Example Example Example Example 3.73.73.73.7

Determine the temperature of water at a state of P=0.5 MPa and h=2890 kJ/kg.

Table ATable ATable ATable A––––7777: Compressed liquid water. Pg 924

Compressed liquid is characterized by

At a given P and T, a pure substance will exist as a compressed liquid if

y y y y →→→→ v, u, or h

•A more accurate relation for h

• A compressed liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid

• The compressed liquid properties depend on temperature much more strongly than they do on pressure.

• A compressed liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid may be approximated as a saturated liquid at the given temperature.at the given temperature.at the given temperature.at the given temperature.

Example 3.8Example 3.8Example 3.8Example 3.8

Determine the internal energy of compressed liquid water at 80°C and 5 Mpa using

a) Data from the compressed liquid tableb) Data from saturated-liquid data

What is the error involved in the second case?

2.6 The ideal gas equation of state

• Equation of state: Any equation that relates the pressure, temperature, and

specific volume of a substance.

Ideal gas equation of

state

43

R: gas constant

M: molar mass (kg/kmol)

Ru: universal gas constant

Different substances have different gas

constants.

Mass = Molar mass × Mole number

Various expressions of ideal gas equation

Ideal gas equation at two states for a fixed mass

44

Properties per unit mole are denoted with a bar on the top.

Determine the mass of the air in a room whose

dimensions are 4 m x 5 m x 6 m at 100 kPa and

25°C.

Technology

Chapter 2