Properties ofProperties ofPure SubstancesPure Substances

Pure SubstancePure SubstancePure SubstancePure Substance A substance that has a fixed (homogeneous and invariable) chemical composition throughout is called a pure substance.

It may exist in more than one phase, but the chemical composition is the same in all phases.

Pure SubstancePure Substance Pure means “…of uniform and invariable

chemical composition (but more than one molecular type is allowed).” This allows air to be a pure substance.

All our substances will be pure. We will drop the use of the word. When we refer to a simple system we mean one filled with a pure substance--a simple, pure system.

Examples of Pure SubstanceExamples of Pure SubstanceExamples of Pure SubstanceExamples of Pure Substance

Water (solid, liquid, and vapor phases) Mixture of liquid water and water

vapor Carbon Dioxide Nitrogen Homogeneous mixture of gases, such as

air, as long as there is no change of phases.

Multiple phases mixture Multiple phases mixture of a Pure Substanceof a Pure Substance

vapor

liquid

vapor

liquid

Water Air

Pure OH 2

Not pure, different condensation temperatures for different components

Thermodynamic PropertiesThermodynamic Properties We have discussed extensive properties

such as m, U, and V (for volume) which depend on the size or extent of a system, and

Intensive properties such as u, v, T, and P (sometimes we write a “p” for pressure, using P and p interchangeably) which are independent of system extent.

Important Questions .….Important Questions .…. How many properties are needed to

define the state of a system? How do we obtain those properties?

Equation of StateEquation of State

Property TablesProperty Tables

Review - State PostulateReview - State Postulate The number of independent intensive

properties needed to characterize the state of a system is n+1 where n is the number of relevant quasiequilibrium work modes.

This is empirical, and is based on the experimental observation that there is one independent property for each way a system’s energy can be independently varied.

Simple systemSimple system A simple system is defined as one for

which only one quasiequilibrium work mode applies.

Simple compressible systems Simple elastic systems Simple magnetic systems Simple electrostatic systems, etc.

CompressibleCompressible

If we restrict our system to being compressible, we define what that quasiequilibrium work mode is:

PdV,W

Pdv

m

Vd P w

m

W

For a simple system,For a simple system, We may write P = P(v,T)

or v = v(P,T)

or perhaps T = T(P,v)

For a simple, pure substanceFor a simple, pure substance

y0 = y(y1,y2), or

P = P(v,T), v = v(P,T), and T = T(P,v)

What do these equations define, in space?

Equations used to relate properties are called “Equations of State”

Equation of StateEquation of State Any two independent, intrinsic properties are

sufficient to fix the intensive state of a simple substance.

One of the major task of Thermodynamics is to develop the equations of state which relate properties at a give state of a substance.

),(210 yyyy

Ideal gas “law” is a simple Ideal gas “law” is a simple equation of stateequation of state

RTPv

M

RR u

mRTPV

Ru = universal gas constant

= 8.3144 (kPa-m3)/(kgmol-K)

= 1.545 (ft-lbf)/(lbmol-R)

Phases of a Pure SubstancePhases of a Pure Substance

Solid phase -- molecules are arranged in a 3D pattern (lattice).

Liquid phase -- chunks of molecules float about each other, but maintain an orderly structure and relative positions within each chunk.

Gas phase -- random motion, high energy level.

Phase Equilibrium

p

heat

ice

p

liquid

ice

P = 1 atmT = -10 oC

liquid

p

liquid

p

vapor

p

vapor

P = 1 atmT = 0 oC

P = 1 atmT = 20 oC

P = 1 atmT = 100 oC

P = 1 atmT = 300 oC

Phase-change ProcessPhase-change Process

Compressed liquid -- not about to evaporate Saturated liquid -- about to evaporate Saturated liquid-vapor mixture --two phase Saturated Vapor -- about to condense Superheated Vapor -- not about to condense

T-v DiagramT-v Diagram

1Com

pres

sed

liqu

id

Saturated mixture

2

Supe

rhea

ted

vapo

r

Isobaric process P = 1 atm

34

5

v

T, Co

20

100

300

P-TP-T Diagram (Phase Diagram) Diagram (Phase Diagram) of Pure Substancesof Pure Substances

P-TP-T Diagram (Phase Diagram) Diagram (Phase Diagram) of Pure Substancesof Pure Substances

GAS @ gGAS

State d

W eight

LIQUID

GAS

W eight

LIQUID @ a

P

T

g

P

T

g

d

P

T

g

d

a

Superheated Vapor

Compressed Liquid

Isothermal ProcessIsothermal Process

P

T

bfa

P

T

b

Gas @ bGas @ b

Q

GAS

STATE f

LIQUID

Q

GASLIQUID

Q

P

T

bf

Superheated Vapor

Subcooled Liquid

Isobaric Process

a

Water Expands on Freezing!Water Expands on Freezing!

Ice floats on top of the water body (lakes, rivers, oceans, soft drinks, etc.).

If ice sinks to the bottom (contracts on freezing), the sun’s ray may never reach the bottom ice layers.

This will seriously disrupt marine life.

Saturation Temperature Saturation Temperature and Pressureand Pressure

Tsat -- Temperature at which a phase change takes place at a given pressure.

Psat -- Pressure at which a phase

change takes place at a given temperature.

Saturation TemperatureSaturation Temperature

Tsat = f (Psat)

p = 1atm = 101.3 kPa, T = 100 C

p = 500 kPa, T = 151.9 C

o

o

*T and P are dependent during phase change

*Allow us to control boiling temperature by controlling the pressure (i.e., pressure cooker).

Latent HeatLatent Heat Latent heat is the amount of energy

absorbed or released during phase change

Latent heat of fusion -- melting/freezing =333.7 kJ/kg for 1 atm H2O

Latent heat of vaporization --boiling/condensation =2257.1 kJ/kg for 1 atm H2O

P

v

Superheated region --substance is 100% vapor

Two-phase or saturation region -- gas

and liquid coexist

Subcooled or compressed liquid region

Satu

rate

d liq

uid

line

Saturated vapor line

Critical point

P-v DiagramP-v Diagram

P-v Diagram of a Pure P-v Diagram of a Pure SubstanceSubstance

P-v Diagram of a Pure P-v Diagram of a Pure SubstanceSubstance

SUPERHEATED

vIsothermal process

T-v Diagram of a T-v Diagram of a Pure SubstancePure Substance

T-v Diagram of a T-v Diagram of a Pure SubstancePure Substance

v

Critical & SupercriticalCritical & SupercriticalCritical & SupercriticalCritical & Supercritical The state beyond which there is no distinct

vaporization process is called the critical point.

At supercritical pressures, a substance gradually and uniformly expands from the liquid to vapor phase.

Above the critical point, the phase transition from liquid to vapor is no longer discrete.

Critical PointCritical Point Point at which the saturated vapor

and saturated liquid lines coincide. If T Tc or P Pc there is no clear

distinction between the superheated vapor region and the compressed liquid region.

Critical PointCritical Point A point beyond which T Tc and a

liquid-vapor transition is no longer possible at constant pressure. If T Tc , the substance cannot be liquefied, no matter how great the pressure.

Substances in this region are sometimes known as “fluids” rather than as vapors or liquids.

Vapor (Steam) DomeVapor (Steam) Dome The dome-shaped region encompassing the

two-phase, vapor-liquid equilibrium region. It is bordered by the saturated liquid line and

the saturated vapor line, both of which end at the triple line and end at the critical point.

The region below the vapor dome is also called: saturated liquid-vapor region, wet region, two-phase region, or saturation region.

THERMODYNAMIC TABLES

STEAM STEAM IS NOT AN IS NOT AN

IDEAL IDEAL GAS!GAS!

Steam TablesSteam Tables Table A-1.1 Saturation water -- temperature table Table A-1.2 Saturation water -- pressure table Table A-1.3 Superheated vapor

P

v

saturation region

p=psat and T=Tsat

superheated region

If T=Tsat , ppsat

If p=psat , T>Tsat

Subcooled or

compressed

liquid region

If T=Tsat, ppsat

If p=psat,TTsat

For WaterFor Water

Two properties are not Two properties are not independent in the vapor dome independent in the vapor dome

(the two-phase region)(the two-phase region)

The temperature and pressure are uniquely related. Knowing a T defines the P and vice versa.

Use quality to determine the state in two-phase region.

Quality is related to the horizontal Quality is related to the horizontal differences of P-v and T-v Diagramsdifferences of P-v and T-v DiagramsQuality is related to the horizontal Quality is related to the horizontal

differences of P-v and T-v Diagramsdifferences of P-v and T-v Diagrams

QualityQualityQualityQuality In a saturated liquid-vapor mixture, the mass fraction

(not volume fraction) of the vapor phase is called the quality and is defined as

The quality may have values between 0 (saturated liquid) and 1 (saturated vapor). It has no meaning in the compressed liquid or superheated vapor regions.

mmm

mmm

mm

gf

g

vaporliquid

vapor

total

vaporx

What is v for something in the What is v for something in the two-phase region?two-phase region?

m

mvmv

m

V V

m

V v

vapgliqfvapliq

x1m

m;

m

mx

tot

liq

tot

vap

v = (1-x)vf + xvg = vf + x(vg - vf) = vf + xvfg

Enthalpy in Two-Phase RegionEnthalpy in Two-Phase Region

H = U + pV

h = u + pv

h = (1-x)hf + xhg = hf + x(hg - hf)

= hf + xhfg

Saturated MixtureSaturated MixtureSaturated MixtureSaturated Mixture In the saturated mixture region, the average value of any intensive property y is determined from

where f stands for saturated liquid and g for saturated vapor.

v = vf + x(vg - vf) = vf + xvfg

u = uf + x(ug - uf) = uf + xufg

h = hf + x(hg - hf) = hf + xhfg

s = sf + x(sg - sf) = sf + xsfg

Saturated MixtureSaturated Mixture

f : saturated liquidg : saturated vapor

Saturated Water (temperature)

Superheated Vapor

Examples 3-2 thru 3-7 Steam Tables A-1.1 and A-1.3

TEAMPLAYTEAMPLAYComplete the table below as a team. The substance is water. Make sure everybody understands how to do it!

P (MPa) T(C) v(m3/kg) x (if appl.)

300 1.0

0.15 0.65

0.50 300

TEAMPLAYTEAMPLAYComplete the table below as a team. The substance is water. Use linear interpolation if needed.

P(MPa) T(C) u (kJ/kg) x (if appl.)

7.0 0.0

7.0 1.0

7.0 0.05

7.0 600

7.0 100

7.0 460