MEL140

Properties of pure substances

Pure substance

• A pure substance has the same chemical composition throughout.

• Are the following confined in a fixed volume pure substances:– Ice (single component, single phase) – A mixture of water and water vapor (single component, multiphase)– Air in gas phase (multi-component, single phase)– Oil in contact with water (multi-component single phase)– A gaseous mixture containing N2,O2,H2O, CO2 obtained from burning

kerosene (multicomponent, single phase) – Liquid air in contact with gaseous air (multicomponent, multiphase)

Objective: evaluating the properties for single component pure substances existing in one or more phases (multiphase).

N

Y

N

YYY

Alert: in chemistry a pure substance is defined such that it consists of one component (chemical species) and therefore must be “non-mixture”. We follow a different definition (see above) in engineering thermodynamics.

Phases

Solid Liquid Gas

A region within matter with distinct molecular arrangement that is homogeneousthroughout that region which is separated from other regions (if any) by distinct boundary surfaces. Physical properties (like density and refractive index) of each phase is different.

The three principal phases:

http://www.chem.purdue.edu/gchelp/atoms/states.html

Phase equilibrium

• A system can be composed of subsystems with different molecular arrangements separated by phase boundaries (phases).

• Phase equilibrium prevails when no transfer of mass happens between phases.

The state postulate• A property is characteristic of the system such as specific volume

(v), temperature (T), pressure (P), (specific) internal energy (u).• A state is the condition of a system as determined by its properties.• A simple compressible system is a system whose only mode of

performing quasi-equilibrium work is through a change of its volume against a pressure.

• The state postulate: The state of a simple compressible system consisting of a pure substance is completely specified by two independent intensive properties.

• The state postulate can be represented by an equation of state such as f(p,v,T)=0 (or say g(p,v,u)=0). It is often convenient to represent this functional relationship by – A surface in p,v,T (or u,p,v) space or more commonly its projections

on (p,v), (T,v) and (p,T) planes.– Tables of properties

The P-v diagramRemove just enough heat to keep temperature constantas the volume is reduced.It will be observed that exceptduring 2-3, pressure also needs to be increased for executing this process in a quasi-equilibrium manner.During 1-2 you 4-5 (notduring 2-3-4)

Shows isotherms on P-v diagram

1

23

The critical state: recapitulation• At the critical state (Tc, Pc), saturated liquid and saturated vapor states are identical (SLL intersects SVL).• Increasing/decreasing pressure at a given temperature leads to condensation/evaporation only if a state lies below the critical isotherm.

Phase change processes

Critical properties of common fluids• Water/steam:

– CP: 374o C (647.1 K), 22 Mpa (~more than 200 atm)at which specific volume 0.003106 m3/kg (~three times less dense than @ STP)– BP at atmospheric pressure (101.325 kPa): 100o C (1 atm)

• Refrigerant 134a or R134a or 1,1,1,2-Tetrafluoroethane in your “freeze”:– CP: 101o C, 4 Mpa (~40 atmosphere)– BP at atmospheric pressure : -26o C, 101.325 kPa (1 atm)

• Nitrogen:– CP: -147o C, 3.4 MPa– BP at atmospheric pressure : -196o C

• Carbon-dioxide:– CP: 31.05oC ,7.39 Mpa (CO2 is not a “gas” in Delhi for six months, i.e. Apr-Sept)– BP at atmospheric pressure: -78.5oC

• Table A.1 (Tc,Pc,vc)• How far a state is away from critical point?

Curious facts:

• Critical isotherm and the gas-vapor nomenclature• Supercritical fluidsT>Tcr and P>Pcr

Principle of corresponding states (van der Waal, 1880)

• Reduced temperature: Tr=T/Tc

• Reduced pressure: Pr=P/Pc

• Reduced volume: vr=v/vc

“my equation of state has a universal form

which can be identified by its predicted

behavior at critical point”

“Other equation of states might also be given similar universal forms by the same procedure”.

Regardless of the substance, there is a universal equation of state connecting the reduced co-ordinates. So, thermodynamic states of different substances “correspond”.

( , )r r rf P Tv

Can be stated as:

Principle of corresponding states (van der Waal, 1880, continued)

• Correspondence means the same reduced co-ordinates should mean the sameness of a third reduced property such as reduced volume.

• Compressibility factor is an important reduced property given by:

• Z signifies departure from ideal gas behavior. More discussion on significance in notes.

• Principle of corresponding states: All fluids when compared at the same Tr and Pr have the same Z and deviate from the ideal gas behavior to about the same degree.

• This principle is the basis of classifying systematizing organizing and compacting experimental measurements on P, V and T.

0r r

r

PVPVZZ

RT T

Critical compressibility of real gases

Phase change processes

Some terminology

• Compressed liquid or sub-cooled liquid: Liquid which is not about to vaporize (State 1)

• Saturated liquid: liquid which is about to vaporize (State 2)

• Saturated vapor: vapor which is about to condense (State 4)

• Saturated liquid-vapor mixture: a mixture of saturated liquid and saturated vapor (State 3)

• Superheated vapor: vapor that is not about to condense (State 5)

Phase change processes

Saturatedliquid

Saturated vapor

Saturated liquid vapor mixture

Superheated vapor

Compressed/subcooled liquid

Latent heat

• The energy absorbed by a system during a phase change process at a given pressure/temperature is called latent heat.– Latent heat of fusion (melting)– Latent heat of vaporization (boiling)

• Latent heat goes to change the molecular potential energy; in-fact temperature, a measure of molecular kinetic energy remains constant during a phase change process.

Saturation temperature, saturation pressure and saturation curve• Phase change processes (e.g. “saturated liquid” boiling to

“saturated vapor”) under a given pressure ( “saturation pressure” or Psat) take place at a given temperature

( “saturation temperature” or Tsat).

• Therefore Psat=f (Tsat). A plot of this function is the saturation curve

Saturation curve for water

Property diagram for phase change processes: the T-v diagram.

234

Construct at different pressures

The critical pointThe state (“point”) at whichthe saturated liquid andthe saturated vapor states are identical.

For water

The T-v diagram: saturated liquid line and the saturated vapor line

Saturated liquid and saturated vapor lines meet at the critical point.

Shows isobarson T-v diagram

The P-v diagram

Remove weightsto change pressureduring 1-2, 4-5 (notduring 2-3-4)

Shows isotherms on P-v diagram

Extending the P-v diagram to include solid phase

P-v diagram of a substance whichcontracts on freezing (mostexcept water)

a

a solid at temperature lowerthan melting point

b

b solid begins melting

c

c solid completely melted

d

d liquid begins to vaporize

e

e liquid completely vaporized

Extending the P-v diagram to include solid phase

P-v diagram of a substance whichexpands on freezing(e.g. water)

Saturated liquid linesSaturatedsolid line

a

a ice at -10oC, 1 atm

b

b ice begins melting (0oC), 1 atm

c

c ice completely melted(0oC), 1 atm

d

d water begins to vaporize(100oC), 1 atmee water completely vaporized (100oC), 1 atm

SOLID

LIQUID

The triple line

• The states where all three phases co-exist in equilibrium lie on a straight line on the P-V or T-v diagram known as a triple line.

• All the “triple states” appear as a point on the p-T diagram and the corresponding (T,v) is called a “triple point”.

• Triple point of water: (0oC, 0.61 kPa)

The P-T diagram (“phase diagram”)

The P-v-T surface

For substances which contract on freezing

For substances which expand on freezing (such as water).

Enthalpy: a combination property

• Enthalpy (h):– h=u+pv– Enthalpy is useful for studying processes (such as

vaporization, heat transfer) taking place at constant pressure and processes that involve flow work

Objective

• Evaluate properties of states corresponding to:– saturated liquid and saturated vapor – saturated liquid-vapor mixtures– superheated vapor– compressed/sub-cooled liquid

Saturated liquid and saturated vapor

• Subscript f represents “saturated liquid state”

• Subscript g represents “saturated vapor state”

• Subscript i represents saturated solid state.

• Propertyfg=Propertyg-

Propertyf– e.g. v

fg =vg-vf represents volume change on vaporization

– hfg = =hg-hf represents the “latent heat” or enthalpy of vaporization.

From Table A-4

Specified

Saturated liquid and saturated vapor

• Saturated states lie on the curve f(Psat

, Tsat)=0 and can therefore be

specified by specifying either Psat,

or Tsat

• Table A-4 for water: (Psat,vf,vg,vfg,uf,ug,

ufg,hf,hg,hfg,sf,sg,sfg) listed against Tsat

• Table A-5 for water: (Tsat,vf,vg,vfg,uf,ug,

ufg,hf,hg,hfg,sf,sg,sfg)

listed against Psat

• Same data in Tables A-4 and A-5

From Table A-4

Saturated liquid and saturated vapor

• Subscript f represents “saturated liquid state”

• Subscript g represents “saturated vapor state”

• Propertyfg=Propertyg-

Propertyf

– e.g. vfg =vg-vf represents volume

change on vaporization– hfg = =hg-hf represents the

“latent heat” or enthalpy of vaporization (for vaporization under constant pressure)

From Table A-4

Saturated liquid-vapor mixtures

• Refer to same Tables A-4 and A-5.• The proportion of saturated vapor in the mixture is

indicated by a new property “quality” or “dryness fraction”:

• The average value of a specific extensive property y (such as v,u,h) etc. for the mixture can be calculated from

mass of saturated vapor

total mass of the mixtureg

f g

m

mx

m

f fgy y xy

Saturated liquid-vapor mixtures• Refer to same Tables A-4 and A-5.• The proportion of saturated vapor in the mixture is indicated by a new

property “quality” or “dryness fraction”:

• x=0 for saturated liquid• 0<x<1 for saturated liquid-vapor mixture• x=1 for saturated vapor• x is undefined for compressed liquid and superheated vapor• The average value of a specific extensive property y (such as v,u,h) etc. for the

mixture can be calculated from

mass of saturated vapor

total mass of the mixtureg

f g

m

mx

m

f fgy y xy

• At least two properties need to be given tospecify the state according to state postulate• Usually either T or P and another property is given:• At a superheated state:

– P<Psat @ given T – T> Tsat @ P– v>vg @ P/T– u>ug @ P/T– h>hg @ P/T

• Visit Table A-6 for water

Superheated vapor

Properties of pure substances (continued)

MEL140

Compressed liquid

• At a compressed liquid state– P>Psat @ given T– T<Tsat @ given P– v<vf @ given P/T– u<uf @ given P/T– h<hf @ given P/T

• Usually compressed liquid tables are not available except Table A-7 for water at P> 0.5 MPa

Approximately evaluating properties at the compressed liquid state• For a compressed liquid, properties are weakly

dependent on p.• Treat compressed liquid as a saturated liquid at the

given temperature.• Evaluate:

– v'vf@T– u'uf@T– h'hf?– Usually better approximation for h is:

• h=u+pv'uf+pvf=hf-psatvf+pvf =hf+(p-psat)vf using v'vf and u'uf@T and hf=(uf+ psatvf).

8x10-4 10-2 10-1 100 101 102 10310-1

100

101

102

103

104

105

v [m3/kg]

P [

kPa]

10°C

100°C

SteamNBS

8x10-4 10-3 3x10-310-1

100

101

102

103

104

105

v [m3/kg]

P [

kPa]

10°C

100°C

SteamNBS

At given T, v is not sensitive to p.

If no v is tabulated at given (P,T) find vf@T=Tsat using saturation table (Table A.4 for water)

Evaluate compressed liquid v at (T,p)

Determining the state (summary)

Saturated liquid-vapormixture

(A.4,A.5 for water)

Compressed/subcooled liquid (A.7, A.4 if not A.7 for water)

Superheated vapor(A.6 for water)

P=Psat(T) P>Psat @ T P<Psat@T

T=Tsat(P) T<Tsat @ P T>Tsat@T

vf<v<vg v<vf@P/T v>vg@T

uf<u<ug u<uf@P/T u>ug@P/T

hf<h<hg h<hf@P/T h>hg@P/T

x=(y-yf)/yfg where y=v/u/h(0<x<1)

x undefined x undefined