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).
Y
Y
Y
N
Y
N
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
A region within matter with distinct molecular arrangement that is homogeneous
throughout 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:
Solid
Liquid
Gas
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 diagram
3
Remove just enough heat
to keep temperature constant
as the volume is reduced.
It will be observed that except
during 2-3, pressure also
needs to be increased for
executing this process in a
quasi-equilibrium manner.
During 1-2 you 4-5 (not
during 2-3-4)
2
1
Shows isotherms on
P-v diagram
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:
•
Refrigerant 134a or R134a or 1,1,1,2-Tetrafluoroethane in your “freeze”:
•
Nitrogen:
– 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)
–
–
CP: 101o C, 4 Mpa (~40 atmosphere)
BP at atmospheric pressure : -26o C, 101.325 kPa (1 atm)
– 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 fluidsT>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
Regardless of the substance, there is a
universal equation of state connecting the
reduced co-ordinates. So, thermodynamic
states of different substances “correspond”.
“my equation of state
has a universal form
which can be identified
by its predicted
behavior at critical
point”
Can be stated as:
v r  f ( Pr , T r )
“Other equation of states
might also be given similar
universal forms by the same
procedure”.
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 
PV
RT
•
 Z0
Pr V r
Tr
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.
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
Compressed/
subcooled liquid
Saturated vapor
Saturated
liquid
Superheated vapor
Saturated liquid
vapor mixture
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.
234
Construct at
different pressures
The critical point
The state (“point”) at which
the saturated liquid and
the saturated vapor states are
identical.
For water
The T-v diagram: saturated liquid line and the
saturated vapor line
Shows isobars
on T-v diagram
Saturated liquid and saturated vapor lines meet at the critical point.
The P-v diagram
Remove weights
to change pressure
during 1-2, 4-5 (not
during 2-3-4)
Shows isotherms on
P-v diagram
Extending the P-v diagram to include solid
phase
a solid at temperature lower
than melting point
b solid begins melting
c solid completely melted
d liquid begins to vaporize
e liquid completely vaporized
a
b
c
d
e
P-v diagram of a
substance which
contracts on
freezing (most
except water)
Extending the P-v diagram to include solid
phase
a ice at -10oC, 1 atm
Saturated liquid lines
Saturated
solid line
LIQUID
a c b d
SOLID
e
b ice begins melting
(0oC), 1 atm
c ice completely melted
(0oC), 1 atm
d water begins to vaporize
(100oC), 1 atm
e water completely
vaporized (100oC), 1 atm
P-v diagram of a
substance which
expands on freezing
(e.g. water)
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=PropertygPropertyf
Specified
From Table A-4
–
e.g. v
fg =vg-vf
represents volume
change on vaporization
– hfg = =hg-hf represents the
“latent heat” or enthalpy of
vaporization.
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=PropertygPropertyf
–
e.g. v
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
fg =vg-vf
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
m ass of saturated vapor
total m ass of the m ixture

mg
m f  mg
• The average value of a specific extensive property y (such
as v,u,h) etc. for the mixture can be calculated from
y  y f  xy fg
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
m ass of saturated vapor
total m ass of the m ixture
•
•
•
•
•

mg
m f  mg
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
y  y f  xy fg
Superheated vapor
• At least two properties need to be given to
specify 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
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).
Evaluate compressed liquid v at (T,p)
SteamNBS
105
SteamNBS
104
5
10
P [kPa]
103
104
100°C
102
101
10 T,
At given
v is not
10
8x10
sensitive
to p.
10°C
0
-1
-4
3
P [kPa]
10
102
3x10-3
10-3
3
v [m /kg]
100°C
101
0
10
10-1
8x10-4
If no v is tabulated at given (P,T)
find vf@T=Tsat using saturation table (Table
A.4 for water)
10°C
10-2
10-1
100
3
v [m /kg]
101
102
103
Determining the state (summary)
Saturated liquid-vapor
mixture
(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