Chapter 3 Properties of Pure Substances

AE 2031 APPLIED THERMODYNAMICS S. Y. B. Tech.
PROPERTIES OF
PURE SUBSTANCES
Prof. Aniket Suryawanshi
Asst. Prof. Automobile Engg. Dept.
R. I. T. Rajaramnagar

OUTLINE OF CHAPTER
PHASE CHANGE OF PURE SUBSTANCE.
PHASE CHANGE TERMINOLOGY.
PROPERTY DIAGRAM.
FORMATION AND PROPERTIES OF STEAM.
USE OF STEAM TABLE AND MOLLIER CHART.
ENTROPY CHANGES OF STEAM (NUMERICALS ONLY).
P-V-T SURFACE.

What is a Pure Substance ?
 A substance that has a fixed chemical composition throughout.
 A pure substance can exist in more than one phase, but its
chemical composition must be the same in each phase.
PURE SUBSTANCE
Examples:
 Drinking water with ice cubes can be regarded as a pure substance because each phase has the
same composition.
 A fuel-air mixture in the cylinder of an automobile engine can be regarded as a pure substance
until ignition occurs.

PURE SUBSTANCE
• Air is a mixture of several gases, but it
is considered to be a pure substance.
Is pure substance comprised of two or more chemical element or compound?
 Can be single element: Such as, N2, H2, O2
 Compound: Such as Water, H2O, C4H10,
 Mixture such as Air,
 2-phase system such as H2O.
A pure substance is comprised of a single
chemical element or compound.

PURE SUBSTANCE
Single Chemical Element 1
Compound or Mixture
Single Chemical Element 2
+

• Because the mixture is homogeneous or
uniform, the composition is the same
throughout.
• As long as the composition remains
constant and uniform throughout, this
mixture can be treated as a pure substance.
We call this a pseudocomponent.
A Homogeneous (uniform) Mixture can
often be treated as a Pure Substance.
• Consider the Heterogeneous Mixture
shown here. The composition near the
top of the vessel is very different from
the composition near the bottom of the
vessel.
A Heterogeneous (or non-uniform)
Mixture cannot be treated as a Pure
Substance.
Homogeneous Heterogeneous
PURE SUBSTANCE

Molecules move randomly with three different
types of motions are vibration, rotation and
translation.
Molecules are separated by large distances and
travel a long way between collisions.
GAS PHASE

LIQUID PHASE
Molecules move randomly with all three types
of motions, are vibration, rotation and
translation.
But they are much closer together and cannot
travel very far between collisions.

SOLID PHASE
Atoms or molecules have all three types of
motion, but they are very close together. As a
result, they cannot travel far at all before they
collide.
Each molecule moves about within a small
space and does not tend to wander.
In a solid, the attractive and repulsive forces between the molecules
tend to maintain them at relatively constant distances from each other.

PHASE
Homogeneity in physical structure means that the matter is all solid, or all liquid, or all
vapor (gas).
A quantity of matter that is homogeneous throughout in both chemical composition and
physical structure.
Examples:
►The air we breathe is a gas phase consisting of a mixture of different gases.
►Drinking water with ice cubes contains two phases of water: liquid and solid.
►Vinegar and olive oil salad dressing contains two different liquid phases.
PHASE:-

PHASE CHANGE
Principle Phases: Solid (ice), Liquid (Water), and Gas (Water Vapor).
• Sunlight causes water molecules to leave the solid phase and enter the liquid phase.
• Sunlight also causes water molecules to leave the liquid phase and enter the gas phase.

PHASE EQUILIBRIUM
Consider a glass of ice water placed inside a sealed, perfectly insulated container.
Initially, the ice begins to melt and the water
begins to evaporate.
Eventually, the ice stops melting and the water
stops evaporating.
The system has reached phase equilibrium.
• Phase Equilibrium is characterized by uniform temperature throughout the system
and by no NET changes in the mass or composition of any phases.
• Phase equilibrium turns out to be a central concept in this course.

13
a
SUPERHEATED
VAPOR
SATURATED
VAPOR
COMPRESSED
LIQUID
SATURATED
LIQUID
COEXISTENT LIQUID
AND VAPOR
PHASE CHANGE PROCESS

PROPERTY DIAGRAMS FOR PHASE CHANGE PROCESSES
The variations of properties during phase-change processes are best studied and understood
with the help of property diagrams such as the T-v diagrams for pure substances.
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 (wet
region)

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

with the help of property diagrams such as the P-v diagrams for pure substances.

with the help of property diagrams such as the P-v diagrams for pure substances.
For water,
Ttp = 0.01°C
Ptp = 0.6117 kPa
At triple-point pressure and temperature, a substance exists in three phases in equilibrium.

with the help of property diagrams such as the P-T diagrams for pure substances.
At low pressures (below the triple-point value), solids evaporate without melting
first (sublimation).
Sublimation: Passing
from the solid phase
directly into the vapor
phase.

Temp., T
Pr.,P
S
L
V
Melting
Freezing
Boiling / Evaporation
Condensation
Sublimation
Solidification
0.01 ºC
0.006112 bar
100 ºC
1 atm
TP
TP = Triple Point
All 3 Phases in
Existence..!!
= f (PTP ,TTP)
CP
CP = Critical Point
≡ L and V Phases
have Same Pr.
but ρ difference.
When it vanishes,
it is CP.
PROPERTY DIAGRAM OF WATER
221.2 bar
374.15 ºC

Table I (A-4) and Table II (A-5) :
Liquid – Vapour Saturation State.
Table I : Temp. – based Table II : Pr. – based&
vf , vg uf , ug hf , hg sf , sg
hfg = hg – hf
sf g = sg – sf
Triple Point : uf = 0 kJ/kg.
Sf = 0 kJ/kg.K
TTP = 0.01 ºC
Definition
Critical Point :
L – V diff. vanishes..!!
uf = ug
sf = sg
vf = vg
ufg = ug – uf
STEAM TABLE

Examples: saturated liquid and saturated vapor states of water on
T-v and P-v diagrams.

Examples: Saturated liquid-vapor mixture states on T-v and P-v
diagrams.
SATURATED LIQUID–VAPOR MIXTURE

SATURATED LIQUID–VAPOR MIXTURE
Quality, x : The ratio of the mass of vapor to the total mass of the mixture. Quality is
between 0 and 1 0: sat. liquid, 1: sat. vapor.
The properties of the saturated liquid are the same whether it exists alone or in a
mixture with saturated vapor.
The relative
amounts of
liquid and
vapor phases
in a saturated
mixture are
specified by
the quality x. A two-phase system can be treated
as a homogeneous mixture for
convenience.
Temperature and pressure
are dependent properties
for a mixture.

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.
At a specified P,
superheated
vapor exists at a
higher h than the
saturated vapor.
Compared to saturated vapor, superheated
vapor is characterized by
SUPERHEATED VAPOR

Compressed liquid is characterized by
y  v, u, or h
A more accurate relation for h
A compressed liquid may
be approximated as a
saturated liquid at the
given temperature.
The compressed liquid properties
depend on temperature much more
strongly than they do on pressure.
COMPRESSED LIQUID OR SUB-COOLED LIQUID

AE 2031 APPLIED THERMODYNAMICS S. Y. B. Tech.28
Reference State and Reference Values
• The values of u, h, and s cannot be measured directly, and they are calculated from measurable
properties using the relations between properties.
• However, those relations give the changes in properties, not the values of properties at specified
states.
• Therefore, we need to choose a convenient reference state and assign a value of zero for a
convenient property or properties at that state.
• The reference state for water is 0.01°C and for R-134a is -40°C in tables.
• Some properties may have negative values as a result of the reference state chosen.
• Sometimes different tables list different values for some properties at the same state as a result of
using a different reference state.
• However, In thermodynamics we are concerned with the changes in properties, and the reference
state chosen is of no consequence in calculations.

Any equation that relates the Pressure, Temperature and Sp. Volume of the
substance is known as Equation of State.
In 1662, Robert Boyle, observed that Pressure of the gas is inversely proportional to
its Volume.
i.e. PV = C
In 1802, J. Charles, observed that Volume of the gas is directly proportional to its
Temperature.
i.e. V /T= C







v
T
RP OR Pv = RT
This equation is called Ideal Gas Equation of State.
The hypothetical gas that obeys this law, is known as Ideal Gas.
IDEAL GAS AND REAL GAS
Between 1800 - 1802, J. Gay-Lussac, observed that Temperature of the gas is directly
proportional to its Pressure.
i.e. T /P= C

R is the Constant of Proportionality, given by the unit ( kJ / kg.K )
Now, V (Total Volume) = m.v (Sp. Vol.)
PV = mRT→
Thus, for a fixed mass;
2
22
1
11
T
VP
T
VP

Behaviour of a Real Gas approaches to the that of an Ideal Gas, at low densities.
Thus, at low pressures and high temperatures, the density of the gas decreases
and the gas approaches to Ideal Gas.

Ideal gas equation can be used with assumptions of very little or no attraction
force of molecules within the gas and the volume of the molecules is negligibly
small compared to volume of the gas.
For many gases, at low pressures and high temperatures, the force of
intermolecular attraction and volume of molecules compared to the volume of
gas are significantly small and the real gases obeys very closely the ideal gas
equation.
At higher pressure the force of intermolecular attraction and repulsion are
significant and the volume of molecules are also appreciable compared to the
volume of gas.
Behaviour of a Real Gas deviates from an Ideal Gas, at high pressures.

• Ideal gas
• Real gas
Z
Z
PV
RT
RT
PV
M
M














1
Z is the ratio of the “real molar volume” over the
“ideal molar volume” of a substance measured at the
same pressure and temperature.
1
RT
PVM
Z
RT
PVM

EQUATIONS OF STATE FOR GASES

Z-FACTOR CHART FOR VARIOUS GASES

Z-FACTOR CHART FOR LOW REDUCED PRESSURES

COMPRESSIBILITY CHARTS FACTORS
• The use of compressibility chart requires knowledge of critical parameter
given in factor and TR for several gases.
• The results obtained by using compressibility chart are accurate within few
percentage.
• The deviation of real gas behaviour from that of ideal gas is greatest in
vicinity of the critical point.
• Only one compressibility factor chart can be used to determine volumetric
properties of any pure fluid by using its reduced properties.
• The shape of this chart is in general.

PSEUDO-REDUCED PROPERTIES
• Better results can be obtained for some gases which having multicomponent
systems, in this case the coordinates used are “pseudo-reduced coordinates”
• For a mixture you can use the “pseudo-reduced property” charts as for a pure
component.
• For mixtures the same type of charts apply but using “pseudo-reduced
properties” which are defined similarly as the ratio of pressure (or temperature)
with “pseudo-reduced critical pressure" (or temperature). These pseudo-critical
properties are an average of the critical properties of the components in the
mixture.
“All fluids when compared at the same reduced temperature and reduced pressure, have
approximately the same compressibility factor, and all deviate from ideal gas behavior to
about the same degree”

PSEUDOCRITICAL PROPERTIES OF NATURAL GASES
cr
pr
P
P
P 
cr
pr
T
T
T 
Pseudo-reduced Pressure
Pseudo-reduced Temperature
Pseudo-reduced specific volume
crcr
pr
PRT
v
v
/


COMPRESSIBILITY FACTOR Z AS A FUNCTION OR PSEUDOREDUCED PRESSURE
COMPRESSIBILITY CHART WITH PSEUDO-REDUCED PROPERTIES

Que. 1. Determine the specific volume of refrigerant-134a at 1 MPa and 500c, using
a)The ideal gas equation of state
b)The generalized compressibility chart.

kgm
P
RT
v /026325.0
1000
)323)(0815.0( 3

a) By using Ideal Gas Equation:

Z = 0.84
Pr=0.246
246.0
059.4
1

cr
pr
P
P
P
863.0
2.374
323

cr
pr
T
T
T
}Z=0.84
v= Z videal
v= 0.84 x 0.026325
v= 0.022113 m3/kg
b) By using Compressibility charts:

Que. 2. Determine the pressure of water vapor at 3500c and 0.035262 m3/kg, using
a) the steam table
b) the ideal gas equation of state
c) the generalized compressibility chart.
MPaP 0.7
a) By using Steam Table:

b) By using Ideal Gas Equation:
MPa
v
RT
P 15.8
035262.0
)623)(4615.0(


c) By using Compressibility charts:
605.2
)1006.22/()1.647)(4615.0(
035262.0
/ 3



crcr
actual
pr
PRT
v
v
}96.0
1.647
623

cr
pr
T
T
T
Pcr = 0.31
P = Ppr x Pcr
P = 0.31 x 22.06
P = 6.84 MPa

MOLLIER CHARTS (h-s diagram)

Que. 3. Determine the amount of heat removed from system at 1 bar and 4500c, to 1
bar and 4000c using Mollier chart.
NUMERICALS ON MOLLIER CHARTS (h-s diagram)

Que. 4. Determine the specific enthalpy at 10 bar, using Mollier chart.
a) When steam is dry and saturated vapor.
b) When steam has dryness fraction 0.9.
c) When steam is heated with 500c degree of superheat.

Degree of Superheat = 500 c
hsup=2872 KJ/kg
hsat=2778 KJ/kg
h = 2574 KJ/kg

Application of Ideal Gas Equation is limited to a specific range.
Therefore, it is required to have more accurate predictions for a substance, over a
larger region and without limitations.
Several equations are proposed by various scientists and researchers.
1. Van der Waal’s Equation of State (1873) :
  RTbv
v
a
p 





 2
a and b are Constants.
This equation takes into account :
1. Intermolecular attraction forces.
2. Volume occupied by the molecules themselves.

2. Beattie – Bridgeman Equation of State (1928) :
  232
1
v
A
Bv
vT
c
v
TR
p u














v
a
AA 10 






v
b
BB 10
Where, And
= molar volume in m3/kg-mol
Ru = Universal gas constant = 8.314 kJ/kg-mol-K
v

3. Benedict – Webb - Rubin Equation of State (1940) :
2
236322
0
00 1
1 vu
u
u
e
vvT
c
v
a
v
aTbR
vT
C
ATRB
v
TR
p

 















Where,
P = pressure in kPa
T = Absolute temperature in K
v

4. Redlich-Kwong Equation of State (1949) :
2/1
)( Tbvv
a
bv
TR
p u




c
cu
P
TR
a
5.22
427.0Where, And
v
c
cu
P
TR
b 0866.0

5. Virial Equation of State :
......1 432
v
d
v
c
v
b
v
a
RT
pv

RT
a
A 1Where, And
v
......1 4
4
3
3
2
21 pApApApA
RT
pv

22
2
2
TR
ab
A



Thank You !

Chapter 3 Properties of Pure Substances

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