Chapter: 7 Phase Change Process of Pure Substance
Brij Bhooshan
Basic and Applied Thermodynamics
Chapter: 7 Phase Change Process of Pure
Substance
Prepared By
Brij Bhooshan
Asst. Professor
B. S. A. College of Engg. And Technology
Mathura, Uttar Pradesh, (India)
Supported By:
Purvi Bhooshan
In This Chapter We Cover the Following Topics
7.1 Properties and Important Definitions
7.2 Graphical Representation Of P-V-T Data for Pure Substances
7.3 p-v Diagram for A Pure Substance
References:
1. M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 6e,
John Wiley & Sons, Inc., New York, 2008.
2. G. J. Van Wylen, R. E. Sonntag, C. Borgnakke, Fundamentals of Thermodynamics, John
Wiley & Sons, Inc., New York, 1994.
3. J. P. Holman, Thermodynamics, 4e, McGraw-Hill, New York, 1988.
4. F. W. Sears, G. L. Salinger, Thermodynamics, Kinetic theory, and Statistical
Thermodynamics, 3e, Narosa Publishing House, New Delhi, 1998.
5. Y. A. Cengel and M. A. Boles, Thermodynamics: An Engineering Approach, 2e, McGrawHill, New York, 1994.
6. E. Rathakrishnan, Fundamentals of Engineering Thermodynamics, 2e, PHI Learning
Private Limited, New Delhi, 2008.
7. P. K. Nag, Basic and Applied Thermodynamics, 1e, McGraw-Hill, New Delhi, 2010.
8. V Ganesan, Gas Turbine, 2e, Tata McGraw-Hill, New Delhi, 2003.
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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
Page 1
Chapter: 7 Phase Change Process of Pure Substance
Brij Bhooshan
9. Y. V. C. Rao, An Introduction to Thermodynamics, 1e, New Age International (P)
Limited, Publishers, New Delhi, 1998.
10. Onkar Singh, Applied Thermodynamics, 2e, New Age International (P) Limited,
Publishers, New Delhi, 2006.
Please welcome for any correction or misprint in the entire manuscript and your
valuable suggestions kindly mail us [email protected].
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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
Page 2
Chapter: 7 Phase Change Process of Pure Substance
Brij Bhooshan
There are certain situations when two phases of a pure substance coexist in equilibrium. As
a commonly used substance water may be taken up to demonstrate the basic principles
involved. However, all pure substances exhibit the same general behavior. Pure substance
refers to the “substance with chemical homogeneity and constant chemical composition.”
H2O is a pure substance as it meets both the above requirements. Any substance, which
undergoes a chemical reaction, cannot be pure substance.
7.1 PROPERTIES AND IMPORTANT DEFINITIONS
Pure substance as defined earlier is used for operating various systems, such as steam is
used for power generation in steam power plants. Hence, for thermodynamic analysis
thermodynamic properties are required. Pressure and temperature are the properties that
can be varied independently over wide range in a particular phase. Therefore, the
behaviour of properties of pure substance have to be studied and mathematical
formulations be made for their estimation.
Various dependent properties discussed ahead shall be enthalpy, internal energy, specific
volume, entropy etc.
We shall remember the following definitions:
a) Sensible heating: It refers to the heating of substance in single phase. It causes rise
in temperature of substance. In case of cooling in above conditions it shall be called
sensible cooling.
b) Latent heating: It is the heating of substance for causing its phase change without
any change in it’s temperature. If heat is extracted for causing phase change without
any change in its temperature it will be called latent cooling.
c) Normal boiling point: It is the temperature at which vapour pressure equals to
atmospheric pressure and at this temperature phase change from liquid to gas
begins.
d) Melting point: It is the temperature at which phase change from solid to liquid takes
place upon supplying latent heat.
e) Saturated State: A state at which a phase change begins or ends. Saturation state of
a substance refers to the state at which its phase transformation takes place without
any change in pressure and temperature. These can be saturated solid state,
saturated liquid state and saturated vapour state. For example saturated vapour
state refers to the state of water at which its phase changes to steam without
varying pressure and temperature.
f) Saturation Temperature: Temperature at which phase change (liquid-vapour) begins
or ends at a given pressure
It refers to the temperature at which substance changes its phase for any given
pressure. For water at 1 atm pressure the saturation temperature is 100°C.
g) Saturation Pressure: It is the pressure at which phase change begins or ends at a
specified temperature.
It is the pressure at which substance changes its phase for any given temperature.
Such as at any given temperature water shall get converted into steam at a definite
pressure only, this pressure is called saturation pressure corresponding to given
temperature.
For water at 100°C the saturation pressure is 1 atm pressure.
h) Saturated Liquid: It is the substance at
which is fully liquid (no-vapour).
i) Saturated Vapour: It is the substance at
which is fully vapour (no-liquid).
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Chapter: 7 Phase Change Process of Pure Substance
j)
k)
l)
m)
n)
o)
Brij Bhooshan
Subcooled Liquid: If the temperature of the liquid (T) is less then
then the liquid
is called sub-cooled liquid.
Superheated Vapour: If the temperature of the vapour (T) is greater than
then
the vapour is called superheated vapour.
Triple point: Triple point of a substance refers to the state at which substance can
coexist in solid, liquid and gaseous phase in equilibrium. For water it is 0.01°C i.e. at
this temperature ice, water and steam can coexist in equilibrium.
Critical states: “Critical state refers to that state of substance at which liquid and
vapour coexist in equilibrium.” In case of water at 22.12 MPa, and 374.15°C the
water and vapour coexist in equilibrium, thus it is the highest pressure and
temperature at which distinguishable water and vapour exist together.
Specific volume at critical point for water is 0.00317 m3/kg.
Dryness fraction: It is the mass fraction of vapour in a mixture of liquid and vapour
at any point in liquid-vapour mixture region. It is generally denoted by ‘x’. It is also
called quality of steam.
Compressed liquid or subcooled liquid: Liquid at temperature less than saturation
temperature corresponding to a given pressure is called compressed liquid or
subcooled liquid. Degree of subcooling is given by the temperature difference
between liquid temperature and saturation temperature of liquid at given pressure.
Degree of subcooling = Saturation temperature at given pressure – Temperature of
liquid.
p) Superheated steam: Steam having temperature more than the saturation
temperature corresponding to given pressure is called superheated steam. Amount
of superheating is quantified by degree of superheating. Degree of superheating is
given by difference between temperature of steam and saturation temperature at
given pressure.
Degree of superheating = Temperature of steam – Saturation temperature at given pressure.
7.2 GRAPHICAL REPRESENTATION OF P-v-T DATA FOR PURE SUBSTANCES
The commonly used thermodynamic diagrams are
 Pressure versus Temperature (P − T)
 Pressure versus Volume (P − v)
 Temperature versus Volume (T − v)
 Temperature versus entropy (T − S)
 Enthalpy versus entropy (h − S)
 Pressure versus enthalpy (P − h)
Pressure-Temperature Diagram
For water, at 100 kPa, the saturation temperature is 99.60C. Alternatively at 99.60C, the
saturation pressure is 100 kPa. Quite often, the saturation pressure is called the vapour
pressure.
Refer to Diagram 7.1, the segment 1-T represents sublimation process during which solid
and vapour phases coexist in equilibrium. The segment 2-T represents fusion process
during which solid and liquid phases coexist in equilibrium. The segment T-C represents
vapourization.
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Copyright by Brij Bhooshan @ 2010
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Chapter: 7 Phase Change Process of Pure Substance
P
Fusion
2
SOLID
1
9
C
LIQUID
T
Brij Bhooshan
Vaporization
VAPOUR
Sublimation
T
Diagram 7.1
Sublimation curve
1-T separates solid and vapour. 2-T separates solid and liquid and T-C separates liquid and
vapour. Three curves meet at T, which is called the triple-point, where all the three phasessolid, liquid and vapour coexist in equilibrium. At the triple point no thermodynamic
property of the system can be varied independently. The system is said to be invariant.
Along, 1-T, or T-C, the system is univariant , that is only one thermodynamic property of
the system can be varied independently. The system is bivariant in the single phase’s
region. The curve 2-T can be extended indefinitely, the curve T-C terminates at point C
which is called the critical point.
The critical point represents highest temperature and pressure at which both the liquid
phase and vapour phase can coexist in equilibrium. At the critical point, the specific
volumes and all other thermodynamic properties of the liquid phase and the vapour phase
are identical.
Tc and Pc are called the critical temperature and critical pressure, respectively. If the
substance exists as a liquid on the curve T−C, it is called saturated liquid, and if it exists as
a vapour, it is called a saturated vapour. Under the constant pressure, the line abc indicates
melting, a’, b’, c’- sublimation and a”, b”, c”- vaporization.
7.3 p-v DIAGRAM FOR A PURE SUBSTANCE
Assume a unit mass of ice (solid water) at −10°C and 1 atm contained in a cylinder and
piston machine (Diagram 7.2). Let the ice be heated slowly so that its temperature is
always uniform. The changes which occur in the mass of water would be traced as the
temperature is increased while the pressure is held constant. Let the state changes of water
be plotted on p-v coordinates. The distinct regimes of heating, as shown in Diagram 7.3,
are:
1 atm
Q
Diagram 7.2 Heating of H2O at a constant pressure of 1 atm
1−2 The temperature of ice increases from −10°C to 0°C. The volume of ice would increase,
as would be the case for any solid upon heating. At state 2, i.e. 0°C, the ice would start
melting.
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Chapter: 7 Phase Change Process of Pure Substance
Brij Bhooshan
2−3 Ice melts into water at a constant temperature of 0°C. At state 3, the melting process
ends. There is a decrease in volume, which is a peculiarity of water.
3−4 The temperature of water increases, upon heating, from 0°C to 100°C. The volume of
water increases because of thermal expansion.
4−5 The water starts boiling at state 4 and boiling ends at state 5. This phase change from
liquid to vapour occurs at a constant temperature of 100°C (the pressure being constant
at 1 atm). There is a large increase in volume.
5−6 The vapour is heated to, say, 250°C (state 6). The volume of vapour increases from
to
.
Water existed in the solid phase between 1 and 2, in the liquid phase between 3 and 4, and
in the gas phase beyond 5. Between 2 and 3, the solid changed into the liquid phase by
absorbing the latent heat of fusion and between 4 and 5, the liquid changed into the vapour
phase by absorbing the latent heat of vaporization, both at constant temperature and
pressure.
The states 2, 3, 4 and 5 are termed as saturation states. A saturation state is a state from
which a change of phase may occur without a change of pressure or temperature. State 2 is
a saturated solid state because a solid can change into liquid at constant pressure and
temperature from state 2. States 3 and 4 are both saturated liquid states. In state 3, the
liquid is saturated with respect to solidification, whereas in state 4, the liquid is saturated
with respect to vaporization. State 5 is saturated vapour state, because from state 5, the
vapour can condense into liquid without a change of pressure or temperature.
If the heating of ice at −10°C to steam at 250°C were done at a constant pressure of 2 atm,
similar regimes of heating would have been obtained with similar saturation states 2, 3, 4
and 5, as shown in Diagram 7.3. All the state changes of the system can similarly be plotted
on the p-v coordinates, when it is heated at different constant pressures. All the saturated
solid states 2 at various pressures are joined by a line, as shown in Diagram 7.4.
P
2 atm
1 atm
3
4
1
2
5
6
Large volume change
3
4
1
2
5
6
3
4
1
2
5
6
0.5 atm
V
Diagram 7.3 Changes in the volume of water during heating at constant pressure
Similarly, all the saturated liquid states 3 with respect to solidification, all the saturated
liquid states 4 with respect to vaporization, and all the saturated vapour states 5, are joined
together.
The line passing through all the saturated solid states 2 (Diagram 7.4) is named as
saturated solid line. The lines passing through all the saturated liquid states 3 and 4 with
respect to solidification and vaporization respectively are referred as the saturated liquid
lines, and the line passing through all the saturated vapour states 5, is the saturated
vapour line. The saturated liquid line with respect to vaporization and the saturated vapour
line incline towards each other and form what is termed as the saturation or vapour dome.
The two lines meet at the critical state.
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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
Page 6
Chapter: 7 Phase Change Process of Pure Substance
P
Sat. Solid line
Critical state
S
+
3 L
3
2
4
2
4
3 4
2
3 4
5
5
2
5
L+V
S
V
5
1
Saturated
liquid line
Brij Bhooshan
S+V
6
Sat. Vapour line
Triple point line
V
Diagram 7.4 p-v diagram of water, whose volume decreases on melting
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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2010
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