Post on 01-Aug-2020
1
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
1
© S
am
ee
r K
ha
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eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Phase Diagrams
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
2
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Increasing the temperature isobarically
T-v diagram of
constant-pressure
phase-change
processes of a
pure substance at
various pressures
numerical values
are for water.
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
3
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Temperature - Volume diagram
4
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
4
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Pressure – Volume diagram
The pressure is gradually
reduced by removing the weights
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
5
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
P-v-T surfacesRemembering:
(i) The State Postulate: The state of a simple
compressible substance is fixed by any two
independent, intensive properties
and
(ii) Any equation with two independent variables in
the form z = z (x, y) represents a surface
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
6
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
P-v-T Surfaceof a substance
that expands on freezing.
Orthogonal projection of P-v-T
surface
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
7
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
P-v-T Surfaceof a substance
that contracts on freezing.
Orthogonal projection of P-v-T
surface
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
8
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
P-v diagrams
liquid + vapor
solid + vapor
Triple line
liq
uid
So
lid
+li
qu
id
so
lid
Critical point
vapor
Substances that contract on freezing
liquid + vapor
solid + vapor
Triple line
liq
uid
So
lid
+li
qu
id
so
lid
Critical point
vapor
Substances that expand on freezing
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
9
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
PVT surface for ideal gases
10
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
10
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Phase transformationsSublimation line: Solid and Vapor
phase is in equilibrium
Fusion line: Solid and Liquid phase
is in equilibrium
Vaporization line: Liquid and Vapor
phase is in equilibrium
Triple point: All the three phases
are in equilibrium
Above critical point: No sharp
distinction in the liquid and vapor
phases
For water,
Ttp = 0.01°C
Ptp = 0.6117 kPa
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
11
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Phase diagramsAlong AB line: rate at which solid sublimes to form a
gas=rate at which gas condenses to form a solid
Along BC line: rate at which liquid boils to form a
gas=rate at which gas condenses to form a liquid
Along BD line: rate at which solid melts to form a
liquid=rate at which liquid freezes to form a solid
The triple point is the temperature and pressure at which
all three phases can exist in equilibrium.
Above the critical point, molecules are unable to liquify.
The heat of fusion is the amount of energy given off
when a substance freezes (or the amount of energy the
substances requires to liquefy).
The heat of vaporization is the amount of energy given
off when a gas liquefies (or the amount of energy needed
to vaporize the liquid).
(Note the difference between the two figures)
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
12
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Phase diagram of water
Allotropic forms of
solid phases:
Pure substances can
exist in a number of
different solid phases
Pure substances can have multiple ‘triple points’
but there exists only one triple point where all the
three phases can exist together.
The other ‘triple points’ can have two solid phases
and one liquid phase or three solid phases
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
13
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Regelation
Regelation is the phenomenon
of melting under pressure and
freezing again when the
pressure is reduced.
Regelation occurs only for substances, such as ice,
that have the property of expanding upon freezing,
for the melting points of those substances decrease
with increasing external pressure.
The melting point of ice falls by 0.0072 °C for each
additional atm of pressure applied. For example, a
pressure of 500 atmospheres is needed for ice to
melt at −4 °C.
These two examples, usually cited, as NOT due to regelation
14
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
14
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Phase diagram of Carbon-dioxide
The triple-point pressure is greater than
normal atmospheric pressure which is
very unusual.
At one atmosphere, we see CO2 either as
a gas or as a solid.
Therefore, the commonly observed
phase- transition under conditions of
atmospheric pressure of about 100
kPa is a sublimation from solid
directly to vapor, without passing
through a liquid phase, which is why
solid carbon dioxide is commonly
referred to as dry ice.
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
15
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Supercritical fluids
Supercritical CO2
Supercritical N2
16
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
16
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Property tables
• For most substances, the relationships among thermodynamic
properties are too complex to be expressed by simple equations.
• Therefore, properties are frequently presented in the form of tables.
• Some thermodynamic properties can be measured easily, but others
cannot and are calculated by using the relations between them and
measurable properties.
• The results of these measurements and calculations are presented
in tables in a convenient format.
In your text book, Please see Tables A-4 and A-5
Table A-4: Saturation properties of water temperature basis
Table A-5: Saturation properties of water pressure basis
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
17
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Enthalpy: A new property
It’s a Combination Property
The combination (u + Pv) is
frequently encountered in the
analysis of control volumes.
The product
pressure volume has energy units.
(N/m2 )*(m3)
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
18
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
A quick look at the property tables
Table
A4/A5
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Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
19
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Table A-4
20
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
20
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Table A-5
21
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
21
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Table A-6 and A-7Superheated water vapor
Compressed liquid water
22
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
22
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Van der Waals equation of state
23
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
23
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Percentage error: Equations of State
For Nitrogen
24
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
24
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Percentage error with ideal gas law
For Water
25
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
25
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Compressibility chart
26
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
26
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Compressibility chart
27
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
27
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
Compressibility chart
28
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Kanpur 208016
India
28
© S
am
ee
r K
ha
nd
eka
rESO201A
Thermodynamics
Instructor: Dr. Sameer Khandekar
Tel: 7038; e-mail: samkhan@iitk.ac.in
End of Lecture