The document discusses entropy and the second law of thermodynamics. It defines the objectives as applying the second law to processes, defining entropy to quantify second law effects, and establishing the increase of entropy principle. It then defines entropy as an abstract property, discusses Clausius inequality and how Clausius realized he discovered entropy. The key points are that entropy is a state function, its change depends on initial and final states only, and the change between two states is the same for reversible and irreversible processes. It also provides an equation for determining entropy change during isothermal heat transfer.
Engineering Thermodynamics-second law of thermodynamics Mani Vannan M
This file consists of content which covers the basics of second law of thermodynamics,heat reservoir,heat source ,heat sink,refrigerator, heat pump,heat engine,carnot theorem,carnot cycle and reversed carnot cycle
Second law of thermodynamics (and third law of thermodynamics) as taught in introductory physical chemistry (including general chemistry). Covers concepts such as entropy, Gibbs free energy, and phase equilibrium.
Engineering Thermodynamics-second law of thermodynamics Mani Vannan M
This file consists of content which covers the basics of second law of thermodynamics,heat reservoir,heat source ,heat sink,refrigerator, heat pump,heat engine,carnot theorem,carnot cycle and reversed carnot cycle
Second law of thermodynamics (and third law of thermodynamics) as taught in introductory physical chemistry (including general chemistry). Covers concepts such as entropy, Gibbs free energy, and phase equilibrium.
In this PPT have have covered
1. Basic thermodynamics definition
2. Thermodynamics law
3. Properties , cycle, Process
4. Derivation of the Process
5.Formula for the numericals.
This topic is use full for those students who want to study basic thermodynamics as a part of their University syllabus.
Most of the university having basic Mechanical engineering as a subject and in this subject Thermodynamics is a topic so by this PPT our aim is to give presentable knowledge of the subject
First law of thermodynamics as taught in introductory physical chemistry (includes general chemistry material). Covers concepts such as internal energy, heat, work, heat capacity, enthalpy, bomb calorimetry, Hess's law, thermochemical equations, bond energy, and heat of formations.
This presentation gives you information om Clausius Statement, its proof, Entropy change for Open System and reversible and irreversible processes with simple explanation and day to day examples.
In this PPT have have covered
1. Basic thermodynamics definition
2. Thermodynamics law
3. Properties , cycle, Process
4. Derivation of the Process
5.Formula for the numericals.
This topic is use full for those students who want to study basic thermodynamics as a part of their University syllabus.
Most of the university having basic Mechanical engineering as a subject and in this subject Thermodynamics is a topic so by this PPT our aim is to give presentable knowledge of the subject
First law of thermodynamics as taught in introductory physical chemistry (includes general chemistry material). Covers concepts such as internal energy, heat, work, heat capacity, enthalpy, bomb calorimetry, Hess's law, thermochemical equations, bond energy, and heat of formations.
This presentation gives you information om Clausius Statement, its proof, Entropy change for Open System and reversible and irreversible processes with simple explanation and day to day examples.
The Entropy is a thermodynamic property of a working substance and serves as a valuable tool in the second law analysis of engineering devices.
Entropy is a function of a quantity of heat which shows the possibility of conversion of that into work.
Entropy is a thermodynamic property; it can be viewed as a measure of disorder i.e. More disorganized a system the higher its entropy.
“ When a system undergoes a complete cyclic process, the integral of around the cycle is less than zero.”
Mathematically : ( ) ≤ 0
δQ is energy flow into the system due to heating and T being absolute temperature of the body when that energy is absorbed.
The following equation must be found true for any cyclical process that is possible, reversible or not.
Subject: ME8391 Engineering Thermodynamics
Topic: Basic Concepts & First law of Thermodynamics
B.E. Mechanical Engineering
Second year, III Semester.
[Anna University R-2017]
The second law of thermodynamics is explored in this lecture. Topics covered include:
Introduction to the second law
Thermal energy reservoirs
Heat engines
Thermal efficiency
The 2nd law: Kelvin-Planck statement
Refrigerators and heat pumps
Coefficient of performance (COP)
The 2nd law: Clasius statement
Perpetual motion machines
Reversible and irreversible processes
Irreversibility's, Internal and externally reversible processes
The Carnot cycle
The reversed Carnot cycle
The Carnot principles
The thermodynamic temperature scale
The Carnot heat engine
The quality of energy
The Carnot refrigerator and heat pump
Mass flow and energy analysis of control systems is the focus of this lecture
Conservation of mass
Mass and volume flow rates
Mass balance for a steady flow process
Mass balance for incompressible flow
Flow work and the energy of a flowing fluid
his lecture examines both work and energy in closed systems and categorises the different types of closed systems that will be encountered.
Moving boundary work
Boundary work for an isothermal process
Boundary work for a constant-pressure process
Boundary work for a polytropic process
Energy balance for closed systems
Energy balance for a constant-pressure expansion or compression process
Specific heats
Constant-pressure specific heat, cp
Constant-volume specific heat, cv
Internal energy, enthalpy and specific heats of ideal gases
Energy balance for a constant-pressure expansion or compression process
Internal energy, enthalpy and specific heats of incompressible substances (Solids and liquids)
Identifying the correct properties of a substance is of vital importance. Many of these properties are distilled from property tables. This lecture addresses how to identify these properties.
Pure substance
Phases of a pure substance
Phase change processes of pure substances
Compressed liquid, Saturated liquid, Saturated vapor, Superheated vapor Saturated temperature and Satuated pressure
Property diagrams for phase change processes
The T-v diagram, The P-v diagram, The P-T diagram, The P-v-T diagram
Property tables
Enthalpy
Saturated liquid, Saturated vapor, Saturated liquid vapor mixture, Superheated vapor, compressed liquid
Reference state and Reference values
The ideal gas equation of state
Is water vapor an ideal gas?
Lecture covering the basic concepts required for the module:
Systems and control volumes
Properties of a system
Density and specific gravity
State and equilibrium
The state postulate
Processes and cycles
The state-flow process
Temperature and the zeroth law of thermodynamics
Temperature scales
Pressure
Variation of pressure with depths
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
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The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
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This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
1. ENTROPY
Lecture 10
Keith Vaugh BEng (AERO) MEng
Reference text: Chapter 8 - Fundamentals of Thermal-Fluid Sciences, 3rd Edition
Yunus A. Cengel, Robert H. Turner, John M. Cimbala
McGraw-Hill, 2008
4. OBJECTIVES
Apply the second law of thermodynamics to
processes.
}
Define a new property called entropy to quantify
the second-law effects.
5. OBJECTIVES
Apply the second law of thermodynamics to
processes.
}
Define a new property called entropy to quantify
the second-law effects.
Establish the increase of entropy principle.
6. OBJECTIVES
Apply the second law of thermodynamics to
processes.
}
Define a new property called entropy to quantify
the second-law effects.
Establish the increase of entropy principle.
Calculate the entropy changes that take place
during processes for pure substances*,
incompressible substances, and ideal gases.
* we’re limiting our studies to pure substances (2010)
8. ENTROPY
Entropy is a somewhat abstract property and it is
difficult to give a physical description of without
considering the microscopic state of the system
}
9. ENTROPY
Entropy is a somewhat abstract property and it is
difficult to give a physical description of without
considering the microscopic state of the system
}
The second law of thermodynamics often leads to
expressions that involve inequalities.
10. ENTROPY
Entropy is a somewhat abstract property and it is
difficult to give a physical description of without
considering the microscopic state of the system
}
The second law of thermodynamics often leads to
expressions that involve inequalities.
An irreversible heat engine is less efficient than a
reversible one operating between the same two
thermal reservoirs
11. ENTROPY
Entropy is a somewhat abstract property and it is
difficult to give a physical description of without
considering the microscopic state of the system
}
The second law of thermodynamics often leads to
expressions that involve inequalities.
An irreversible heat engine is less efficient than a
reversible one operating between the same two
thermal reservoirs
Another important inequality that has major
consequences in thermodynamics is Clausius
inequality
13. Clausius inequality is expressed as;
δQ
— ≤0
∫T
the validity of the Clausius inequality is
demonstrated on pages 298/9 of the reference text.
The system considered in the
development of the Clausius inequality.
14. Clausius inequality is expressed as;
δQ
— ≤0
∫T
the validity of the Clausius inequality is
demonstrated on pages 298/9 of the reference text.
Clausius realized he had discovered a new
thermodynamic property and named it entropy
with designation of S. It is defined as;
δQ
dS =
T int, rev
( kJ K )
The system considered in the
development of the Clausius inequality.
15. Clausius inequality is expressed as;
δQ
— ≤0
∫T
the validity of the Clausius inequality is
demonstrated on pages 298/9 of the reference text.
Clausius realized he had discovered a new
thermodynamic property and named it entropy
with designation of S. It is defined as;
δQ
dS =
T int, rev
( kJ K )
The entropy change of a system during a
process can be determined by integrating
The system considered in the between the initial and final states
development of the Clausius inequality.
2 δQ
ΔS = S2 − S1 = ∫ 1
T int, rev
( kJ K )
16. The entropy change between two specified
states is the same whether the process is
reversible or irreversible
17. A quantity whose cyclic integral is zero
(i.e. a property like volume)
δQ
—T int, rev = 0
∫
The entropy change between two specified
states is the same whether the process is
reversible or irreversible
18. A quantity whose cyclic integral is zero
(i.e. a property like volume)
δQ
—T int, rev = 0
∫
The entropy change between two specified
states is the same whether the process is
reversible or irreversible
The net change in volume
(a property) during a
cycle is always zero
19. A quantity whose cyclic integral is zero
(i.e. a property like volume)
δQ
—T int, rev = 0
∫
The entropy change between two specified
states is the same whether the process is
reversible or irreversible
The net change in volume
(a property) during a
cycle is always zero
Entropy is an extensive property of a system
20. A special case: Internally reversible
isothermal heat transfer processes
21. A special case: Internally reversible
isothermal heat transfer processes
2 δQ
ΔS = ∫
1
T int, rev
22. A special case: Internally reversible
isothermal heat transfer processes
2 δQ
ΔS = ∫
1
T int, rev
2 δQ
= ∫
1 T
0 int, rev
24. A special case: Internally reversible
isothermal heat transfer processes
2 δQ
ΔS = ∫
1
T int, rev
2 δQ
= ∫
1 T
0 int, rev
1 2
=
T0 ∫ (δ Q )
1 int, rev
ΔS =
Q
T0 } This equation is particularly useful
for determining the entropy changes
of thermal energy reservoirs
25. EXAMPLE 8 - 1
A piston cylinder device contains liquid vapor
mixture at 300 K. During a constant pressure process,
}
750 kJ of heat is transferred to the water. As a result,
part of the liquid in the cylinder vaporizes. Determine
the entropy change of the water during this process.
26. SOLUTION
Heat is transferred to a liquid vapor mixture
of water in a piston cylinder device at
constant pressure. The entropy change of
water is to be determined
27. SOLUTION
Heat is transferred to a liquid vapor mixture
of water in a piston cylinder device at
constant pressure. The entropy change of
water is to be determined
ASSUMPTIONS
No irreversibility's occur within the system
boundaries during the process.
28. SOLUTION ANALYSIS
Heat is transferred to a liquid vapor mixture We take the entire water (liquid + vapor) in the
of water in a piston cylinder device at cylinder as the system. This is a closed system
constant pressure. The entropy change of since no mass crosses the system boundary during
water is to be determined the process. We note that the temperature of the
system remains constant at 300 K since the
ASSUMPTIONS temperature of a pure substance remains constant
at the saturation value during a phase change
No irreversibility's occur within the system
process at constant pressure.
boundaries during the process.
29. SOLUTION ANALYSIS
Heat is transferred to a liquid vapor mixture We take the entire water (liquid + vapor) in the
of water in a piston cylinder device at cylinder as the system. This is a closed system
constant pressure. The entropy change of since no mass crosses the system boundary during
water is to be determined the process. We note that the temperature of the
system remains constant at 300 K since the
ASSUMPTIONS temperature of a pure substance remains constant
at the saturation value during a phase change
No irreversibility's occur within the system
process at constant pressure.
boundaries during the process.
The system undergoes an internally reversible,
isothermal process and thus its entropy change can
be determined directly
Q 750kJ
ΔS = = = 2.5 kJ K
Tsys 300K
NOTE - Entropy change of the system is positive
as expected since heat transfer is to the system
30. The increase of entropy principle
A cycle composed of a reversible and an
irreversible process
31. The increase of entropy principle
δQ 2 δQ 1 δQ
— ≤ 0 → ∫1 T + ∫2 T int, rev ≤ 0
∫T
A cycle composed of a reversible and an
irreversible process
32. The increase of entropy principle
δQ 2 δQ 1 δQ
— ≤ 0 → ∫1 T + ∫2 T int, rev ≤ 0
∫T
A cycle composed of a reversible and an
irreversible process
33. The increase of entropy principle
δQ 2 δQ 1 δQ
— ≤ 0 → ∫1 T + ∫2 T int, rev ≤ 0
∫T
2 δQ 2 δQ
∫ + S1 − S0 ≤ 0 → S2 − S1 ≥ ∫
1 T 1 T
A cycle composed of a reversible and an
irreversible process
34. The increase of entropy principle
δQ 2 δQ 1 δQ
— ≤ 0 → ∫1 T + ∫2 T int, rev ≤ 0
∫T
2 δQ 2 δQ
∫ + S1 − S0 ≤ 0 → S2 − S1 ≥ ∫
1 T 1 T
A cycle composed of a reversible and an
irreversible process
35. The increase of entropy principle
δQ 2 δQ 1 δQ
— ≤ 0 → ∫1 T + ∫2 T int, rev ≤ 0
∫T
2 δQ 2 δQ
∫ + S1 − S0 ≤ 0 → S2 − S1 ≥ ∫
1 T 1 T
δQ The equality holds for an internally
dS ≥ reversible process and the inequality
T for an irreversible process
A cycle composed of a reversible and an
irreversible process
36. The increase of entropy principle
δQ 2 δQ 1 δQ
— ≤ 0 → ∫1 T + ∫2 T int, rev ≤ 0
∫T
2 δQ 2 δQ
∫ + S1 − S0 ≤ 0 → S2 − S1 ≥ ∫
1 T 1 T
δQ The equality holds for an internally
dS ≥ reversible process and the inequality
T for an irreversible process
2 δQ
ΔSsys = S2 − S1 = ∫ + Sgen
1 T
A cycle composed of a reversible and an
irreversible process
37. The increase of entropy principle
δQ 2 δQ 1 δQ
— ≤ 0 → ∫1 T + ∫2 T int, rev ≤ 0
∫T
2 δQ 2 δQ
∫ + S1 − S0 ≤ 0 → S2 − S1 ≥ ∫
1 T 1 T
δQ The equality holds for an internally
dS ≥ reversible process and the inequality
T for an irreversible process
2 δQ
ΔSsys = S2 − S1 = ∫ + Sgen
1 T
A cycle composed of a reversible and an
irreversible process Sgen = ΔStotal = ΔSsys + ΔSsurr ≥ 0
Some entropy is generated or created during an irreversible process
and this generation is due entirely to the presence of irreversibility's.
38. A system and its surrounding form an
isolated system
39. The entropy change of an isolated system is
the sum of the entropy changes of its
components, and is never less than zero.
A system and its surrounding form an
isolated system
40. The entropy change of an isolated system is
the sum of the entropy changes of its
components, and is never less than zero.
A system and its surrounding form an ΔSisolated ≥ 0
isolated system
41. The entropy change of an isolated system is
the sum of the entropy changes of its
components, and is never less than zero.
A system and its surrounding form an ΔSisolated ≥ 0
isolated system
Sgen = ΔStotal = ΔSsys + ΔSsurr ≥ 0
42. The entropy change of an isolated system is
the sum of the entropy changes of its
components, and is never less than zero.
A system and its surrounding form an ΔSisolated ≥ 0
isolated system
Sgen = ΔStotal = ΔSsys + ΔSsurr ≥ 0
> Irreversible process
The increase of
Sgen = Reversible process
entropy principle < Impossible process
43. A comment on entropy
The entropy change of a system can
be negative, but the entropy
generation cannot.
44. A comment on entropy
Processes can occur in a certain direction only,
not in any direction. A process must proceed in
the direction that complies with the increase of
entropy principle, that is, Sgen ≥ 0. A process that
violates this principle is impossible.
The entropy change of a system can
be negative, but the entropy
generation cannot.
45. A comment on entropy
Processes can occur in a certain direction only,
not in any direction. A process must proceed in
the direction that complies with the increase of
entropy principle, that is, Sgen ≥ 0. A process that
violates this principle is impossible.
Entropy is a non-conserved property, and there
is no such thing as the conservation of entropy
principle. Entropy is conserved during the
idealized reversible processes only and increases
during all actual processes.
The entropy change of a system can
be negative, but the entropy
generation cannot.
46. A comment on entropy
Processes can occur in a certain direction only,
not in any direction. A process must proceed in
the direction that complies with the increase of
entropy principle, that is, Sgen ≥ 0. A process that
violates this principle is impossible.
Entropy is a non-conserved property, and there
is no such thing as the conservation of entropy
principle. Entropy is conserved during the
idealized reversible processes only and increases
during all actual processes.
The performance of engineering systems is
The entropy change of a system can degraded by the presence of irreversibility's, and
be negative, but the entropy
generation cannot.
entropy generation is a measure of the
magnitudes of the irreversibility's during that
process. It is also used to establish criteria for
the performance of engineering devices.
47. Entropy change of pure substances
Entropy is a property and therefore its value for
a system is fixed provided that state of that
system is also fixed.
Schematic of the T-s
diagram for water.
48. Entropy change
ΔS = mΔS = m ( s2 − s1 ) ( kJ K )
The entropy of a pure substance is
determined from the tables (like other
properties).
49. QUESTION 8 - 39
A well insulated rigid tank contains 2kg of a saturated
liquid vapor mixture of water at 100 kPa. Initially
three quarters of the mass is in the liquid phase. An
}
electric resistance heater placed in the tank is now
turned on and kept on until all the liquid in the tank is
vaporized. Determine the entropy change of the
steam during this process.
50. SOLUTION
An insulated rigid tank contains a
saturated liquid-vapor mixture of
water at a specified pressure. An
electric heater inside is turned on
and kept on until all the liquid
vaporized. The entropy change of
the water during this process is to
be determined.
51. SOLUTION
An insulated rigid tank contains a
saturated liquid-vapor mixture of
water at a specified pressure. An
electric heater inside is turned on
and kept on until all the liquid
vaporized. The entropy change of
the water during this process is to
be determined.
H2O
2 kg
100 kPa
We
52. SOLUTION ANALYSIS
An insulated rigid tank contains a From the steam tables (A-4 through A-6)
saturated liquid-vapor mixture of
water at a specified pressure. An
electric heater inside is turned on
and kept on until all the liquid
vaporized. The entropy change of
the water during this process is to
be determined.
H2O
2 kg
100 kPa
We
53. SOLUTION ANALYSIS
An insulated rigid tank contains a From the steam tables (A-4 through A-6)
saturated liquid-vapor mixture of P1 v1 = v f + x1v fg
water at a specified pressure. An
electric heater inside is turned on x1 s1 = s f + x1s fg
and kept on until all the liquid
vaporized. The entropy change of
the water during this process is to
be determined.
H2O
2 kg
100 kPa
We
54. SOLUTION ANALYSIS
An insulated rigid tank contains a From the steam tables (A-4 through A-6)
saturated liquid-vapor mixture of P1 v1 = v f + x1v fg
water at a specified pressure. An
electric heater inside is turned on x1 s1 = s f + x1s fg
and kept on until all the liquid
vaporized. The entropy change of v1 = v f + x1v fg
the water during this process is to v1 = 0.001 + ( 0.25 ) (1.6941 − 0.001)
be determined. 3
v1 = 0.4243 m kg
H2O
2 kg
100 kPa
We
55. SOLUTION ANALYSIS
An insulated rigid tank contains a From the steam tables (A-4 through A-6)
saturated liquid-vapor mixture of P1 v1 = v f + x1v fg
water at a specified pressure. An
electric heater inside is turned on x1 s1 = s f + x1s fg
and kept on until all the liquid
vaporized. The entropy change of v1 = v f + x1v fg
the water during this process is to v1 = 0.001 + ( 0.25 ) (1.6941 − 0.001)
be determined. 3
v1 = 0.4243 m kg
s1 = s f + x1s fg
H2O s1 = 1.3028 + ( 0.25 ) ( 6.0562 )
2 kg
100 kPa s1 = 2.8168 kJ kg ⋅ K
We
56. SOLUTION ANALYSIS
An insulated rigid tank contains a From the steam tables (A-4 through A-6)
saturated liquid-vapor mixture of P1 v1 = v f + x1v fg
water at a specified pressure. An
electric heater inside is turned on x1 s1 = s f + x1s fg
and kept on until all the liquid
vaporized. The entropy change of v1 = v f + x1v fg
the water during this process is to v1 = 0.001 + ( 0.25 ) (1.6941 − 0.001)
be determined. 3
v1 = 0.4243 m kg
s1 = s f + x1s fg
H2O s1 = 1.3028 + ( 0.25 ) ( 6.0562 )
2 kg
100 kPa s1 = 2.8168 kJ kg ⋅ K
v2 = v1
We s2 = 6.8649 kJ kg ⋅ K
sat. vapor
Then the entropy change of the steam becomes
57. SOLUTION ANALYSIS
An insulated rigid tank contains a From the steam tables (A-4 through A-6)
saturated liquid-vapor mixture of P1 v1 = v f + x1v fg
water at a specified pressure. An
electric heater inside is turned on x1 s1 = s f + x1s fg
and kept on until all the liquid
vaporized. The entropy change of v1 = v f + x1v fg
the water during this process is to v1 = 0.001 + ( 0.25 ) (1.6941 − 0.001)
be determined. 3
v1 = 0.4243 m kg
s1 = s f + x1s fg
H2O s1 = 1.3028 + ( 0.25 ) ( 6.0562 )
2 kg
100 kPa s1 = 2.8168 kJ kg ⋅ K
v2 = v1
We s2 = 6.8649 kJ kg ⋅ K
sat. vapor
Then the entropy change of the steam becomes
ΔS = m ( s2 − s1 ) = ( 2kg ) ( 6.8649 − 2.8168 ) kJ kg ⋅ K
ΔS = 8.10 kJ K
58. Isentropic processes
A process during which the entropy
remains constant is called an isentropic
process
During an internally reversible, adiabatic
(isentropic) process, the entropy remains
constant.
59. Isentropic processes
A process during which the entropy
remains constant is called an isentropic
process
The isentropic process appears
as a vertical line segment on a
T-s diagram.
During an internally reversible, adiabatic
(isentropic) process, the entropy remains
constant.
60. Isentropic processes
A process during which the entropy
remains constant is called an isentropic
process
The isentropic process appears
as a vertical line segment on a
T-s diagram.
During an internally reversible, adiabatic
(isentropic) process, the entropy remains
Δs = 0 or s 2 − s1 ( kJ
kg ⋅K)
constant.
61. QUESTION 8 - 44
An insulated piston-cylinder device contains 0.05 m3
of saturated refrigerant 134a vapor at 0.8 MPa
pressure. The refrigerant is now allowed to expand in
}
a reversible manner until the pressure drops to 0.4
MPa. Determine;
a. The final temperature in the cylinder
b. The work done by the refrigerant
62. SOLUTION
An insulated cylinder is initially
filled with saturated R-134a vapor
at a specified pressure. The
refrigerant expands in a reversible
manner until the pressure drops to
a specified value. The final
temperature in the cylinder and the
work done by the refrigerant are to
be determined.
63. SOLUTION
An insulated cylinder is initially
filled with saturated R-134a vapor
at a specified pressure. The
refrigerant expands in a reversible
manner until the pressure drops to
a specified value. The final
temperature in the cylinder and the
work done by the refrigerant are to
be determined.
R-134a
0.8 MPa
0.05 m3
64. SOLUTION ASSUMPTIONS
An insulated cylinder is initially 1. The kinetic and potential energy
filled with saturated R-134a vapor changes are negligible.
at a specified pressure. The
refrigerant expands in a reversible
manner until the pressure drops to
a specified value. The final
temperature in the cylinder and the
work done by the refrigerant are to
be determined.
R-134a
0.8 MPa
0.05 m3
65. SOLUTION ASSUMPTIONS
An insulated cylinder is initially 1. The kinetic and potential energy
filled with saturated R-134a vapor changes are negligible.
at a specified pressure. The 2. The cylinder is well-insulated and thus
refrigerant expands in a reversible heat transfer is negligible.
manner until the pressure drops to
a specified value. The final
temperature in the cylinder and the
work done by the refrigerant are to
be determined.
R-134a
0.8 MPa
0.05 m3
66. SOLUTION ASSUMPTIONS
An insulated cylinder is initially 1. The kinetic and potential energy
filled with saturated R-134a vapor changes are negligible.
at a specified pressure. The 2. The cylinder is well-insulated and thus
refrigerant expands in a reversible heat transfer is negligible.
manner until the pressure drops to 3. The thermal energy stored in the
a specified value. The final cylinder itself is negligible.
temperature in the cylinder and the
work done by the refrigerant are to
be determined.
R-134a
0.8 MPa
0.05 m3
67. SOLUTION ASSUMPTIONS
An insulated cylinder is initially 1. The kinetic and potential energy
filled with saturated R-134a vapor changes are negligible.
at a specified pressure. The 2. The cylinder is well-insulated and thus
refrigerant expands in a reversible heat transfer is negligible.
manner until the pressure drops to 3. The thermal energy stored in the
a specified value. The final cylinder itself is negligible.
temperature in the cylinder and the 4. The process is stated to be reversible.
work done by the refrigerant are to
be determined.
R-134a
0.8 MPa
0.05 m3
68. SOLUTION ASSUMPTIONS
An insulated cylinder is initially 1. The kinetic and potential energy
filled with saturated R-134a vapor changes are negligible.
at a specified pressure. The 2. The cylinder is well-insulated and thus
refrigerant expands in a reversible heat transfer is negligible.
manner until the pressure drops to 3. The thermal energy stored in the
a specified value. The final cylinder itself is negligible.
temperature in the cylinder and the 4. The process is stated to be reversible.
work done by the refrigerant are to
be determined.
ANALYSIS
a. This is a reversible adiabatic (i.e., isentropic)
process, and thus s2 = s1. From the refrigerant
tables (Tables A-11 through A-13),
R-134a
0.8 MPa
0.05 m3
69. SOLUTION ASSUMPTIONS
An insulated cylinder is initially 1. The kinetic and potential energy
filled with saturated R-134a vapor changes are negligible.
at a specified pressure. The 2. The cylinder is well-insulated and thus
refrigerant expands in a reversible heat transfer is negligible.
manner until the pressure drops to 3. The thermal energy stored in the
a specified value. The final cylinder itself is negligible.
temperature in the cylinder and the 4. The process is stated to be reversible.
work done by the refrigerant are to
be determined.
ANALYSIS
a. This is a reversible adiabatic (i.e., isentropic)
process, and thus s2 = s1. From the refrigerant
tables (Tables A-11 through A-13),
v1 = vg@0.8 MPa = 0.02561 m3
kg
P1 = 0.8MPa
u1 = u g@0.8 MPa = 246.79 kJ kg
R-134a sat. vapor
0.8 MPa s1 = sg@0.8 MPa = 0.91835 kJ kg ⋅ K
0.05 m3
71. V 0.05m 3
m= = m3
= 1.952kg
v1 0.025621 kg
s2 − s f 0.91835 − 024761
P2 = 0.4MPa x2 = = = 0.9874
s fg 0.67929
s2 = s1
u2 = u f + x2 u fg = 63.62 + ( 0.9874 ) (171.45 ) = 232.91 kJ kg
72. V 0.05m 3
m= = m3
= 1.952kg
v1 0.025621 kg
s2 − s f 0.91835 − 024761
P2 = 0.4MPa x2 = = = 0.9874
s fg 0.67929
s2 = s1
u2 = u f + x2 u fg = 63.62 + ( 0.9874 ) (171.45 ) = 232.91 kJ kg
T2 = Tsat @0.4 MPa = 8.91°C
73. V 0.05m 3
m= = m3
= 1.952kg
v1 0.025621 kg
s2 − s f 0.91835 − 024761
P2 = 0.4MPa x2 = = = 0.9874
s fg 0.67929
s2 = s1
u2 = u f + x2 u fg = 63.62 + ( 0.9874 ) (171.45 ) = 232.91 kJ kg
T2 = Tsat @0.4 MPa = 8.91°C
b. We take the contents of the cylinder as the system. This is a closed system since no
mass enters or leaves. The energy balance for this adiabatic closed system can be
expressed as
74. V 0.05m 3
m= = m3
= 1.952kg
v1 0.025621 kg
s2 − s f 0.91835 − 024761
P2 = 0.4MPa x2 = = = 0.9874
s fg 0.67929
s2 = s1
u2 = u f + x2 u fg = 63.62 + ( 0.9874 ) (171.45 ) = 232.91 kJ kg
T2 = Tsat @0.4 MPa = 8.91°C
b. We take the contents of the cylinder as the system. This is a closed system since no
mass enters or leaves. The energy balance for this adiabatic closed system can be
expressed as
Ein − Eout = ΔEsystem
14 2 4 3 123
Net energy transfer Change in internal, kinetic,
by heat, work and mass potential, etc... energies
− Wb, out = ΔU
Wb, out = m ( u1 − u2 )
75. V 0.05m 3
m= = m3
= 1.952kg
v1 0.025621 kg
s2 − s f 0.91835 − 024761
P2 = 0.4MPa x2 = = = 0.9874
s fg 0.67929
s2 = s1
u2 = u f + x2 u fg = 63.62 + ( 0.9874 ) (171.45 ) = 232.91 kJ kg
T2 = Tsat @0.4 MPa = 8.91°C
b. We take the contents of the cylinder as the system. This is a closed system since no
mass enters or leaves. The energy balance for this adiabatic closed system can be
expressed as
Ein − Eout = ΔEsystem Substituting, the work done during this isentropic
14 2 4 3 123 process is determined to be
Net energy transfer Change in internal, kinetic,
by heat, work and mass potential, etc... energies
− Wb, out = ΔU Wb, out = m ( u1 − u2 )
Wb, out = m ( u1 − u2 ) = (1.952kg ) ( 246.79 − 232.91) kJ kg = 27.09kJ
76. Property diagrams involving entropy
On a T-S diagram, the area under the process curve
represents the heat transfer for internally reversible
processes.
77. Property diagrams involving entropy
δ Qint, rev = TdS
On a T-S diagram, the area under the process curve
represents the heat transfer for internally reversible
processes.
78. Property diagrams involving entropy
δ Qint, rev = TdS
2
Qint, rev = ∫ T dS
1
On a T-S diagram, the area under the process curve
represents the heat transfer for internally reversible
processes.
79. Property diagrams involving entropy
δ Qint, rev = TdS
2
Qint, rev = ∫ T dS
1
δ qint, rev = Tds
On a T-S diagram, the area under the process curve
represents the heat transfer for internally reversible
processes.
80. Property diagrams involving entropy
δ Qint, rev = TdS
2
Qint, rev = ∫ T dS
1
δ qint, rev = Tds
2
qint, rev = ∫ T ds
1
On a T-S diagram, the area under the process curve
represents the heat transfer for internally reversible
processes.
81. Property diagrams involving entropy
δ Qint, rev = TdS
2
Qint, rev = ∫ T dS
1
δ qint, rev = Tds
2
qint, rev = ∫ T ds
1
Qint, rev = T0 ΔS
On a T-S diagram, the area under the process curve
represents the heat transfer for internally reversible
processes.
82. Property diagrams involving entropy
δ Qint, rev = TdS
2
Qint, rev = ∫ T dS
1
δ qint, rev = Tds
2
qint, rev = ∫ T ds
1
Qint, rev = T0 ΔS
qint, rev = T0 Δs
On a T-S diagram, the area under the process curve
represents the heat transfer for internally reversible
processes.
83. Property diagrams involving entropy
For adiabatic steady-flow devices,
the vertical distance ∆h on an h-s
diagram is a measure of work, and
the horizontal distance ∆s is a
measure of irreversibility's.
Mollier diagram: The h-s diagram
84. Entropy
Clausius inequality
The Increase of entropy principle
Example 8-1
A comment on entropy
Entropy change of pure substances
Question 8-39
Isentropic processes
Question 8-44
Property diagrams involving entropy
What is entropy?
The T ds relations
Entropy change of liquids and solids
The entropy change of ideal gases
Reversible steady-flow work
Minimizing the compressor work
Isentropic efficiencies of steady-flow devices
Entropy balance
Editor's Notes
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The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n
The entropy generation Sgen is always a positive quantity or zero.\nCan the entropy of a system during a process decrease?\n