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Petroleum Engineering Thermodynamics
Chapter 7
Entropy
Dr
...
Jufar
Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh,
Perak, Malaysia | Tel: +605 368 7045 | Fax: +605 365 5670
e-mail : shiferaw
...
com
...
2
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4
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• Define a new property called entropy to quantify the secondlaw effects
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• Calculate the entropy changes that take place during
processes for pure substances, incompressible substances,
and ideal gases
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• Derive the reversible steady-flow work relations
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• Introduce and apply the entropy balance to various systems
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2
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4
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6
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8
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10
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Entropy
The increase of entropy principle
Entropy change of pure substances
Isentropic process
Property diagram involving entropy
The T-ds relations
Entropy change of liquids and solids
The entropy change of ideal gases
Reversible steady-flow work
Isentropic efficiencies of steady flow devices
Entropy balance
ENTROPY
=
Clasius
inequality
Formal
definition
of entropy
The system considered in the
development of the Clausius
inequality
...
ENTROPY
A quantity whose cyclic
integral is zero (i
...
, a
property like volume)
Entropy is an extensive
property of a system
...
The net change
in volume (a
property) during
a cycle is always
zero
...
THE INCREASE OF ENTROPY PRINCIPLE
The equality holds for an internally
reversible process and the inequality for
an irreversible process
...
Some entropy is generated or created during an irreversible process, and
this generation is due entirely to the presence of irreversibilities
...
Can the entropy of a system during a process decrease?
THE INCREASE OF ENTROPY PRINCIPLE
The entropy change of an isolated system
is the sum of the entropy changes of its
components, and is never less than zero
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SOME REMARKS ABOUT ENTROPY
The entropy change of a system
can be negative, but the entropy
generation cannot
...
Processes can occur in a certain
direction only, not in any direction
...
A
process that violates this principle is
impossible
...
Entropy is a nonconserved property, and
there is no such thing as the
conservation of entropy principle
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3
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It is
also used to establish criteria for the
performance of engineering devices
...
What is the rate of cooling produced by this refrigerator?
Calculate the total rate of entropy change
Is this refrigerator completely reversible?
ENTROPY CHANGE OF PURE SUBSTANCES
Entropy is a property, and thus the
value of entropy of a system is fixed
once the state of the system is fixed
...
The entropy of a pure substance is
determined from the tables (like
other properties)
...
During an internally reversible,
adiabatic (isentropic) process,
the entropy remains constant
...
PROPERTY DIAGRAMS INVOLVING ENTROPY
On a T-S diagram,
the area under
the process curve
represents the
heat transfer for
internally
reversible
processes
...
Mollier diagram: The h-s diagram
EXAMPLE 2
o The T-S Diagram of the Carnot cycle
Show the Carnot cycle on a T-S diagram and indicate the areas that
represent the heat supplied QH, heat rejected QL, and the net work output
Wnet, out on this diagram
...
Reversible Isothermal Expansion (process 1-2, TH = constant)
Reversible Adiabatic Expansion (process 2-3, temperature drops from TH to TL)
Reversible Isothermal Compression (process 3-4, TL = constant)
Reversible Adiabatic Compression (process 4-1, temperature rises from TL to TH)
SOLUTION TO EXAMPLE 2
WHAT IS ENTROPY?
Boltzmann
relation
A pure crystalline substance at absolute zero
temperature is in perfect order, and its
entropy is zero (the third law of
thermodynamics)
...
Disorganized energy does not create much
useful effect, no matter how large it is
...
In the absence of friction,
raising a
weight by a rotating shaft
does not
create any disorder
(entropy), and thus
energy is not degraded
during this
process
...
(The increase in the
entropy of the cold
body more than
offsets the decrease in
the entropy of
the hot body
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The entropy of a hot coffee decreases as it cools
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2
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The paddle wheel does 200 kJ of work on
the ideal gas
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Determine the
entropy change of the ideal gas
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Heat in the amount of 100 kJ is
transferred directly from a hot
reservoir at 1200 K to a cold
reservoir at 600 K
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THE T-dS RELATIONS
the first T ds, or Gibbs equation
the second T ds equation
The T ds relations are valid for
both reversible and irreversible
processes and for both closed and
open systems
...
For an isentropic process of an incompressible substance
THE ENTROPY CHANGE OF IDEAL GASES
From the first T ds relation
From the second T ds relation
A broadcast from
channel IG
...
VARIABLE SPECIFIC HEATS (EXACT ANALYSIS)
We choose absolute zero as the reference
temperature and define a function s° as
On a unit–mass basis
On a unit–mole basis
The entropy of an ideal gas
depends on both T and P
...
ISENTROPIC PROCESSES OF IDEAL GASES
Constant Specific Heats (Approximate Analysis)
Setting this eq
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ISENTROPIC PROCESSES OF IDEAL GASES
Variable Specific Heats (Exact Analysis)
Relative Pressure and Relative Specific Volume
exp(s°/R) is
the relative
pressure Pr
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The use of Pr data for
calculating the final
temperature during
an isentropic process
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Reversible work
relations for steadyflow and closed
systems
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A reversible turbine delivers more
work than an irreversible one if both
operate between the same end
states
...
Why?
P-v diagrams of isentropic,
polytropic, and isothermal
compression processes between the
same pressure limits
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P-v and T-s diagrams
for a two-stage
steady-flow
compression process
...
ISENTROPIC EFFICIENCIES OF STEADY-FLOW DEVICES
The isentropic process involves no
irreversibilities and serves as the ideal
process for adiabatic devices
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ISENTROPIC EFFICIENCIES OF COMPRESSORS AND PUMPS
When kinetic and
potential energies
are negligible
For a
pump
Isothermal
efficiency
The h-s diagram
of the actual and
isentropic
processes of an
adiabatic
compressor
...
Can you use isentropic efficiency for a nonadiabatic compressor?
Can you use isothermal efficiency for an
adiabatic compressor?
ISENTROPIC EFFICIENCY OF NOZZLES
If the inlet velocity of the
fluid is small relative to
the exit velocity, the
energy balance is
Then,
The h-s diagram
of the actual and
isentropic
processes of an
adiabatic nozzle
...
ENTROPY BALANCE
Entropy Change of a
System, ∆Ssystem
When the properties of the
system are not uniform
Energy and entropy
balances for a system
...
No entropy accompanies work as it crosses the
system boundary
...
MECHANISMS OF ENTROPY TRANSFER, Sin AND Sout
2 Mass Flow
Entropy transfer by mass:
When the properties of the mass
change during the process
Mass contains entropy as well as
energy, and thus mass flow into or
out of system is always accompanied
by energy and entropy transfer
...
Mechanisms of entropy transfer for a
general system
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CONTROL VOLUMES
The entropy of a
substance always
increases (or remains
constant in the case of
a reversible process)
as it flows through a
single-stream,
adiabatic, steady-flow
device
...
EXAMPLES
Entropy balance for heat
transfer through a wall
Entropy balance for a
throttling process
ENTROPY GENERATED WHEN A HOT BLOCK IS DROPPED IN A LAKE
or
Entropy Generation in a Heat Exchanger
ENTROPY GENERATION ASSOCIATED WITH A HEAT TRANSFER
PROCESS
Graphical representation of entropy generation
during a heat transfer process through a finite
temperature difference