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Advanced Thermodynamics - Mazlan 2019
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UNIVERSITI TEKNOLOGI MALAYSIA
Introduction
Advanced ThermodynamicsProf. Dr. Mazlan Abdul WahidSchool of Mechanical Engineering
Faculty of EngineeringUniversiti Teknologi Malaysiawww.fkm.utm.my/~mazlan
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Advanced Thermodynamics - Mazlan 2019
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UNIVERSITI TEKNOLOGI MALAYSIA
MMJ1413 ADVANCED THERMODYNAMICS SEM 2012-13 2
FME, UTM SKUDAISYNOPSISThis advanced course in engineering thermodynamicsprovides a strong foundation in the fundamentals of thermalsciences for further advanced research. Students shall beexposed to the restrictions on possible properties andsystems. Basic and further treatment of the First andSecond law of Thermodynamics will be given. Exergyanalysis will be discussed regarding fundamental concepts,techniques and application in various systems. A simplifiedtreatment of statistical thermodynamics will be covered withemphasis on the wave functions which helps promote agreater understanding of the foundations, laws, propertiesand applications in thermodynamics. This is one of thefundamental courses in a postgraduate program in ThermalEngineering.
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Importance
This course will prepare the students and give astrong grounding in fundamentals to pursueadvanced research and studies in the ThermalSciences. From the same foundation, apracticing engineer can also apply the principlesstudied to investigate and improve theperformance of a thermal device such as powerplant, combustion engine and heat exchangers.This is one of the basic courses for apostgraduate student in Thermal Engineering.
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Advanced Thermodynamics - Mazlan 2019
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UNIVERSITI TEKNOLOGI MALAYSIA
COURSE LEARNING OUTCOMES
1. Discuss thermodynamic problems (associated postulates) and apply thermodynamics relations to solve the problems.
2. Assess and determine the thermodynamically optimal operating regime for systems using exergy concept.
3. Outline the fundamental statistical concepts underlying the properties/energy of matter with wave functions.
4. Evaluate and interpret the thermodynamic properties/energy of system of independent particles that constitute thermodynamic systems.
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Advanced Thermodynamics - Mazlan 2019
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TOPICS OR COURSE CONTENT
•Basic Problems of Thermodynamics – State Postulates•The Structure of Thermodynamics•The Laws of Thermodynamics:
•Zeroth Law of Thermodynamics•First Law of Thermodynamics•Second Law of Thermodynamics•Third Law of Thermodynamics
•Exergy/Availability for Closed and Open System, Entropy minimization •Thermodynamic Variables and Relations: Maxwell Relations, Entropy, Gibbs, etc•Statistical Thermodynamics: Energy Storage in Particles, Statistical Models, Statistical Laws – Boltzmann, Bose-Eistein, Fermi-Dirac, Partition functions, Maxwell-Boltzmann Distribution
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Advanced Thermodynamics - Mazlan 2019
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REFERENCES
•Advanced Engineering Thermodynamics, Adrian Bejan, Wiley 2006.
•Thermodynamics in Materials Science, Robert T. DeHoff, McGraw-Hill, 1993.
•Thermodynamics: An Engineering Approach, Yunus Cengel and Michael Boles, McGraww Hills, 2006.
•Fundamentals of Engineering Thermodynamics, Michael J. Moran and Howard N. Shapiro, 6th Edition, Wiley, 2008.
•Fundamentals of Statistical Thermodynamics, Richard E. Sonntag and Gordon J.Van Wylen, Krieger Publishing Co., 2nd ed., 1985.
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Advanced Thermodynamics - Mazlan 2019
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UNIVERSITI TEKNOLOGI MALAYSIA
ASSESSMENT
1. Test 1 & 2 (25% each) = 50%2. Assignments = 10%3. Project = 40%
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Thermodynamics in Science and
Engineering
Origin of the term:
Thermodynamics --- Study of how transfer of heatinfluences matter.
Now:
Thermodynamics --- Encompasses all of theinfluences and interrelationships that affect thecondition of matter --- thermal, mechanical,chemical, gravitational, surface, electrical,magnetic, atomic, ...
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Levels of Thermodynamics
Phenomenological --- Focuses on the
phenomena that matter can experience as
exposed by experimental observation.
Statistical --- Explains & predicts the
properties of matter from their structure.
Quantum Mechanics --- Explains why the
structure of matter is as it is observed.
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Thermodynamics
• Thermodynamics is the study of thermal processes in macroscopic systems.
• It is usually assumed that a classical thermodynamic system is a continuum, with properties that vary smoothly from point to point.
• The number of molecules in a macroscopic system is typically of the order NA = 6.02 x 1026 (Avogadro’s number).
• At STP (0oC and 1 atm), 1 kmole of a gas occupies 22.4 m3.
• The molecular density at STP is 6.02 x 1026/22.4
≈ 2.7 x1025 molecules/m3 (Loschmidt’s number).
• Thus, a cube of side 1 mm contains about 1016 molecules, while a cube of side 10 nm contains about 10 molecules.
• Clearly, the continuum model breaks down in the latter case.
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Thermodynamics
• The central concept of thermodynamics is temperature, which cannot be expressed in terms of the fundamental quantities of mass, length and time.
• Temperature is a statistical parameter, which may be defined precisely only for a macroscopic system.
• In this course, we study equilibrium thermodynamics from the standpoints of both classical thermodynamics and statistical thermodynamics.
• Given time, the alternative approach of Information Theory will be introduced.
• We ignore the more difficult topic of non-equilibrium thermodynamics, except for a brief foray into kinetic theory.
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Statistical Thermo
• The foundation of statistical mechanics may be given in the Fundamental Postulate, that an isolated system is equally likely to be in any of its accessible states.
• Largely the work of Boltzmann and Gibbs in the late nineteenth century, statistical mechanics was a microscopic theory, which explained the underpinnings of classical mechanics
• Gibbs paradox (1875), showed that the correct results of entropy-change calculations occurred only if the gas molecules were considered to be individually distinguishable.
• Although the advent of quantum mechanics in the nineteen twenties, brought a revolution in our understanding of physics, statistical mechanics entered the new physics unscathed.
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Statistical Thermo
• The foundation of statistical mechanics is the Fundamental
Postulate, that an isolated system is equally likely to be in any of its accessible states.
• To illustrate the postulate in the simplest manner, consider a system consisting of three weakly-interacting half-integer spins, in which just one of the three spins is “up”.
• The fundamental postulate states that, if the system is in thermal equilibrium, there is an equal probability of finding any one of the spins “up”.
• From this simple hypothesis, it is possible to deduce all of classical thermodynamics, understand its statistical underpinning, and introduce the concept of the partition function Z, leading to Bose-Einstein and Fermi-Dirac statistics.
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Quantum mechanics is a branch of physics dealing
with physical phenomena at microscopic scales, where
the action is on the order of the Planck constant.
Quantum mechanics departs from classical mechanics
primarily at the quantum realm of atomic and subatomic
length scales. Quantum mechanics provides a
mathematical description of much of the dual particle-
like and wave-like behavior and interactions of energy
and matter.
Quantum mechanics
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Thermal Contact
We know that if we have two objects at different
temperatures and we place them in thermal contactwith each other, the temperatures of the two objectswill change until they reach the same value.
This idea is also part of the
Zeroth Law of Thermodynamics.
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Zeroth Law of Thermodynamics
Two systems, separately in thermal equilibrium with a third
system, are in thermal equilibrium with each other.
• The property which the three systems have in common is
known as temperature θ.
• Thus the zeroth law may be expressed as follows:
if θ1 = θ2 and θ1 = θ3, then θ2 = θ3.
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Zeroth Law of Thermodynamics
– If two things are at the same temperature:
TA = TB
and one of them is at the same temperature as something else:
TB = Tc
then, all three things are at the same temperature or all three bodies are at thermal equilibrium with each other.
TA =TB = Tc
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“Conservation of Energy”:
Energy is conserved/fixed, does not destroyed,
but can be inter-converted.
First Law of Thermodynamics
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Second Law of Thermodynamics
Tells us whether chemical and physical processes are
favourable or not i.e. which direction is favourable e.g.,
melting, not freezing, of ice is favoured at 25ºC
But-tells us nothing about the speed of a process
‘The entropy of an isolated system will tend to increase to
a maximum value’
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Entropy (S):
-Systems of molecules have a tendency towards
randomization (disorder)- measured by entropyhigh randomness = high entropy
-Not necessarily toward the lowest energy state
S = k ln W
- an entropy of zero can only occur in a perfect crystal at a
temperature of absolute zero (0K or -273ºC), where W=1
S is entropy
k is the Boltzmann constant
W is the number of sub-states of equal energy
(i.e., different ways in which molecules
can be arranged in a system)
Water flowing downhill loses energy, but ice
melting gains (absorbs) energy
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Diffusion as an entropy-driven process
here the system is at
equilibrium because
molecules are distributed
randomly
here the system is
disturbed and has
become more ordered
(non-random)
here the system is
back to equilibrium
- the drive toward equilibrium is a consequence of the
tendency of the entropy to increase; entropy never decreases
(i.e., the transition from (c) to (b) would never occur
spontaneously)
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System
The collection of material we choose to examine
is called the system. It may be simple, such as
“a mole of neon gas”, or a very complicated
process in a complicated apparatus.
The important thing is that we define the system
in a convenient way for whatever calculations
we plan to do.
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Surroundings
Everything outside the system is the
surroundings.
The system and surroundings together make
up the universe.
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States
The state of a system is just the form in which
we find it to exist a any time.
For the sorts of systems we will look at, the
state is described by a small number of
properties which we can measure.
These state functions include pressure,
volume, temperature, composition, etc.
What other state functions can you think of?
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Standard States
It is useful to define a standard or reference
state for all materials.
Standard states are used so that information
about materials can be put in tables and used in
calculations.
We can look up the density, heat capacity and heat of formation of ethane gas at 25 ºC and 101.325 kPa.
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Standard States
It is useful to define a standard or reference
state for all materials.
Usually, the standard state is just the most stable
form of that material at the standard pressure of
101 325 Pa and a standard temperature of
298.15 K (25 oC).
For solutes, we use a 1.0 molal solution under
the same conditions.
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State Functions
x
y
z
Consider two different journeys from x to y.
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State Functions
x
z
Consider two different journeys from x to y.The first is taken by a adventurer, who climbsup to z and falls down the steep slope to y.
y
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State Functions
x
z
Consider two different journeys from x to y. The first is taken by a adventurer, who climbs up to z and falls down the steep slope to y.The second is taken by an engineer who simply blasts a tunnel through from x to y.
y
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State Functions
x
z
The first journey covers a distance xzy and the second just xy. However, the difference in height is just h in each case.
y
h
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State Functions
x
z
Thus the height defines a state function in thatthe difference in height is independent of path.The distance, on the other hand, does depend onpath and is not related to a state function.
y
h
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Systems
• A system is the portion of the physical world being studied.
• The system plus surroundings comprise a universe.
• The boundary between a system and its surroundings is the system wall.
• If heat cannot pass through the system wall, it is termed an adiabatic wall, and the system is said to be thermally isolated or thermally insulated.
• If heat can pass through the wall, it is termed a diathermal wall.
• Two systems connected by a diathermal wall are said to be in thermal contact.
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Systems
• An isolated system cannot exchange mass or energy with its
surroundings.
• The wall of an isolated system must be adiabatic.
• A closed system can exchange energy, but not mass, with its
surroundings.
• The energy exchange may be mechanical (associated with a volume
change) or thermal (associated with heat transfer through a diathermal
wall).
• An open system can exchange both mass and energy with its
surroundings.
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Isolated, Closed and Open Systems
Isolated
System
Neither energy
nor mass can be
exchanged.
Closed
System
Energy, but not
mass can be
exchanged.
Open
System
Both energy and mass
can be exchanged.
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Thermodynamic Variables
• Thermodynamic variables are the observable macroscopic
variables of a system, such as P, V and T.
• If the are used to describe an equilibrium state of the system,
they are known as state variables.
• Extensive variables depend on the size of the system; e.g.
mass, volume, entropy, magnetic moment.
• Intensive variables do not depend on size; e.g. pressure,
temperature, magnetic field.
• An extensive variable may be changed to an intensive
variable, known as a specific value, by dividing it by a
suitable extensive variable, such as mass, no.of kmoles, or no.
of molecules.
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Equilibrium States
• An equilibrium state is one in which the properties of the system do not change with time.
• In many cases, an equilibrium state has intensive variables which are uniform throughout the system.
• A non-equilibrium state may contain intensive variables which vary in space and/or time.
• An equation of state is a functional relationship between the state variables; e.g. if P,V and T are the state variables, then the equation of state has the form f(P, V, T) =0.
• In 3-dimensional P-V-T space,
an equilibrium state is represented by a point,
and the equation of state is represented by a surface.
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Processes
• A process refers to the change of a system from one equilibrium state to another.
• The initial and final states of a process are its end-points.
• A quasistatic process is one that takes place so slowly that the system may be considered as passing through a succession of equilibrium states.
• A quasistatic process may be represented by a path (or line) on the equation-of-state surface.
• If it is non-quasistatic, only the end-points can be shown.
• A reversible process is one the direction can be reversed by an infinitessimal change of variable.
• A reversible process is a quasistatic process in which no dissipative forces, such as friction, are present.
• A reversible change must be quasistatic, but a quasistatic process need not be reversible; e.g. if there is hysteresis.
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Processes
• An isobaric process is one in which the pressure is constant.
• An isochoric process is one in which the volume is constant.
• An isothermal process is one in which the temperature is constant.
• An adiabatic process is one in which no heat enters or leaves the system; i.e. Q = 0.
• An isentropic process is one in which the entropy is constant.
• It is a reversible adiabatic process.
• If a system is left to itself after undergoing a non-quasistatic process, it will reach equilibrium after a time t much longer than the longest relaxation time τ involved; i.e. t » τ.
• Metastable equilibrium occurs when one particular relaxation time τ0 is much longer than the time ∆t for which the system is observed; i.e. τ0» ∆t .