2/20/2013 1 C H A P T E R R R R R R R R 1 Advanced Thermodynamics Advanced Thermodynamics - Mazlan 2013 Mazlan 2013 FKM FKM UNIVERSITI TEKNOLOGI MALAYSIA UNIVERSITI TEKNOLOGI MALAYSIA Chapter 1 Introduction Advanced Thermodynamics Assoc. Prof. Dr. Mazlan Abdul Wahid Faculty of Mechanical Engineering Universiti Teknologi Malaysia www.fkm.utm.my/~mazlan C H A P T E R R R R R R R R 1 Advanced Thermodynamics Advanced Thermodynamics - Mazlan 2013 Mazlan 2013 FKM FKM UNIVERSITI TEKNOLOGI MALAYSIA UNIVERSITI TEKNOLOGI MALAYSIA MMJ1413 ADVANCED THERMODYNAMICS SEM 2012-13 2 FME, UTM SKUDAI SYNOPSIS This advanced course in engineering thermodynamics provides a strong foundation in the fundamentals of thermal sciences for further advanced research. Students shall be exposed to the restrictions on possible properties and systems. Basic and further treatment of the First and Second law of Thermodynamics will be given. Exergy analysis will be discussed regarding fundamental concepts, techniques and application in various systems. A simplified treatment of statistical thermodynamics will be covered with emphasis on the wave functions which helps promote a greater understanding of the foundations, laws, properties and applications in thermodynamics. This is one of the fundamental courses in a postgraduate program in Thermal Engineering.
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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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TOPIC/CONTENT
•Basic Problems of Thermodynamics – State Postulates•The Structure of Thermodynamics•Overview of Laws of Thermodynamics: First, Second and Third, Exergy/Availability for Closed and Open System, Entropy minimization •Thermodynamic Variables and Relations: Maxwell Relations, Entropy, Gibbs, etc•Unary Heterogeneous Systems•Multicomponent, Homogeneous Nonreacting Systems•Multicomponent Heterogeneous Systems•Statistical Thermodynamics: Energy Storage in Particles, Statistical Models, Statistical Laws – Boltzman, Bose-Eistein, Fermi-Dirac, Partition functions, Maxwell-Boltxman Distribution, Schrodinger Equation, Monatomic Gases and Wave Functions – Translation and Harmonic Oscillation, Diatomic and Polyatomic Gases
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Thermodynamics
• Thermodynamicsis the study of thermal processesin macroscopicsystems.
• 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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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-interactinghalf-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 realmof atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-likebehavior and interactions of energy and matter.
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Thermal Contact
We know that if we have two objects at differenttemperatures and we place them in thermal contactwith each other, the temperatures of the two objectswill change until they reach the same value.
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Thermal Equilibrium and the Zeroth Law
• If warm and cool objects are placed in thermal contact, energy, known as heat, flows from the warm to the cold object until thermal equilibrium is established.
• 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:
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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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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 examineis 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 systemin a convenient way for whatever calculationswe plan to do.
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Standard StatesIt is useful to define a standard or referencestate 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
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.The second is taken by an engineer who simply blasts a tunnel through from x to y.
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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.
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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 notdepend 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.
• Example: the specific heat is normally (heat capacity)/(mass).
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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
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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 entropyis 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 longestrelaxation 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 .