chapter 1 introduction advanced thermodynamicsmazlan/?download=adv thermo chapter 1.pdfadvanced...

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Advanced Thermodynamics Advanced Thermodynamics -- Mazlan 2013Mazlan 2013

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UNIVERSITI TEKNOLOGI MALAYSIAUNIVERSITI TEKNOLOGI MALAYSIA

Chapter 1

Introduction

Advanced ThermodynamicsAssoc. Prof. Dr. Mazlan Abdul WahidFaculty of Mechanical EngineeringUniversiti Teknologi Malaysiawww.fkm.utm.my/~mazlan

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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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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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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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REFERENCES

•Thermodynamics in Materials Science, by Robert T. DeHoff, McGraw-Hill, 1993.

•Adrian Bejan: Advanced Engineering Thermodynamics, Wiley 2006.

•Richard E. Sonntag and Gordon J.Van Wylen: Fundamentals of Statistical Thermodynamics, Krieger Publishing Co.2nd ed., 1985.

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ASSESSMENT

1. Test 1 & 2 (20% each) = 40%2. Assignment and Project = 20%3. Final Exam = 40%

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Thermodynamics in Science and Engineering

Origin of the term: Thermodynamics --- Study of how transfer of heat

influences matter.Now:Thermodynamics --- Encompasses all of the

influences 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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UNIVERSITI TEKNOLOGI MALAYSIAUNIVERSITI TEKNOLOGI MALAYSIA 1

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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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 thermodynamicsfrom 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-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.

Quantum mechanics

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Thermodynamics

• Zeroth Law of Thermodynamics– Temperature

• First Law of Thermodynamics– Conservation of energy.

• Thermochemistry• Standard Enthalpy of Formation• Hess’s Law

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The ‘laws of thermodynamics’ are simply statements about our experience with the world.

The first law of thermodynamics is:

The change in the energy of a system isequal to the work done on the system plusthe heat transferred into it.

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Thermodynamics

• Zeroth Law of Thermodynamics– Temperature

• First Law of Thermodynamics– Conservation of energy.

• Thermochemistry• Standard Enthalpy of Formation• Hess’s Law

• Second Law of Thermodynamics– Entropy of the universe always goes up when

something happens• Chemical equilibrium• Phase equilibrium

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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.

This idea is also part of the

Zeroth Law of Thermodynamics.

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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:

TA = Tc

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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:

if θ1 = θ2 and θ1 = θ3, thenθ2 = θ3.

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“conservation of energy”:

Energy cannot be created or destroyed in chemical processes, but can only 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 entropy

high 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 entropyk is the Boltzmann constantW is the number of sub-states of equal energy

(i.e., different ways in which moleculescan be arranged in a system)

Water flowing downhill loses energy, but icemelting 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 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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SurroundingsEverything outside the system is the surroundings.

The system and surroundings together make up the universe.

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StatesThe state of a system is just the form in whichwe 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 StatesIt is useful to define a standard or referencestate 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 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

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 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.

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 mustbe 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 SystemNeither energy nor mass can be exchanged.

ClosedSystem

Energy, but not mass can be exchanged.

OpenSystem

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 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

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 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 .

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