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Thermodynamics Y Y Shan

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Statistical thermodynamics, being the microscopic theory, can be thought of as

a bridge between macroscopic and microscopic properties of physical systems. With the

development of atomic and molecular theories in the late 19th century, thermodynamics

was given a molecular interpretation.

Essentially, statistical thermodynamics is an approach to thermodynamics situated

upon statistical mechanics, which focuses on the derivation of macroscopic results from

first principles. It can be opposed to its historical predecessor phenomenological

thermodynamics, which gives scientific descriptions of phenomena with avoidance of

microscopic details. The statistical approach is to derive all macroscopic properties

(temperature, volume, pressure, energy, entropy, etc.) from the properties of moving

constituent particles and the interactions between them (including quantum phenomena).

It was found to be very successful and thus is commonly used.

The study of thermodynamics is important because many machines and modern

devices change heat into work (such as an automobile engine) or turn work into heat (or

cooling, as in a refrigerator). It can be applied to a wide variety of topics in scienceand

engineering, such as engines, phase transitions, chemical reactions, transport phenomena,

and even black holes. The results of thermodynamics are essential for other fields of

physics and for chemistry, chemical engineering, aerospace engineering, mechanical

engineering, cell biology, biomedical engineering, and materials science.

For e.g. thermal energy converts to mechanical energy:

Typical thermodynamic system - heat moves from hot (boiler) to cold (condenser),

(both not shown) and workis extracted, in this case by a series of pistons.

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Historical notes:

Sadi Carnot, the "father of thermodynamics", who in 1824 published Reflectionson the Motive Power of Fire, a discourse on heat, power, and engine efficiency. The

paper outlined the basic energetic relations between the Carnot engine, the Carnot cycle,

and Motive power. This marks the start of thermodynamics as a modern science.

The term thermodynamics was coined by James Joule in 1858 to designate the

science of relations between heat and power. By 1849, "thermo-dynamics", as a

functional term, was used in William Thomson's paperAn Account of Carnot's Theory of

the Motive Power of Heat. The first thermodynamic textbook was written in 1859 by

William Rankine, originally trained as a physicist and a civil and mechanical engineering

professor at the University of Glasgow

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Part I Classical thermodynamicsThe Macroscopic theory

Chapter 1 The Zeroth law of thermodynamics and the temperature

1.1Basic concepts:vocabularies associated with thermodynamics

(i) System (thermodynamic system), Surroundings(environment) and Boundary:

In thermodynamics, interactions between substance of large ensembles of objects

(such as gas, liquid, and solids, which contains large number of atoms, molecules) are

studied and categorized. Central to this are the concepts of systemand surroundings.

A thermodynamicsystem, originally called a working substance, is composed oflarge number of particles, whose average motions define its macro properties.

A boundaryseparates the system from the rest of the universe, being referred to as

the environment or surroundings (sometimes called a reservoir). The possible

exchanges of work, heat, or matter between the system and the surroundings take

place across this boundary. Boundaries are of four types: fixed, moveable, real, and

imaginary

A system can be anything, for example a piston, a solutionin a test tube, a living

organism, or a planet, etc

There are four typical thermodynamic systems: Thermodynamics is basically

concerned with the flow and balance of energy and matter in a thermodynamic

system. Four types of thermodynamic systems are distinguished depending on the

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kinds of interaction and energy exchange taking place between the system and its

surrounding environment:

1. Isolated systems: matter and energy may not cross the boundary. No matter and

energy(heat, work) exchange with the surrounding.

2. Closed systemsare able to exchange energy (heat and work) but matter may not

cross the boundary.

3. Open systems: exchanging energy (heat and work) and matter with their

environment. There are five dominant classes of systems:

4. Adiabatic Systems heat must not cross the boundary.

(ii) State and State parameters (state coordinates) and function of state for

thermodynamic systems.State: For a state of a thermodynamic system,the macroscopic condition can be

described by its particular thermodynamic parameters. That is, any state of any system

can be described by a set of parameters, such as temperature(T), pressure(P), density,

composition, independently of its surroundings.

State parameters: These particular parameters are therefore called

thermodynamic state parameters (or state coordinates). They are all macroscopic

physical quantities, which can be measurable, such as P, V, T, E, B, etc. Athermodynamic system is described by a number of thermodynamic parameters (e.g.

temperature, volume, pressure). The number of parameters (or coordinates) needed to

describe the system is the dimension of the state spaceof the system.

There are FOUR kinds of state coordinates, namely: Geometrical (such as

volume), Mechanical (such as pressure), Chemical (such as composition or mole), and

electromagnetic parameters(such as intensities of electric and magnetic fields)

State parameters can also be classified as Intensive and extensive quantities:

An intensive quantity (also intensive variable) is a physical quantity whose

value does not depend on the amount of the substance. Examples of intensive quantities

include: temperature, pressure, density, viscosity, electric field, chemical potential,etc.

An extensive quantity (also extensive variable or extensive parameter) is a

physical quantity, whose value is proportional to the size of the system it describes.

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Examples of extensive quantities include: mass, length, volume, energy, entropy,

electrical resistance, heat etc.

At least two independent state coordinates are needed to describe any

thermodynamic system, an intensive one and an extensive one.

(iii) Function of state (or state function):

There is an optimal ensemble of independent parameters that uniquely specify

thermodynamic state, and all other state parameters (measurable macroscopic quantities)

can be derived from these. Those relationships between the derived parameters and the

original independent parameters are called Function of State.

Also, when a system changes from one state to another continuously, a state

function is a function that the change of its value between the two states only dependsupon the parameters' values at the endpoints of the path.

For example, we know for ideal gas, PV=nRT=f(T), from state 1 at T1, to

state2 at T2, the change of the function

)()( 12 TTnRPVf == ,

only dependents on the endpoints of the temperature values, T2 and T1. The product

f=PVis therefore a state functionof the system.

A state function describes the equilibrium state of a system. For example, internalenergy, enthalpy and entropy are state functions. They can describe quantitatively an

equilibrium state of thermodynamic systems. At the same time, mechanical work and

heat are process functions because they describe quantitatively the transition between

equilibrium states of thermodynamic system.

(iv) Thermal equilibrium state

As time passes in an isolated system, internal differences in the system tend to

even out and pressures and temperatures tend to equalize, as do density differences. A

system in which all equalizing processes have gone practically to completion, is

considered to be in a stateof thermodynamic equilibrium

In thermodynamic equilibrium, a system's macro physical properties are, by definition,

unchanging in time.

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1.2 Thermal equilibrium and theZeroth Law of Thermodynamics

(i) Thermal equilibrium: It is observed that a higher temperatureobject which is in

contact with a lower temperature object will transfer heatto the lower temperature object.

The objects will approach the same temperature, and in the absence of loss to other

objects, they will then maintain a constant temperature. They are then said to be in

thermal equilibrium. Thermal equilibrium is the subject of the Zeroth Law of

Thermodynamics.

(ii) The Zeroth law: it states that if two systems are at the same time in thermal

equilibrium with a third system, they are in thermal equilibriumwith each other.

If A and C are in thermal equilibrium with B, then A is in thermal equilibrium

with B. Practically this means that all three are at the same temperature, and it forms the

basis for comparison of temperatures.

History: The term zeroth law was coined by Ralph H. Fowler. The law is more

fundamental than any of the others. However, the need to state it explicitly as a law was

not perceived until the first third of the 20th century, long after the other three laws

named as such, hence the zero numbering.

1.3

Concept of temperature: a unique state parameter (different from the other the four

kinds state parameters)

Macroscopically, temperature means the sensations of hotness or coldness of an

object.

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In the microscopic view, temperature is associated with the agitation, vibration, or

motion of the micro-particles (atoms, molecules) inside the macro-object.

A scientific understanding of the concept of temperature builds upon thermal

equilibrium. It is often claimed (for instance by Max Planck) that the Zeroth law proves

that we can define a temperature function, or more informally, that we can 'construct a

thermometer'. This is because when two systems are in thermal equilibrium, they will

show the same physical property, and this unique physical property is called

temperature, i.e., the temperaturesof the two thermal equilibrium systems are the same.

The Zeroth law is the basis for the definition of temperature.

1.4

Temperature scale, Temperature measurement and thermometers

(i) Temperature scale: The Celsius, Kelvin, and Fahrenheit temperature scales areshown in relation to the phase change temperatures of water. The Kelvin scale is called

absolute temperature and the Kelvin is the SI unit for temperature.

The triple point of water is 273.16 K, and that is an international standard temperature

point. The freezing point of water at one atmosphere pressure, 0.00C, is 0.01K below

that at 273.15 K. If you want to be really precise about it, the boiling point is 373.125 K,

or 99.75 C. But for general purposes, just 0 C and 100 C are precise enough.

(ii) Temperature measurement and thermometers: Measuring temperature relies on

measuring some physical property of a working material that varies with temperature, so

that thermometers, devices for measuring temperature, have been developed. Some of

the thermometers are:

(a) Bulb thermometer

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This is based on the fact that the volume of the working matter in the bulb

(sometimes colored alcohol or metallic liquid mercury) grows bigger when heated and

smaller when cooled, i.e, the change of volume is proportional to the change of

temperature

(b) liquid crystal thermometeris a type of thermometerthat contains heat-sensitive

liquid crystals in a plastic strip that change color to indicate different temperatures.

Temperature changes can affect the color of a liquid crystal, which makes them useful for

temperature measurement. The resolution of liquid crystal sensors is in the 0.1Crange.

Disposable liquid crystal thermometers have been developed for home and medical use,

and they can read body temperature by being placed against someones forehead and are

safer than a mercury-in-glass thermometer

(c) Resistance thermometers, also called resistance temperature detectors, are

temperature sensors that exploit the predictable change in electrical resistance of some

materials with changing temperature. As they are almost invariably made of platinum,

they are often called platinum resistance thermometers.

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(d) Semiconductor thermometers: silicon bandgap temperature sensor is an

extremely common form of temperature thermometer used in electronic equipment. Its

main advantage is that it can be included in a silicon integrated circuit. The principle of

the sensor is that the bandgap (and therefore its forward voltage) of a silicon diode is

temperature-dependent.

(e) Thermocouples: In electronics, this kind of thermometers is a widely used type of

temperature sensor. The principle of operation is based on the thermoelectric effect,

which says that when any conductor (such as a metal) is subjected to a thermal gradient,

it will generate a voltage. This effect was discovered by the German-Estonian physicist

Thomas Johann Seebeckin 1821.

(f) Infrared thermometers(or infrared pyrometer): they measure temperatureusing

blackbody radiation (generally infrared) emitted from objects (the radiation is

temperature dependent). They are sometimes called non-contact thermometers to

describe the devices ability to measure temperature from a distance. By knowing the

amount of infrared energy emitted by the object, the object's temperature can be

determined.

A doctor's IR thermometer in use

In principle, by scanning the infrared thermometer, the temperature patterns

across the surface of an object can be recorded and a thermal image related to the spottemperature can be constructed (i.e. a subject called Infrared thermography).

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A 2D-tempearture pattern

constructs a thermographic image of a dog.

1.5 Equation of state:

In thermodynamics, an equation of state is a formula describing the interconnection

between various macroscopically measurable properties of a system, i.e usually an

relationship between state parameters(coordinates) and the temperature of the system.

More specifically, It is a thermodynamic equation describing the state of matter under a

given set of physical conditions, providing a mathematical relationship between two or

more state parametersassociated with the matter, such as its temperature,T, pressure, P,

volumeV. A typical equation of state can be written as:

0),,( =Tyxf

x, ycan be the volume Vand pressure Por other state parameters (macro quantities)

of the system.

Equations of state are useful in describing the properties of gases, fluids, mixtures of

fluids, solids.

(i)

Equation of state for Gas

(a) The ideal gas law:equation of state for ideal gas

In 1834 mile Clapeyroncombined Boyle's Law and Charles' law into the first

statement of the ideal gas law, which was originally determined empirically and issimply

kTNnRTPVA

==

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n = number of moles R = universal gas constant = 8.3145 J/mol K N = number of molecules k = Boltzmann constant = 1.38066 x 10-23J/K = 8.617385 x 10-5eV/K k = R/NA

NA= Avogadro's number = 6.0221 x 10

23

/mol

(b) The van der Waals equation of state

The ideal gas lawtreats the molecules of a gas as point particles with perfectly elastic

collisions. This works well for dilute gases in many experimental circumstances. But

gas molecules are not point masses, and there are circumstances where the properties

of the molecules have an experimentally measurable effect.

A modification of the ideal gas law was proposed by Johannes D. van der Waals in

1873 to take into account molecular size and molecular interaction forces. It is usually

referred to as the van der Waals equation of state, one of the first to perform markedly

better than the ideal gas law:

The constants a and bhave positive values and are characteristic of the individual gas.

The van der Waals equation of state approaches the ideal gas law PV=nRTas the values

of these constants approach zero. The constant a provides a correction for the

intermolecular forces. Constant b is a correction for finite molecular size and its value is

the volume of one mole of the atoms or molecules

(ii) Equation of state for liquid: Such empirical equations can be found in many

references discussing specific liquids

(ii) Equation of state for solid: For e.g., paramagnetic materials, its equation of

state has the expression:

0),,( =TBMf , which is typically expressed as the Curies Law:

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Which relates the magnetization of the material to the applied magnetic field and

temperature.

Mis the resulting magnetisation. Bis the magnetic flux densityof the applied field,

measured in teslas. Tis absolute temperature, measured in kelvins. Cis a material-

specific Curie constant. This relation was discovered experimentally (by fitting the

results to a correctly guessed model) by Pierre Curie.

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