Lecture #2 Zeroth Law

8/2/2019 Lecture #2 Zeroth Law

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ENGG 109: FLUIDS MECHANICS with THERMODYNAMICS

Thermodynamics Lecture #2: ZEROTH LAW

Lecturer: Dr Eann A. Patterson

ENGG109: FLUID MECHANICS with THERMODYNAMICSLecture #2: ZEROTH LAW

Eann A. Patterson

School of Engineering


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LEARNING OBJECTIVES: Weeks 7-8

Explain the basic concepts of thermodynamics, such as

systems, state, state postulate, equilibrium, process, cycle,

pure substance and ideal gas

Discuss zeroth law of thermodynamics and review concepts

of temperature and temperature scales

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Zeroth Law

Its an afterthought; not dignified with a name until the

early 20th century, by then the 1stand 2ndlaws were so

well-established that there was no hope of going back

and renumbering

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Mechanical Equilibrium

Connect system A and B and if nothing happens, we know

they are in equilibrium.

Now connect B to C; and if nothing happens, we know

nothing will happen when we connect A to C.

Peter Atkins in The Laws of Thermodynamics: A Very Short

Introduction, OUP, 2010 uses pressurised cylinders connected by a

tubes containing a piston. I am going to use a weighing balance as an

analogy.

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Thermal Equilibrium

Tear your sheet of paper into three equal size pieces, and

label them A, B and C.

What happens when you hold one of them, say C?

We can describe the paper as being thermally sensitive

Now, put A and B on the bench overlapping one another.

Are they different colours?

They should be the same colour, so they are in thermal equilibrium

Separate A and B, then put B and C together. Is there any

change in colour?

No. So, if A is in thermal equilibrium with B, and B is in thermal

equilibrium with C, then C be in thermal equilibrium with A.

This is the Zeroth Law go on try it.

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Zeroth Law

Zeroth Law implies there is a property that enables us to

anticipate when two systems are in thermal equilibrium;

we call it temperature

We can summarise the Zeroth Law statement of thermal

equilibrium by saying

A, B & C are at the same temperature

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Through and Warm

Walls that allow heat to pass through, i.e. conduct, are

called diathermic

from the Greek for through and warm.

Insulated walls that are impassable to heat are known as

adiabatic.

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Image: scottchan / FreeDigitalPhotos.net

THERMOMETER

Pick-up your piece of paper labelled B; what happens?

Paper that changes colour with temperature is called thermochromic

A thermometer is a special case of system B

A system with a property that changes when put in contact with a

system with diathermic walls

Your skin is a diathermic wall, or boundary for a system we usually call

your body

Thermochromic paper is not a very good thermometer because it is

only sensitive over a small temperature range

Prefer to use a column of mercury or electrical resistance

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Temperature Scales

Swedish astronomer, Anders Celsius (1701-44) devised a

scale where water froze at 100 and boiled at 0

German instrument maker, Daniel Fahrenheit, 1686-1736first to use a mercury thermometer.

0: lowest temperature of salt, ice, water mixture

100 : his body temperature (portable but unreliable standard)

Water freezes at 32 F and boils at 212 F

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Image: arztsamui / FreeDigitalPhotos.net


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Absolute Temperature

Temporary advantage of Fahrenheit scale

Negative numbers rarely needed with technology of the day

Intuitive to set as the lowest attainable temperature

So, today we use Kelvin Scale

Kelvin Scale

0is thermodynamically absolute zero (defined by 3rd Law)

Degrees same size as for Celsius scale

Water freezes at 273K and boils at 373K

Rankine Scale

0is thermodynamically absolute zero (defined by 3rd Law)

Degrees same size as for Fahrenheit scale

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Statistical Thermodynamics

Thermodynamics emerged during 19th century

with steam engines and the drive for competitive advantage

before everyone was convinced about the existence of atoms.

You can do classical thermodynamics without believing in atoms

Insight gained if we think about what is happening inside a

system

this branch of thermodynamics is called statistical thermodynamic.s

Statistical thermodynamics is about accounting for the bulk properties

of matter in terms of its constituent atoms. Statistical because we dont look at the behaviour of individual atoms

but the average behaviour of a myriad of atoms.

e.g. pressure on a wall/skin

11Image:a

frica/FreeDigitalPhotos.n

et


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Quantum mechanics

Atoms can only exist with certain energies

Collection of atoms will consist of

some in the lowest energy state (ground)

some in the next higher energy state

and so on, with diminishing numbers in the higher states.

When atoms settle into an equilibrium population

(though with a few jumping between energy states but creating no

net change in the population distribution)

population distribution can be found from a knowledge of the energystates and a single parameter,

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Image: Rawich / FreeDigitalPhotos.net


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Boltzmann Distribution

Distribution of atoms over allowed energy states is known as

the Boltzmann distribution (Ludwig Boltzmann, 1844-1906)

where 0 is the lowest (ground) energy state

For higher energy states, population decreases exponentially

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Ee

E =

0

Population of energy state,E

Population of energy state, 0


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Image: Ambro / FreeDigitalPhotos.net

Boltzmann Constant

It turns out that

where kis called Boltzmanns constant

for T in Kelvin, = 1.38 x 10-23 J/K

1 Joule is energy of 50g ball dropped from 2m, or a single

heart beat

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kT

1=


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= 1/kT Temperature tells us the most probable population

distribution of atoms over available energy states

high T, low : many states have significant populations

low T; high : only lower states have significant populations

So, temperature is a parameter that summarises the relative

populations of energy levels in a system at equilibrium

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is a more natural parameter for temperature than T

T=0K is unattainable in a finite number of steps is hard to appreciate

but easier to appreciate that = is unattainable (3rd Law)

is not practical Water freezes at =2.65x1020J-1 and boils at 1.94x1020J-1

Todays temperature is about 2.56x1020J-1

k is a just a conversion factor

Because Celsius and Fahrenheit did their work before Boltzmann

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Ideal gas

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RTp =Image : xedos4 / FreeDigitalPhotos.net

Consider a swarm of molecules moving at different speeds in

different directions

Speed is proportional to kinetic (translational) energy

Boltzmann distribution describes distribution of translational energies

So, can relate speed of molecules to temperature (Maxwell-Boltzmann

distribution)

Thus, temperature is a measure of average molecular speed

e.g. on a warm day (25C) average speed of molecules is 4% higher than on

a cold day (0 C).

At higher temperature molecules will collide more often and

faster with boundary walls, leading to higher pressure


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Lecturer: Dr Eann A Patterson 18

Image: dan / FreeDigitalPhotos.net

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Lecture #2 Zeroth Law