Definition of TemperatureR R f bRon Reifenberger

Birck Nanotechnology CenterPurdue UniversityyJanuary 11, 2012

Lecture 11

A Brief History

• Prior to 18th Century, society supports advances in medicine (health) and astronomy (navigation; time keeping)

• Other realms of science were viewed as a purely philosophic endeavor – not much in the way of experiments

• mid 18th Century (1750’s); transition from rural to urban • mid 18th Century (1750 s); transition from rural to urban society – start of Industrial Revolution; “How is heat converted to work in a steam engine?”

19th C t (1800 1850) i ti t d t • 19th Century (1800-1850) scientists were encouraged to study engines and their efficiency; is a perpetual motion machine possible?

• Two “Laws of Thermodynamics” emerge

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YEAR Electricity and Magnetism 1st Law Thermodynamics 2nd Law ThermodynamicsFr ncis H uksb first l ctr st tic

TIMELINES

1706 Francis Hauksbee - first electrostatic generator

1733 Charles de Cisternay Dufay - electrified objects repel as  well  as  attract

1738 Bernoulli uses idea of “atomic” motion to calculate pressuremotion to calculate pressure

1745 Bishop Von Kleist & Cunaeus of Leyden - Leyden jar (first capacitor)

1746 – Ben Franklin - simple theory of electricity; two polarities of charge

J Black - discovers heat capacity latent ~1760

J. Black discovers heat capacity, latent heat; inherently contradicts the calorique

theory

1760-75J. Watt – invents steam engine (condenser)

1785 Chales Coulomb; force law for 1785

electrostatics

1779 Wm. Cleghorn – formulated coherent calorique theory

1790Count Rumford (Benj. Thompson)

questions caloric theory while boring out canons in Bavaria

1794 Boulton and Watt - commercial steam engines; first attempts to define work,

power, horsepower, etc.

1798 Count Rumford – established connection

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1798between mechanical work and heat

1800 Alexandre Volta – first electric battery

1819 Hans Christian Oersted – magnetic field from current

Andre Marie Ampere – first theory of the Herapath links heat with “atomic” 1820 Andre Marie Ampere first theory of the magnetic field

Herapath links heat with atomic motion

1821 Michael Faraday – primitive electric motor

1824 Carnot formulates 2nd Law; supports calorique theorycalorique theory

1827 Georg Ohm – Ohm’s Law

1830 William Sturgeon – first electromagnet

1831 Michael Faraday – electromagnetic induction

1833 Joesph Henry – self inductance

1834 Heinrich Lenz – Lenz’s Law

1837 Samuel Morse – first telegraph

1842 James Prescott Joule – heat produced by electric current

J.R. von Mayer – (heat + work) is conserved; initial formulation of 1st Lawelectric current conserved; initial formulation of 1st Law

1843-49 Joule’s quantitative experiments

1845 Waterston first suggests that energy of gas “molecules” is proportional to

temperatureG h ff h ff’ l f 1846 Gustav Kirchoff – Kirchoff’s laws of

electric circuits

1847 Helmholtz: conservation of energy, 1st Law of Thermodynamics

1850s – J.P. Joule – quantified heat & k in m n s m h ni l

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1850s work in many ways – mechanical, electrical, etc.; Calorique theory of heat

finally overturned

1858 Clausius introduces concept of mean free path

1859 Maxwell introduces idea of a distribution function

1865 James Clerk Maxwell – unified theory of electricity and magnetism

Clausius introduces concept of thermodynamic entropy; Loschmidt

estimates the size of an atom

1868

Boltzmann extends Maxwell’s mathematical derivation of distribution function with distribution function with

considerable physical insight

1872

Boltzmann’s transport equation proves that the MB distribution function is the ONLY one possible for a gas in

thermal equilibriumT i El i i d M i b J1873 Treatise on Electricity and Magnetism  by James  

Clerk Maxwell  

1875 Henry Rowland – rotating static charge creates magnetic field

1876 Alexander Graham Bell – telephone

1877 Boltzmann: S=k ln(w)1877 Boltzmann: S=kBln(w)

1879 Thomas Edison – electric lamp

1884 Stefan-Boltzmann T4 law – connects thermodynamics with E&M

1886 William Stanley – electric transformer and transmission of ac voltagesand transmission of ac voltages

1887 Heinrich Hertz – generation and detection of electromagnetic waves

Clausius, Maxwell, Boltzmann – kinetic theory of a gas (late 1800s)

1887 Oliver Heaviside – reworks Maxwell’s theory – FOUR Maxwell equations

1888 Nikola Tesla – alternating current; long-

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1888distance electrical transmission

1902Gibbs publishes Elementary Principles

in Statistical Mechanics

Why did it take ~150 years to sort all this out? A confusion between Temperature and Heat.f mp

We all have a qualitative feel for what “heat”, “hot”, “cold”, etc. means, but how do we turn , , . m n , u w w u n

these qualitative feelings into quantitative concepts?

The answer to this question relies on an understanding how microscopic properties (atoms) translate into macroscopic measurable quantities

The Science of Thermodynamics

translate into macroscopic measurable quantities.

y

Thermodynamics fundamentally was developed to understand the relationship between heat to understand the relationship between heat

and work6

While developing the Science of Thermodynamics, many Fundamental Conceptual problems arisemany Fundamental Conceptual problems arise

I I H t C n d?I. Is Heat Conserved?

II. Is Cold the Opposite of Hot?

III. How to Quantify Temperature?

…….

Without a Science of Thermodynamics, many of these basic concepts are not well-defined

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Example I: Water Wheel vs. Steam Engine

Steam in

Steam in

W k i Work is produced

Water in = Water out + Work

Heat in ? ? Heat out + WorkWater is conserved Heat in ?=? Heat out + WorkWater is conserved.

Is Heat conserved? 8

Example II: Is “Hot” the opposite of “Cold”?

• Most people would claim that “Hot” and “Cold” are opposites.

• To make something hot, we add heat (measured in thermal units) b h because heat is energy.

• You can always provide “more heat” by adding more energy, so you can always make an object “hotter”.always make an object hotter .

• Therefore, by subtracting energy, you must have “less heat”; an object will get colder.

• But….., you can only cool to -273.15oC, you can't get any colder.

• Since you can’t go any colder, you cannot continue to subtract more y g y , yheat (or add “more cold”)?

• How then can “cold” be the opposite of “hot”?

• “Cold” is only a word used to describe the “absence of heat”.9

Example III: Temperature – a way to quantify the “hotness” or “coldness” of an object

Which object is colder?

Styrofoam cup Piece of metal

You can’t even trust your sense of touch!Thermodynamic Laws

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The Big Picture

Four Laws of Thermodynamics0th Law: Definition of thermal equilibrium0 Law: Definition of thermal equilibrium

1st Law: U = Q - W – quantity of energy; in a closed system energy can be exchanged but it can not be created or d t d destroyed

2nd Law: Definition of Entropy – quality of energy: when transforming “organized, useful” energy, some of it always g g gy ydeteriorates into “disorganized, non-useable” energy

3rd Law: The entropy of a system at zero absolute temperature is a well-defined constant because a system at temperature is a well defined constant because a system at zero temperature exists in its lowest energy (ground) state. Its entropy is determined only by the degeneracy of the ground state. (Nernst 1906-1912).g ( )

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Highly accurate measures of temperature are hard to find!temperature are hard to find!

• based on easily measured property of a common substance

• easy to calibrate

• the physical property chosen to indicate temperature should t i ll i i l T imonotonically increase in value as T increases

• physical property must be measurable over a wide range of temperatures

• readily reproduced in other laboratories

Thermoscopes12

A simple constant-volume gas thermoscopethermoscope

calibrated masses mmasses, m

moveable calibration

markpiston, area A

Force mgPressurePiston Area

Agas

substance whose

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5

:[ / ] ( )1 1.01 10

Piston Areaunits N m Pascal Pa

atm Pa

A

substance whose temperature you want to measure

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Implementation of a Constant Volume Gas Thermoscope

PExperiment showed this was a particularly reliable thermometer

Patm

thermometer

ρatmP mgP

A

mh

atmh gP

P h

AA

A

atmP hg T

T=C1 P + C2 1 atm = 760 mm of Hg = 760 Torr

Thermometers have scales printed on them; thermoscopes do not.

one click14

Defining Temperatures using a Constant Volume

Can add (or remove)

Hg

Patm =Const.

gGas Thermoscope

PtP and P are pressures

P

Po and P100 are pressures measured at fixed points.

calibration mark

V

What is tC(temperature of

liquid bath)?P - P

tC = x 100 (for Celsius scale)Pt - Po

P100 - Po Which gas is best??15

Which Gas is Best?(measuring the boiling point of sulfur)(measuring the boiling point of sulfur)

Pt

Thermometers16

All Temperature Thermometers Rely on Fixed PointsRely on Fixed Points

tC= 5/9 (tF-32) tF = 9/5 tC + 32tC= 5/9 (tF-32) F 9/ C

Fixed PointsFixed PointsFixed PointsFixed Points

h 1 4 ’ h 1 In the 1840’s there were ~18 different thermometer scales; each country had their own! Negative Temperatures?

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Negative Temperatures?

This value does not depend on gas used

V1

depend on gas used

V2

V3V3

Defines Absolute Zero as –273.15oC

T = tC + 273.15 (Kelvin Scale) Note that temperature DIFFERENCES are the same18

The range of temperatures is enormous!

e!gn

itud

e

“Standard Temperature” = 273 K

of

mag

orde

rs

~ 20

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0th Law of Thermodynamics

If objects A and B have the same temperature as object C then objects A temperature as object C, then objects A

and B are also in thermal equilibrium with each other

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