heat and thermometer

1. Shahjahannotes:TemperatureandThermometers
We all have a feel forwhat temperature is.We evenhave asharedlanguage thatwe use to
qualitativelydescribetemperature.The waterinthe showerorbathtubfeelshotorcoldor
warm.The weatheroutside is chilly or steamy.We certainlyhave agood feel forhow one
temperature isqualitativelydifferentthananothertemperature.We maynotalwaysagree on
whetherthe roomtemperature istoohotor too coldor just right.But we will likelyall agree
that we possessbuilt-inthermometersformakingqualitative judgmentsaboutrelative
temperatures.
What is Temperature?
Despite ourbuilt-infeelfortemperature,itremainsone of those conceptsinscience thatisdifficultto
define.Itseemsthatatutorial page exploringthe topicof temperatureand thermometersshouldbegin
witha simple definitionof temperature.Butitisat thispointthatI'm stumped.SoI turn to that familiar
resource, Dictionary.com...where Ifinddefinitionsthatvaryfromthe simple-yet-not-too-enlightening
to the too-complex-to-be-enlightening.Atthe riskof doinga bellyflopinthe pool of enlightenment,I
will listsome of those definitionshere:
 The degree of hotnessorcoldnessof a body or environment.
 A measure of the warmthor coldnessof an objector substance withreference tosome
standardvalue.
 A measure of the average kineticenergyof the particlesinasample of matter,expressedin
termsof unitsor degreesdesignatedonastandard scale.
 A measure of the abilityof asubstance,or more generallyof anyphysical system,totransfer
heatenergyto anotherphysical system.
 Anyof variousstandardizednumerical measuresof thisability,suchasthe Kelvin,Fahrenheit,
and Celsiusscale.
For certain,we are comfortable withthe firsttwo
definitions - the degree ormeasure of how hotor coldan
objectis.But our understandingof temperature isnot
furtheredbysuchdefinitions.The thirdandthe fourth
definitionsthatreference the kineticenergyof particlesand
the abilityof a substance totransferheatare scientifically
accurate. However,these definitionsare fartoo
sophisticatedtoserve asgoodstartingpointsfora
discussionof temperature.Sowe will resigntoa definitionsimilartothe fifthone thatislisted -

2. Shahjahannotes:TemperatureandThermometers
temperature canbe definedasthe readingona thermometer.Admittedly,thisdefinitionlacksthe
powerthat isneededforelicitingthe much-desiredAha!Now IUnderstand! moment.Nonethelessit
servesasa greatstartingpointfor thislessononheatandtemperature.Temperature iswhatthe
thermometerreads.Whateveritisthattemperature isa measure of,itisreflectedbythe readingona
thermometer.Soexactlyhowdoesathermometerwork?How doesitreliably meterwhateveritisthat
temperature isameasure of?
How a ThermometerWorks
Today,there are a varietyof typesof thermometers.The type thatmostof us are familiarwithfrom
science classisthe type that consistsof a liquidencasedinanarrow glass column.Olderthermometers
of thistype usedliquidmercury.Inresponse toourunderstandingof the healthconcernsassociated
withmercuryexposure,thesetypesof thermometersusuallyuse some type of liquidalcohol.These
liquidthermometers are basedonthe principal of thermal expansion.Whenasubstance getshotter,it
expandstoa greatervolume.Nearlyall substancesexhibitthisbehaviorof thermal expansion.Itisthe
basisof the designandoperationof thermometers.
As the temperature of the liquidinathermometerincreases,itsvolume increases.The liquidisenclosed
ina tall,narrowglass(or plastic) columnwithaconstantcross-sectional area.The increase involume is
thusdue to a change inheightof the liquidwithinthe column.The increase involume,andthusinthe
heightof the liquidcolumn,isproportional tothe increase intemperature.Suppose thata10-degree
increase intemperature causesa1-cmincrease inthe column'sheight.Thena20-degree increase in
temperature willcause a2-cm increase inthe column'sheight.Anda30-degree increase intemperature
will cause s3-cm increase inthe column'sheight.The relationshipbetweenthe temperatureandthe
column'sheightislinearoverthe small temperature range for whichthe thermometerisused.This
linearrelationshipmakesthe calibrationof athermometerarelativelyeasytask.
The calibrationof any measuringtool involvesthe placementof divisionsormarksuponthe tool to
measure a quantityaccuratelyincomparisontoknown
standards.Anymeasuringtool - evenameterstick - must
be calibrated.The tool needs divisionsormarkings;for
instance,ametersticktypicallyhasmarkingsevery1-cm
apart or every1-mmapart. These markingsmustbe
accuratelyplacedandthe accuracy of theirplacementcan
onlybe judgedwhencomparingittoanotherobjectthat
ispreciselyknowntohave acertainlength.
A thermometeriscalibratedbyusingtwoobjectsof knowntemperatures.The typical processinvolves
usingthe freezingpointandthe boilingpointof pure water.Waterisknownto freeze at0°C and to boil
at 100°C at an atmosphericpressure of 1atm. By placinga thermometerinmixture of ice waterand

3. Shahjahannotes:TemperatureandThermometers
allowingthe thermometerliquidtoreacha stable height,the 0-degree markcanbe placeduponthe
thermometer.Similarly,byplacingthe thermometerinboilingwater(at1 atm of pressure) andallowing
the liquidlevel toreacha stable height,the 100-degree markcanbe placeduponthe thermometer.
Withthese twomarkingsplaceduponthe thermometer,100 equallyspaceddivisionscanbe placed
betweenthemtorepresentthe 1-degree marks.Since there isalinearrelationshipbetweenthe
temperature andthe heightof the liquid,the divisionsbetween0degree and100 degree canbe equally
spaced.Witha calibratedthermometer,accurate measurementscanbe made of the temperature of
any objectwithinthe temperature range forwhichithasbeencalibrated.
Temperature Scales
The thermometercalibrationprocessdescribedabove resultsinwhatisknownasa centigrade
thermometer.A centigrade thermometerhas100 divisionsorintervalsbetweenthe normal freezing
pointand the normal boilingpointof water.Today,the centigrade scale isknownasthe Celsiusscale,
namedafterthe SwedishastronomerAndersCelsiuswhoiscreditedwithitsdevelopment.The Celsius
scale isthe mostwidelyacceptedtemperaturescale usedthroughoutthe world.Itisthe standardunit
of temperature measurementinnearlyall countries,the mostnotableexceptionbeingthe United
States.Usingthisscale,a temperature of 28 degreesCelsiusisabbreviatedas28°C.
Traditionallyslowtoadoptthe metricsystemandotheracceptedunitsof measurements,the United
Statesmore commonlyusesthe Fahrenheittemperature scale.A thermometercanbe calibratedusing
the Fahrenheitscale inasimilarmanneraswas describedabove.The differenceisthatthe normal
freezingpointof waterisdesignatedas32 degreesandthe normal boilingpointof wateris designated
as 212 degreesinthe Fahrenheitscale.Assuch,there are 180 divisionsorintervalsbetweenthese two
temperatureswhenusingthe Fahrenheitscale.The Fahrenheitscale isnamedinhonorof German
physicistDaniel Fahrenheit.A temperature of 76 degree Fahrenheitisabbreviatedas76°F. In most
countriesthroughoutthe world,the Fahrenheitscale hasbeenreplacedbythe use of the Celsiusscale.

4. Shahjahannotes:TemperatureandThermometers
Temperaturesexpressedbythe Fahrenheitscale canbe convertedtothe Celsiusscale equivalentusing
the equationbelow:
°C = (°F- 32°)/1.8
Similarly,temperaturesexpressedbythe Celsiusscale canbe convertedtothe Fahrenheitscale
equivalentusingthe equationbelow:
°F= 1.8•°C + 32°
The KelvinTemperature Scale
While the CelsiusandFahrenheitscalesare the mostwidelyusedtemperaturescales,thereare several
otherscalesthat have beenusedthroughouthistory.Forexample,there isthe Rankine scale,the
Newtonscale andthe Romerscale,all of whichare rarelyused.Finally,there isthe Kelvintemperature
scale,whichisthe standardmetricsystemof temperature measurementandperhapsthe mostwidely
usedtemperature scale amongscientists.The Kelvintemperature scale issimilartothe Celsius
temperature scale inthe sense thatthere are 100 equal degree incrementsbetweenthe normal freezing
pointand the normal boilingpointof water.However,the zero-degree markonthe Kelvintemperature
scale is273.15 unitscoolerthanitis on the Celsiusscale.Soatemperature of 0 Kelvinisequivalenttoa
temperature of -273.15 °C. Observe thatthe degree symbol isnotusedwiththissystem.Soa
temperature of 300 unitsabove 0 Kelvinisreferredtoas300 Kelvinandnot300 degree Kelvin;sucha
temperature isabbreviatedas300 K.ConversionsbetweenCelsiustemperaturesandKelvin
temperatures(andvice versa) canbe performedusingone of the twoequationsbelow.
°C = K - 273.15°
K = °C + 273.15

5. Shahjahannotes:TemperatureandThermometers
The zero pointonthe Kelvinscale isknownasabsolute zero.Itisthe lowesttemperature thatcanbe
achieved.The conceptof anabsolute temperature minimumwaspromotedbyScottishphysicistWilliam
Thomson(a.k.a.LordKelvin) in1848. Thomsontheorizedbasedonthermodynamicprinciplesthatthe
lowesttemperaturewhichcouldbe achievedwas-273°C.Priorto Thomson,experimentalistssuchas
RobertBoyle (late 17th century) were wellaware of the observationthatthe volume (andeventhe
pressure) of asample of gas was dependentuponitstemperature.Measurementsof the variationsof
pressure andvolume withchangesinthe temperaturecouldbe made andplotted.Plotsof volumevs.
temperature (atconstantpressure) andpressure vs.temperature (atconstantvolume) reflectedthe
same conclusion - the volume andthe pressure of a gas reducestozeroat a temperature of -273°C.
Since these are the lowestvaluesof volumeandpressure thatare possible,itisreasonable toconclude
that -273°C wasthe lowesttemperature thatwaspossible.
Thomsonreferredtothisminimumlowesttemperature as absolutezero andarguedthat a temperature
scale be adoptedthat hadabsolute zeroas the lowestvalue onthe scale.Today,thattemperature scale
bearshisname.Scientistsandengineershave beenable tocool matterdownto temperaturescloseto -
273.15°C, butneverbelowit.Inthe processof coolingmatterto temperaturesclose toabsolute zero,a
varietyof unusual propertieshave beenobserved.These propertiesinclude superconductivity,
superfluidityanda state of matter knownasa Bose-Einsteincondensate.
Temperature iswhatthe thermometerreads.Butwhatexactlyistemperatureareflectionof?The
conceptof an absolute zerotemperatureisquite interestingandthe observationof remarkablephysical
propertiesforsamplesof matterapproaching absolutezeromakesone ponderthe topicmore deeply.Is
there somethinghappeningatthe particle level whichisrelatedtothe observationsmade atthe
macroscopiclevel?Isthere somethingdeepertotemperature thansimplythe readingona

6. Shahjahannotes:TemperatureandThermometers
thermometer? Asthe temperature of asample of matterincreasesordecreases,whatishappeningat
the level of atomsandmolecules?Thesequestionswill be addressedon the nextpage of Lesson1.