Thermodynamic properties

Thermodynamic properties

1. Thermodynamic Properties
&
Measurement
Dr. Rohit Singh Lather

2. Important fundamental base SI units
•Mass:Kilogram(kg),Pound(lbm)
–Kilogram(kg):isamassequaltothemassoftheinternationalprototypeofthekilogram(a
platinum-iridiumbarstoredinParis),roughlyequaltothemassofoneliterofwaterat
standardtemperatureandpressure
•Length:Meter(m),Foot(ft)
–Meter(m):thelengthofthepathtraveledbylightinvacuumduringatimeintervalof
1/299792458ofasecond
•Time:seconds(s)
–Second:(s),thedurationof9192631770periodsoftheradiationcorrespondingtothe
transitionbetweenthetwohyperfinelevelsofthegroundstateofthecesium133atom
•Temperature:anequilibriumpropertywhichroughlymeasureshowhotorcoldanobjectis
-Noteoursensesarepoorjudgesoftemperature
-Ourbodiesactuallyhavemoresensitivitytoheatfluxesinsteadoftemperature;
heatleavesourbodymorerapidlywhenincontactwithhighdensityobjectslike
snowrelativetothatoflowdensityobjectslikeair
Introduction
Source: Joseph M. Powers, “Lecture notes on thermodynamics", University of Notre Dame, Notre Dame, Indiana, USA

3. -Kelvin:(K) the fraction 1/273.16 of the thermodynamic temperature of the triple point of water
–Rankine: (
◦
R)
•Energy: roughly speaking, the ability to do work, found from the product of force and distance
–Joule: (J), 1 J = 1 (N m)
–Foot-pound force: (ftlbf)
•Specific Volume: the volume per unit mass, known as v = V/m
-
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,
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•Density:the mass per unit volume, the inverse of specific volume ρ= m/V
Source: Joseph M. Powers, “Lecture notes on thermodynamics", University of Notre Dame, Notre Dame, Indiana, USA

4. Pressure
1 Pa = 1 N/m
2
1 bar = 1 x 10
5
Pa = 0.1 MPa
1 atm= 101325 Pa
1 torr= 133.3 Pa
Static and Dynamic Pressure
The unit of pressure are Pa, psi, atm., bar, torr
force in newton or lb
area in m
2
or in
2
Dynamic Pressure
Pressure exerted by a fluid or gas when it impacts on a
surface or an object due to its motion or flow
Static Pressure
Pressure of fluid or gases that
are stationary or not in motion
•Pressure as the normal component of force per unit area (exerts on solids, gas and liquid)
P =
)
*
Note that stress is not a true pressure since it is not scalar
Pressure is related to momentum, while temperatureis related to kinetic energy

5. •Inmostthermodynamicinvestigationsweareconcernedwithabsolutepressure
•Inthermodynamics,wearealmostalwaysconcernedwiththeabsolutepressureasopposedtothe
gaugepressure
•Mostpressureandvacuumgaugesreadthedifferencebetweentheabsolutepressureandthe
atmosphericpressureexistingatthegauge.Thisisreferredtoasgaugepressure
The gauge and absolute pressures are related via the formula
P
gauge= P
absolute−P
atm.
We nearly always interpret P as an absolute pressure, so we could also say
P
gauge= P −P
atm.
–Pascal:(Pa),1Pa=1N/m
2
;
1bar=105Pa,1atm=1.01325×10
5
Pa=101.325kPa=0.101325MPa
–(psia):1psia=1lbf/in.
2
1atm=14.696psia.
Theadenotesthe“absolute”pressureasopposedtothe“gauge”pressure.
Theunitspsigrefertoagaugepressure

6. •Pressure is a property of fluids, which, by definition cannot support a shear
•Stress comes in three forms:
•Tensile/compressive stresses are related to forces normal to a surface
•Shear stresses are in the plane of the surface
•The bulk modulus is related to hydrostatic forces (pressure)
•Except for the fact that the bulk modulus is measured by applying hydrostatic pressure, stress
relates to properties of solids

7. Absolute zero reference
Pressure
Absolute Pressure
Gauge Pressure
Local atmospheric
Pressure reference
Gauge Pressure
Suction/Vacuum
Gauge Pressure is relative pressure Absolute Pressure is Real Pressure
(p
g>0or p
g< 0
;
while p
abs> 0 always) ∴p
abs= p
g+ p
atm> 0
Gauge Pressure
Pressure measured w.r.t
atmospheric pressure
(unit = psig)
Absolute Pressure
Pressure measured w.r.ta
vacuum
(unit = psia)
Atmospheric Pressure
Pressure on the earth’s surface due to the
weight of gases in the earth’s atmosphere

8. Pressure Measuring Instrument
•The techniques for pressure measurement is depending on pressure level. (moderate, very high,
very low)
Very high pressure level is higher than 1000 bar
Very low pressure level is below than 0.001 bar
Low Pressure Measurement
-McLeod gauge
-Pirani gauge
-Ionization gauge
High Pressure Measurement
-Electrical Resistance pressure gauge
Moderate Pressure Measurement
-Manometer
-Elastic elements (diaphragm, bellows, capsules, bourdon tubes, spiral, helix)

9. Manometer
•Manometer:apressuremeasuringinstrument,usuallylimitedtomeasuringpressuresnearto
atmospheric
•Pressuresbelowatmosphericandslightlyaboveatmospheric,andpressuredifferences(for
example,acrossanorificeinapipe),arefrequentlymeasuredwithamanometer,whichcontains
water,mercury,alcohol,oil,orotherfluids.
•Thetermmanometerisoftenusedtoreferspecificallytoliquidcolumnhydrostaticinstruments
•Manometeristhesimplestdeviceformeasuringstaticpressure
ΔP = m.g.Δh
Pressure line
connected
Fluid
water/ mercury or any
other suitable fluid in
the manometer tube
Column forced down
Fluidrises
Measure the difference
in height of the fluid in
the two columns
Pressure of the inlet can be
expressed in inches of fluid

10. Fluid at P,
mg
P
atmA
PA
P
ATM
A
g
y
Newton's Second Law of motion m
+
,
-
+&
,= P.A − P
atm.A − m.g
For static cases, the acceleration
+
,
-
+&
,= 0
Thus, we require a force balance, i.e. mechanical
equilibrium, which is achieved when
0 = P.A − P
atm.A− m.g
P.A = Patm.A+ m.g
So, Thus, P.A = P
atmA+ ρ.A.H.g
P = P
atm+ ρ.g.H
∆P = P − Patm= Pgauge= ρ.g.H
m.g= ρ.V.g
V is the volume of the fluid
V = A.H
H
m.g= ρ.A.H.g
Source: Joseph M. Powers, “Lecture notes on thermodynamics", University of Notre Dame, Notre Dame, Indiana, USA
ρ

11. Types of Manometer
U-tube Manometer Well-type Manometer Incline-tube Manometer
Photo Source: www.cnx.org

12. •Absolutepressureiszeroreferencedagainsta“perfectvacuum”(it-thevalue-isequaltogauge
pressureplusatmosphericpressure)
•Gaugepressureiszeroreferencedagainstambientairpressure;it-thevalue-isequaltoabsolute
pressureminusatmosphericpressure.Negativesignsareusuallyomitted;oftenexpressedas
“inchesofvacuum”orsomesuch
•Differentialpressureisthedifferenceinpressurebetweentwopoints

13. Mercury Barometer
Photo Source: www.cnx.org
Mercury Barometer measures atmospheric pressure
Pressure due to weight of mercury
equals atmospheric pressure
The atmosphere is able to force
mercury in the tube of a height because
the pressure above the mercury is zero

14. Hydrostatic Pressure
•Hydrostaticpressureisthepressureinaliquid
•Thepressureincreasesasthedepthinaliquidincreases,duetoitsweight
•Intermofequation,P=ρgh
ρ= density in kg/m
3
g = acceleration due to gravity (9.8m/s
2
)
h = depth in liquid in m
P = pressure in Pa
Hydrostaticgauges(suchasthemercurycolumnmanometer)comparepressuretothehydrostatic
forceperunitareaatthebaseofacolumnoffluid
Hydrostaticgaugemeasurementsareindependentofthetypeofgasbeingmeasured,andcanbe
designedtohaveaverylinearcalibration.Theyhavepoordynamicresponse

15. Piston Types Gauge
•Piston-type gauges counterbalance the pressure of a fluid with a solid weight or a spring
•For example dead-weight testers used for calibration and Tire-pressure gauges

16. Mechanical Gauges –Bourdon type, Bellows type
•Keyconcept:pressuredifferenceacrossdifferentareasofinnerandoutersurfacescauses
crescenttoflex
Photo Source: www.cnx.org

17. Heat
•Forquantitativepurposesweutilizethechangeofvolumewhichtakesplaceinallbodieswhen
heatedunderconstantpressure,forthisadmitsofexactmeasurement
•Heatingproducesinmostsubstancesanincreaseofvolume,andthuswecantellwhetherabody
getshotterorcolder,notmerelybythesenseoftouch,butalsobyapurelymechanical
observationaffordingamuchgreaterdegreeofaccuracy
•Theconceptionofheatarisesfromthatparticularsensationofwarmthorcoldnesswhichis
immediatelyexperiencedontouchingabody
Directsensation,however,
-givesnoquantitativescientificmeasureofabody'sstatewithregardtoheat
-Ityieldsonlyqualitativeresults,whichvaryaccordingtoexternalcircumstances
Source: Treatise on Thermodynamics , DR. Max Plank, The University of Berlin, Translated by Alexander OggUniversity of Capetown, S.A. 3
rd
Edition
•Temperature is a measure of the ‘intensity of heat’
•Temperature:
-is a measure of the average kinetic energy of the constituent entities (say molecules)
-is theparameter which determines the distribution of species (say molecules) across various
energy states available.

18. •Iftwobodies,oneofwhichfeelswarmerthantheother,bebroughttogether(forexample,a
pieceofheatedmetalandcoldwater),itisinvariablyfoundthatthehotterbodyiscooled,andthe
colderoneisheateduptoacertainpoint,andthenallchangeceases.Thetwobodiesarethensaid
tobeinthermalequilibrium
•Experience shows that such a state of equilibrium finally sets in, not only when two, but also when
any number of differently heated bodies are brought into mutual contact
A B C
A B C
If a body, A, be in thermal equilibrium with two other bodies, B
and C, then B and C are in thermal equilibrium with one another
A B C
Thermal Equilibrium
Source: Treatise on Thermodynamics , DR. Max Plank, The University of Berlin, Translated by Alexander OggUniversity of Capetown, S.A. 3
rd
Edition

19. Zeroth law of thermodynamics -Axiom
•Theso-calledzerothlawofthermodynamicsistheaxiomwhichisprobablymostfundamental
•Formalizedaftertheso-calledfirstandsecondlaws,andsoitiscalledthezerothlaw
Zeroth law of thermodynamics: When two bodies have equality of temperature with a third
body, then they have equality of temperature
The equivalent statement in mathematical logic is that if x = y and x = z, then y = z; this is in
fact equivalent to the first of Euclid’s common notions: things that are equal to the same thing
are also equal to each other
•Definitionofthezerothlawenablestheuseofathermometerasameasurementdevice
•Ascalehoweverneedstobedefined.
•Theoldmetrictemperaturescale,Celsius(C),wasdefinedsothat0Cisthefreezingpointof
water,and100Cistheboilingpointofwater
Source: Joseph M. Powers, “Lecture notes on thermodynamics", University of Notre Dame, Notre Dame, Indiana, USA

20. •Enableustocomparethedegreeofheatoftwobodies,BandC,withoutbringingtheminto
contactwithoneanother
•Namely,bybringingeachbodyintocontactwithanarbitrarilyselectedstandardbody,A(for
example,amassofmercuryenclosedinavesselterminatinginafinecapillarytube)
•ByobservingthevolumeofAineachcase,itispossibletotellwhetherBandCareinthermal
equilibriumornot
•Iftheyarenotinthermalequilibrium,wecantellwhichofthetwoisthehotter
•Aanarbitrarilyselectednormalvolume,namely,thevolumeofAwheninthermalequilibriumwith
meltingiceunderatmosphericpressure
A SteamAIce
•Thisvolumetricdifference,which,byanappropriatechoiceofunit,ismadetoread100whenAis
incontactwithsteamunderatmosphericpressureiscalledthetemperatureindegrees
CentigradewithregardtoAasthermometricsubstance
Two bodies of equal
temperature are, therefore, in
thermal equilibrium, and vice
versa
The temperature readings of no two thermometric substances agree, in general, except at 0nand 100
The definition of temperature is therefore somewhat arbitrary
Source: Treatise on Thermodynamics , DR. Max Plank, The University of Berlin, Translated by Alexander OggUniversity of Capetown, S.A. 3
rd
Edition

21. •Permanentgases,inparticularwhicharehardtocondense,suchashydrogen,
oxygen,nitrogen,andcarbonmonoxide,andaretakenasthermometricsubstances
•Theyagreealmostcompletelywithinaconsiderablerangeoftemperature,and
theirreadingsaresufficientlyinaccordanceformostpurposes
•Besides,thecoefficientofexpansionofthesedifferentgasesisthesame,as
equalvolumesofthemexpandunderconstantpressurebythesameamountabout
.
,/"
oftheirvolumewhenheatedfrom0
∘
Cto1
∘
C
•Since,also,theinfluenceoftheexternalpressureonthevolumeofthesegases
canberepresentedbyaverysimplelaw,weareledtotheconclusionthat
-theseregularitiesarebasedonaremarkablesimplicityintheirconstitution
-therefore,itisreasonabletodefinethecommontemperaturegivenbythem
simplyastemperature.
-Consequentlyreducethereadingsofotherthermometerstothoseof
thegasthermometer
Source: Treatise on Thermodynamics , DR. Max Plank, The University of Berlin, Translated by Alexander OggUniversity of Capetown, S.A. 3
rd
Edition

22. Thermodynamic Temperature Scale
•Atemperaturescalethatisindependentofthepropertiesofanysubstanceorsubstancesiscalled
athermodynamictemperaturescale
•Alltemperaturescalesarebasedonsomeeasilyreproduciblestatessuchasthefreezingand
boilingpointsofwater,whicharealsocalledtheicepointandthesteampoint,respectively
A Triple Point Cell
Solid Ice, Liquid Water and
Water Vapor
Co-exist in thermal Equilibrium
By international Agreement the temperature of
this mixture has been defined to be 273.16K
Steam Point: A mixture of liquid water and water vapor (with no air)
in equilibrium at 1 atmpressure
Ice Point: A mixture of ice and water that is in equilibrium with air
saturated with vapor at 1 atmpressure

23. •The temperature scales used in the SI and in the English system
Celsius scale
(Swedish astronomer A. Celsius, 1702–1744)
On the Celsius scale, is defined so that 0
∘
C is the freezing point of water, and 100
∘
C is the boiling
point of water
Degree Celsius is commonly used in meteorological observation
Fahrenheit scale
(German instrument maker G. Fahrenheit, 1686–1736)
The corresponding values on the Fahrenheit scale are 32 and 212°F. These are often referred to as
two-point scales since temperature values are assigned at two different points
T(F) = 1.8T (C) + 32

24. The Celsius and Fahrenheit Scales
TC=T−273.15

25. •Volume varies with pressure however, so different values would
be obtained on top of a mountain versus down in the valley, and
so this is not a good standard
•The modern Celsius scale is defined to be nearly the same, but
has
-0.01 C as the so-called triple point of water
− 273.15 ◦C as absolute zero in K
•The triple point of water is defined at the state where three
phase of water (solid, liquid, and gas) are observed to co-exist
•The transformation between the absolute Kelvin scale and the
Celsius scale is given by
K = C + 273.15.
Celsius Scale

26. Kelvin Scale
•ThethermodynamictemperaturescaleintheSIistheKelvinscale,namedafterLordKelvin
•Thetemperatureunitonthisscaleisthekelvin,whichisdesignatedbyK
•ThelowesttemperatureontheKelvinscaleisabsolutezero,or0K
•AtemperaturescalethatturnsouttobenearlyidenticaltotheKelvinscaleistheideal-gas
temperaturescale
The Kelvin scale is related to the Celsius scale by
T(K) = T(C) + 273.15
T(R) = 1.8T(K)
•ThereferencetemperaturechosenintheoriginalKelvinscalewas273.15K(or0°C),whichisthe
temperatureatwhichwaterfreezes(oricemelts)andwaterexistsasasolid–liquidmixturein
equilibriumunderstandardatmosphericpressure(theicepoint)
•Thereferencepointwaschangedtoamuchmorepreciselyreproduciblepoint,thetriplepointof
water,whichisassignedthevalue273.16K

27. Rankine scale
•ThethermodynamictemperaturescaleintheEnglishsystemistheRankinescale,namedafter
WilliamRankine
•ThetemperatureunitonthisscaleistheRankine,whichisdesignatedbyR
•Thetemperaturesonthisscalearemeasuredusingaconstant-volumegasthermometer,whichis
basicallyarigidvesselfilledwithagas,usuallyhydrogenorhelium,atlowpressure.
•Thisthermometerisbasedontheprinciplethat“atlowpressures,thetemperatureofagasis
proportionaltoitspressureatconstantvolume”.
-Thetemperatureofagasoffixedvolumevarieslinearlywithpressureatsufficientlylow
pressures
-Thentherelationshipbetweenthetemperatureandthepressureofthegasinthevesselcanbe
expressed as T =a + bPconstants a and b for a gas thermometer are determined experimentally
Once a and b are known, the temperature of a medium can be calculated from this relation by immersing the
rigid vessel of the gas thermometer into the medium and measuring the gas pressure when thermal
equilibrium is established between the medium and the gas in the vessel whose volume is held constant.
The Rankine scale is related to the Fahrenheit scale by
T(R) = T(F) + 459.67

28. •Anideal-gastemperaturescalecanbedevelopedby
measuringthepressuresofthegasinthevesselattwo
reproduciblepoints(suchastheiceandthesteampoints)
andassigningsuitablevaluestotemperaturesatthosetwo
points
•Consideringthatonlyonestraightlinepassesthroughtwo
fixedpointsonaplane,thesetwomeasurementsare
sufficienttodeterminetheconstantsaandb
•ThentheunknowntemperatureTofamediumcorresponding
toapressurereadingPcanbedeterminedfromthat
equationbyasimplecalculation
•Thevaluesoftheconstantswillbedifferentforeach
thermometer,dependingonthetypeandtheamountofthe
gasinthevessel,andthetemperaturevaluesassignedatthe
tworeferencepoints
•Iftheiceandsteampointsareassignedthevalues0°Cand
100°C,respectively,thenthegastemperaturescalewillbe
identicaltotheCelsiusscale
Ideal Gas Temperature Scale

29. The Constant Volume Gas ThermometerT=CpThe temperature of a body can be defined as , where pis the pressure in the bulb
Assuming at the triple point, we also have with the same constant C.
Therefore,
But only when the gas is of a very small amount, this measurement gives
consistent results among different materials used
This is called the ‘ideal gas temperature’.
Temperature T to be
measured

30. •Inthiscasethevalueoftheconstanta(whichcorrespondstoanabsolutepressureofzero)is
determinedtobe-273.15°Cregardlessofthetypeandtheamountofthegasinthevesselofthe
gasthermometer
•Thisisthelowesttemperaturethatcanbeobtainedbyagasthermometer
•Thuswecanobtainanabsolutegastemperaturescalebyassigningavalueofzerototheconstant
a.
•Inthatcase,T=bP,andthusweneedtospecifythetemperatureatonlyonepointtodefinean
absolutegastemperaturescale
-Absolutegastemperaturescaleisnotathermodynamictemperaturescale,sinceitcannotbe
usedatverylowtemperatures(duetocondensation)andatveryhightemperatures(dueto
dissociationandionization)
-Absolutegastemperatureisidenticaltothethermodynamictemperatureinthetemperature
rangeinwhichthegasthermometercanbeused
•Thus,wecanviewthethermodynamictemperaturescaleatthispointasanabsolutegas
temperaturescalethatutilizesan“ideal”or“imaginary”gasthatalwaysactsasalow-
pressuregasregardlessofthetemperature.
•Ifsuchagasthermometerexisted,itwouldreadzerokelvinatabsolutezeropressure,
whichcorrespondsto-273.15°ContheCelsiusscale