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The Laws ofThe Laws ofThermodynamicsThermodynamics
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Work in ThermodynamicWork in Thermodynamic
ProcessesProcesses State VariablesState VariablesState of a systemState of a system
Description of the system in terms ofDescription of the system in terms of statestatevariablesvariables
PressurePressure
VolumeVolume
TemperatureTemperature
Internal EnergyInternal Energy
AAmacroscopic statemacroscopic state of an isolated systemof an isolated systemcan be specified only if the system is incan be specified only if the system is in
internal thermal equilibriuminternal thermal equilibrium
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WorkWork
WorkWork is an important energyis an important energytransfer mechanism intransfer mechanism inthermodynamic systemsthermodynamic systems
HeatHeatis another energy transferis another energy transfermechanismmechanism
Example: gas cylinder with pistonExample: gas cylinder with piston The gas is contained in a cylinder withThe gas is contained in a cylinder with
a moveable pistona moveable piston
The gas occupies a volume V andThe gas occupies a volume V andexerts pressure P on the walls of theexerts pressure P on the walls of thecylinder and on the pistoncylinder and on the piston
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Work in a Gas CylinderWork in a Gas Cylinder
A force is applied toA force is applied toslowly compress theslowly compress the
gasgas The compression isThe compression is
slow enough for allslow enough for allthe system to remainthe system to remainessentially in thermalessentially in thermal
equilibriumequilibriumW =W = -- PP VV
This is the workThis is the workdonedone onon the gasthe gas
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Work on a Gas CylinderWork on a Gas Cylinder
When the gas is compressedWhen the gas is compressed
VV is negativeis negative The work done on the gas is positiveThe work done on the gas is positive
When the gas is allowed to expandWhen the gas is allowed to expand VV is positiveis positive
The work done on the gas is negativeThe work done on the gas is negative
When the volume remains constantWhen the volume remains constant No work is done on the gasNo work is done on the gas
W =W = -- PP VV
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Notes about the Work EquationNotes about the Work Equation
If the pressure remainsIf the pressure remains
constant during theconstant during theexpansion or compression,expansion or compression,the process is called anthe process is called anisobaricisobaric processprocess
If the pressure changes,If the pressure changes,
the average pressure maythe average pressure maybe used to estimate thebe used to estimate thework donework done
W =W = -- PP VV
Work done on the gas
Work=Area under the curve
W =W = -- PP VV
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PV DiagramsPV Diagrams
Used when the pressureUsed when the pressureand volume are known atand volume are known ateach step of the processeach step of the process
The work done on a gasThe work done on a gasthat takes it from somethat takes it from someinitial state to some finalinitial state to some finalstate is the negative of thestate is the negative of thearea under the curve onarea under the curve onthe PV diagramthe PV diagram This is true whether or notThis is true whether or not
the pressure stays constantthe pressure stays constant
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PV DiagramsPV Diagrams
The curve on the diagram is called theThe curve on the diagram is called the pathpath taken betweentaken betweenthe initial and final statesthe initial and final states
The work done depends on the particular pathThe work done depends on the particular path
Same initial and final states, but different amounts of work areSame initial and final states, but different amounts of work aredonedone
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Other ProcessesOther Processes
IsovolumetricIsovolumetricVolume stays constantVolume stays constant
Vertical line on the PV diagramVertical line on the PV diagram
IsothermalIsothermal Temperature stays the sameTemperature stays the same
AdiabaticAdiabatic
No heat is exchanged with the surroundingsNo heat is exchanged with the surroundings
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Example:Example:
Given:
n = 1 mole
Ti = 96.2 K
Tf= 144.3 K
Vi = 0.2 m3
Vf= 0.3 m3
P = const
Find:
W=?
J
mVVPVPWif
400
2.00.3mPa4000 33
!
!!(!
1. Isobaric expansion:
Calculate work done by expanding gas of1 mole ifinitial pressure is
4000 Pa, initial volume is 0.2 m3, and initial temperature is 96.2 K.
Assume a two processes: (1)isobaric expansion to 0.3 m3, Tf=144.3 K
(2)isothermalexpansion to 0.3 m3
.
Also:
5.12.0
3.03
3
!!!!m
m
V
V
nRVP
nR
VP
T
T
i
f
ii
ff
i
f
A 50%increase in temperature!
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Example:Example:
Given:
n = 1 mole
Ti = 96.2 K
Vi = 0.2 m3
Vf= 0.3 m3
T = const
Find:
W=?
2. Isothermal expansion:
Calculate work done by expanding gas of1 mole ifinitial pressure is
4000 Pa, initial volume is 0.2 m3, and initial temperature is 96.2 K.
Assume a two processes: (1)isobaric expansion to 0.3 m3, Tf=144.3 K
(2)isothermalexpansion to 0.3 m3
.
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Example:Example:
Given:
n = 1 mole
Ti = 96.2 K
Vi = 0.2 m3
Vf= 0.3 m3
T = const
Find:
W=?
Jm
mm
V
VVP
V
VnW
i
f
ii
i
f
3242.0
3.0ln2.0Pa4000
lnln
3
33 !!
!
!
2. Isothermal expansion:
Calculate work done by expanding gas of1 mole ifinitial pressure is
4000 Pa, initial volume is 0.2 m3, and initial temperature is 96.2 K.
Assume a two processes: (1)isobaric expansion to 0.3 m3, Tf=144.3 K
(2)isothermalexpansion to 0.3 m3
.
Also:
Pam
mPa
V
VPP
f
iif
26673.0
2.04000
3
3
!!!
A ~67% decrease in pressure!
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Processes for Transferring EnergyProcesses for Transferring Energy
By doing workBy doing work Requires a macroscopic displacement of the point ofRequires a macroscopic displacement of the point of
application of a forceapplication of a force
By heatBy heat Occurs by random molecular collisionsOccurs by random molecular collisions
Results of bothResults of both Change in internal energy of the systemChange in internal energy of the system
Generally accompanied by measurable macroscopicGenerally accompanied by measurable macroscopicvariablesvariablesPressurePressure
TemperatureTemperature
VolumeVolume
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First Law of ThermodynamicsFirst Law of Thermodynamics
ConsiderConsider energy conservationenergy conservation in thermalin thermalprocesses. Must include:processes. Must include:QQHeatHeat
Positive if energy is transferredPositive if energy is transferred toto the systemthe system
WW
WorkWork
Positive if donePositive if done onon the systemthe system UU
Internal energyInternal energy
Positive if the temperature increasesPositive if the temperature increases
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First Law of ThermodynamicsFirst Law of Thermodynamics
The relationship among U, W, and Q can beThe relationship among U, W, and Q can beexpressed asexpressed as
U = UU = Uff UUii = Q + W= Q + W
This means that the change in internalThis means that the change in internal
energy of a system is equal to the sum ofenergy of a system is equal to the sum ofthe energy transferred across the systemthe energy transferred across the systemboundary by heat and the energyboundary by heat and the energytransferred by worktransferred by work
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Applications of the First LawApplications of the First Law
1. Isolated System1. Isolated SystemAnAn isolated systemisolated system does not interactdoes not interact
with its surroundingswith its surroundings
No energy transfer takes place and noNo energy transfer takes place and nowork is donework is done
Therefore, the internal energy of theTherefore, the internal energy of the
isolated system remains constantisolated system remains constant
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Example:Example:
Given:
n = 1 mole
Vi = 0.2 m3
Vf= 0.3 m3
P = constQ=500 J
Find:
(U=?
J
mVVPVPWif
400
2.00.3mPa4000 33
!
!!(!
1. Isobaric expansion:
If 500 J of heat added to ideal gas that is expanding from 0.2 m3 to 0.3
m3 at a constant pressure of4000 Pa, what is the change in its internal
energy?
Use 1st law of thermodynamics:
JJJWQU
WUQ
100400500 !!!(
(!
What if volume is kept constant?
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Applications of the First LawApplications of the First Law
2. Cyclic Processes2. Cyclic ProcessesA cyclic process is one in which the processA cyclic process is one in which the process
originates and ends at the same stateoriginates and ends at the same state
UUff= U= Uii and
Q=and
Q= --
WW
The net work done per cycle by the gas isThe net work done per cycle by the gas isequal to the area enclosed by the pathequal to the area enclosed by the pathrepresenting the process on a PV diagramrepresenting the process on a PV diagram
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Cyclic Process in a PV DiagramCyclic Process in a PV Diagram
This is an idealThis is an idealmonatomic gas confinedmonatomic gas confinedin a cylinder by ain a cylinder by amoveable pistonmoveable piston
A to B is an isovolumetricA to B is an isovolumetricprocess which increasesprocess which increasesthe pressurethe pressure
B to C is an isothermalB to C is an isothermalexpansion and lowers theexpansion and lowers the
pressurepressure C to A is an isobaricC to A is an isobaric
compressioncompression
The gas returns to itsThe gas returns to itsoriginal state at pointAoriginal state at pointA
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Applications of the First LawApplications of the First Law
3. Isothermal Processes3. Isothermal Processes Isothermal means constantIsothermal means constanttemperaturetemperature
The cylinder and gas are inThe cylinder and gas are inthermal contact with a largethermal contact with a large
source of energysource of energy Allow the energy to transferAllow the energy to transfer
into the gas (by heat)into the gas (by heat)
The gas expands andThe gas expands and
pressure falls to maintain apressure falls to maintain aconstant temperatureconstant temperature
The work done is theThe work done is thenegative of the heat addednegative of the heat added
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Applications of the First LawApplications of the First Law
4.4.Adiabatic Process
Adiabatic Process
Energy transferred by heat is zeroEnergy transferred by heat is zero
The work done is equal to the change in theThe work done is equal to the change in theinternal energy of the systeminternal energy of the system
One way to accomplish a process with no heatOne way to accomplish a process with no heatexchange is to have it happen very quicklyexchange is to have it happen very quickly
In an adiabatic expansion, the work done isIn an adiabatic expansion, the work done is
negative and the internal energy decreasesnegative and the internal energy decreases
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Applications of the First LawApplications of the First Law
5. Isovolumetric Process5. Isovolumetric ProcessNo change in volume, therefore no work isNo change in volume, therefore no work is
donedone
The energy added to the system goes intoThe energy added to the system goes intoincreasing the internal energy of the systemincreasing the internal energy of the system
Temperature will increaseTemperature will increase
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Additional Notes About the FirstAdditional Notes About the First
LawLawThe First Law is a general equation ofThe First Law is a general equation of
Conservation of EnergyConservation of Energy
There is no practical, macroscopic,There is no practical, macroscopic,distinction between the results of energydistinction between the results of energytransfer by heat and by worktransfer by heat and by work
Q and W are related to the properties ofQ and W are related to the properties ofstate for a systemstate for a system
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The First Law and HumanThe First Law and Human
MetabolismMetabolismThe First Law can be applied to living organismsThe First Law can be applied to living organismsThe internal energy stored in humans goes intoThe internal energy stored in humans goes into
other forms needed by the organs and into workother forms needed by the organs and into work
and heatand heatTheThe metabolic ratemetabolic rate ((U /U / T) is directlyT) is directly
proportional to the rate of oxygen consumption byproportional to the rate of oxygen consumption byvolumevolume
Basal metabolic rate (to maintain and run organs, etc.)Basal metabolic rate (to maintain and run organs, etc.)is about 80 Wis about 80 W
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Various Metabolic RatesVarious Metabolic Rates
Fig. T12.1, p. 369
Slide 11
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Heat EngineHeat Engine
AAheat engineheat engine is a device that convertsis a device that convertsinternal energy to other useful forms, suchinternal energy to other useful forms, suchas electrical or mechanical energyas electrical or mechanical energy
Aheat engine carries some workingAheat engine carries some workingsubstance through a cyclical processsubstance through a cyclical process
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Heat EngineHeat Engine
Energy is transferredEnergy is transferredfrom a source at afrom a source at ahigh temperature (Qhigh temperature (Qhh))
Work is done by theWork is done by theengine (Wengine (Wengeng))
Energy is expelled to aEnergy is expelled to asource at a lowersource at a lowertemperature (Qtemperature (Qcc))
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Heat EngineHeat Engine
Since it is a cyclicalSince it is a cyclicalprocess,process, U = 0U = 0 Its initial and finalIts initial and final
internal energies are theinternal energies are thesamesame
Therefore, QTherefore, Qnetnet= W= Wengeng The work done by theThe work done by the
engine equals the netengine equals the net
energy absorbed by theenergy absorbed by theengineengine
The work is equal to theThe work is equal to thearea enclosed by thearea enclosed by thecurve of the PV diagramcurve of the PV diagram
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Thermal Efficiency of a HeatThermal Efficiency of a Heat
EngineEngineThermal efficiencyThermal efficiency is defined as the ratio ofis defined as the ratio ofthe work done by the engine to the energythe work done by the engine to the energyabsorbed at the higher temperatureabsorbed at the higher temperature
e = 1 (100% efficiency) only ifQe = 1 (100% efficiency) only ifQcc = 0= 0 No energy expelled to cold reservoirNo energy expelled to cold reservoir
h
c
h
ch
h
eng
Q
Q1
Q
QQ
Q
W!
!!e
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Second Law of ThermodynamicsSecond Law of Thermodynamics
It is impossible to construct a heatIt is impossible to construct a heatengine that, operating in a cycle,engine that, operating in a cycle,
produces no other effect than theproduces no other effect than theabsorption of energy from a reservoirabsorption of energy from a reservoirand the performance of an equaland the performance of an equal
amount of workamount of work Means thatQMeans thatQcc cannot equal 0cannot equal 0
Some QSome Qcc must be expelled to the environmentmust be expelled to the environment
Means thatMeans thate cannot equal 100%e cannot equal 100%
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Heat Pumps and RefrigeratorsHeat Pumps and Refrigerators
Heat engines can run in reverseHeat engines can run in reverse
Send in energySend in energy
Energy is extracted from the cold reservoirEnergy is extracted from the cold reservoir Energy is transferred to the hot reservoirEnergy is transferred to the hot reservoir
This process means the heat engine isThis process means the heat engine isrunning as a heat pumprunning as a heat pump
A refrigerator is a common type of heat pumpA refrigerator is a common type of heat pump
An air conditioner is another example of a heatAn air conditioner is another example of a heatpumppump
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Summary of the First and SecondSummary of the First and Second
LawsLawsFirst LawFirst Law
We cannot get a greater amount of energy outWe cannot get a greater amount of energy outof a cyclic process than we put inof a cyclic process than we put in
Second LawSecond Law
We cannot break evenWe cannot break even
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Reversible and IrreversibleReversible and IrreversibleProcessesProcesses
AAreversiblereversible process is one in which everyprocess is one in which everystate along some path is an equilibrium statestate along some path is an equilibrium state
And one for which the system can be returned toAnd one for which the system can be returned toits initial state along the same pathits initial state along the same path
AnAn irreversibleirreversible processdoesnot meet theseprocessdoesnot meet theserequirementsrequirements
Most natural processes are irreversibleMost natural processes are irreversible Reversible process are an idealization, but someReversible process are an idealization, but some
real processes are good approximationsreal processes are good approximations
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Carnot EngineCarnot Engine
A theoretical engine developed by Sadi CarnotA theoretical engine developed by Sadi Carnot
Aheat engine operating in an ideal, reversibleAheat engine operating in an ideal, reversiblecycle (now called acycle (now called a Carnot CycleCarnot Cycle) between two) between two
reservoirs is the most efficient engine possiblereservoirs is the most efficient engine possibleCarnots TheoremCarnots Theorem: No real engine operating: No real engine operating
between two energy reservoirs can be morebetween two energy reservoirs can be moreefficient than a Carnot engine operating betweenefficient than a Carnot engine operating between
the same two reservoirsthe same two reservoirs
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Carnot CycleCarnot Cycle
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Carnot Cycle, A to BCarnot Cycle, A to B
A to B is an isothermalA to B is an isothermalexpansionexpansion
The gas is placed inThe gas is placed incontact with the highcontact with the hightemperature reservoirtemperature reservoir
The gas absorbs heatThe gas absorbs heatQQhh
The gas does work WThe gas does work WABABin raising the pistonin raising the piston
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Carnot Cycle, B to CCarnot Cycle, B to C
B to C is an adiabaticB to C is an adiabaticexpansionexpansion
The base of the cylinder isThe base of the cylinder isreplaced by a thermallyreplaced by a thermally
nonconducting wallnonconducting wall No heat enters or leavesNo heat enters or leaves
the systemthe system
The temperature falls fromThe temperature falls fromTT
hhto Tto T
cc The gas does work WThe gas does work WBCBC
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Carnot Cycle, C to DCarnot Cycle, C to D
The gas is placed inThe gas is placed incontact with the coldcontact with the cold
temperature reservoirtemperature reservoirC to D is an isothermalC to D is an isothermal
compressioncompression
The gas expels energyThe gas expels energyQQCC
Work WWork WCDCD is done onis done onthe gasthe gas
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Carnot Cycle, D to ACarnot Cycle, D to A
D to A is an adiabaticD to A is an adiabaticcompressioncompression
The gas is again placedThe gas is again placedagainst a thermallyagainst a thermally
nonconducting wallnonconducting wall So no heat is exchangedSo no heat is exchanged
with the surroundingswith the surroundings
The temperature of theThe temperature of thegas increases from Tgas increases from TCC toto
TThh The work done on the gasThe work done on the gas
is Wis WCDCD
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Carnot Cycle, PV DiagramCarnot Cycle, PV Diagram
The work done by theThe work done by theengine is shown by theengine is shown by thearea enclosed by thearea enclosed by the
curvecurveThe net work is equalThe net work is equal
to Qto Qhh -- QQcc
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Efficiency of a Carnot EngineEfficiency of a Carnot Engine
Carnot showed that the efficiency of theCarnot showed that the efficiency of theengine depends on the temperatures ofengine depends on the temperatures of
the reservoirsthe reservoirs
Temperatures must be in KelvinsTemperatures must be in KelvinsAll Carnot engines operating betweenAll Carnot engines operating between
the same two temperatures will havethe same two temperatures will havethe same efficiencythe same efficiency
h
C
c
T
Te !1
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Notes About Carnot EfficiencyNotes About Carnot Efficiency
Efficiency is 0 if TEfficiency is 0 if Thh = T= TccEfficiency is 100% only if TEfficiency is 100% only if Tcc = 0 K= 0 K
Such reservoirs are not availableSuch reservoirs are not available
The efficiency increases at TThe efficiency increases at Tcc is loweredis loweredand as Tand as Thh is raisedis raised
In most practical cases, TIn most practical cases, Tcc is near roomis near roomtemperature, 300 Ktemperature, 300 K So generally TSo generally Thh is raised to increaseis raised to increase
efficiencyefficiency
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Real Engines Compared to CarnotReal Engines Compared to CarnotEnginesEngines
All real engines are less efficient than theAll real engines are less efficient than theCarnot engineCarnot engine
Real engines are irreversible because of frictionReal engines are irreversible because of friction
Real engines are irreversible because theyReal engines are irreversible because theycomplete cycles in short amounts of timecomplete cycles in short amounts of time
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EntropyEntropy
A state variable related to the Second LawA state variable related to the Second Lawof Thermodynamics, the entropyof Thermodynamics, the entropy
The change in entropy,The change in entropy,
S, between twoS, between twoequilibrium states is given by the energy,equilibrium states is given by the energy,QQrr, transferred along the reversible path, transferred along the reversible pathdivided by the absolute temperature, T, ofdivided by the absolute temperature, T, of
the system in this intervalthe system in this interval
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EntropyEntropy
Mathematically,Mathematically,
This applies only to the reversible path, evenThis applies only to the reversible path, even
if the system actually follows an irreversibleif the system actually follows an irreversiblepathpath
To calculate the entropy for an irreversibleTo calculate the entropy for an irreversibleprocess, model it as a reversible processprocess, model it as a reversible process
When energy is absorbed, Q is positive andWhen energy is absorbed, Q is positive andentropy increasesentropy increases
When energy is expelled, Q is negative andWhen energy is expelled, Q is negative andentropy decreasesentropy decreases
T
QS r!(
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More About EntropyMore About Entropy
Note, the equation defines theNote, the equation defines the change inchange inentropyentropy
The entropy of the Universe increases in allThe entropy of the Universe increases in allnatural processesnatural processes This is another way of expressing the Second Law ofThis is another way of expressing the Second Law of
ThermodynamicsThermodynamics
There are processes in which the entropy of aThere are processes in which the entropy of a
system decreasessystem decreases If the entropy of one system, A, decreases it will beIf the entropy of one system, A, decreases it will be
accompanied by the increase of entropy of another system, B.accompanied by the increase of entropy of another system, B.
The change in entropy in system B will be greater than that ofThe change in entropy in system B will be greater than that ofsystem A.system A.
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Perpetual Motion MachinesPerpetual Motion Machines
Aperpetual motion machine would operateAperpetual motion machine would operatecontinuously without input of energy and withoutcontinuously without input of energy and withoutany net increase in entropyany net increase in entropy
Perpetual motion machines of thePerpetual motion machines of the first typefirst type wouldwouldviolate the First Law, giving out more energy thanviolate the First Law, giving out more energy thanwas put into the machinewas put into the machine
Perpetual motion machines of thePerpetual motion machines of the second typesecond type
would violate the Second Law, possibly by nowould violate the Second Law, possibly by noexhaustexhaust
Perpetual motion machines will never be inventedPerpetual motion machines will never be invented
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Entropy and DisorderEntropy and Disorder
Entropy can be described in terms ofEntropy can be described in terms ofdisorderdisorder
Adisorderly arrangement is much more
Adisorderly arrangement is much moreprobable than an orderly one if the laws ofprobable than an orderly one if the laws of
nature are allowed to act withoutnature are allowed to act withoutinterferenceinterference
This comes from a statistical mechanicsThis comes from a statistical mechanicsdevelopmentdevelopment
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Entropy and Disorder, cont.Entropy and Disorder, cont.
Isolated systems tend toward greater disorder, andIsolated systems tend toward greater disorder, andentropy is a measure of that disorderentropy is a measure of that disorder
S = kS = kBB ln
Wln
W
kkBB is Boltzmanns constantis Boltzmanns constant
W is a number proportional to the probability that theW is a number proportional to the probability that thesystem has a particular configurationsystem has a particular configuration
This gives the Second Law as a statement of what isThis gives the Second Law as a statement of what is
most probably rather than what must bemost probably rather than what must be The Second Law also defines the direction of time ofThe Second Law also defines the direction of time of
all events as the direction in which the entropy of theall events as the direction in which the entropy of theuniverse increasesuniverse increases
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HeatDeath of the UniverseHeatDeath of the Universe
The entropy of the Universe always increasesThe entropy of the Universe always increases
The entropy of the Universe should ultimatelyThe entropy of the Universe should ultimatelyreach a maximumreach a maximum
At this time, the Universe will be at a state of uniformAt this time, the Universe will be at a state of uniformtemperature and densitytemperature and density
This state of perfect disorder implies no energy will beThis state of perfect disorder implies no energy will beavailable for doing workavailable for doing work
This state is called theThis state is called the heat deathheat death of the Universeof the Universe