Fisika Dasar - Minggu 11 Panas 2

8/8/2019 Fisika Dasar - Minggu 11 Panas 2

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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:





.


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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:





.

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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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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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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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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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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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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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

Fisika Dasar - Minggu 11 Panas 2

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