1 Chapter 12 The Laws of Thermodynamics. 2 Work in Thermodynamic Processes – State Variables State of a system State of a system Description of the system.

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Chapter 12Chapter 12

The Laws of The Laws of ThermodynamicsThermodynamics

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Work in Thermodynamic Work in Thermodynamic Processes – State Processes – State VariablesVariables

State of a systemState of a system Description of the system in terms of Description of the system in terms of

state variablesstate variables PressurePressure VolumeVolume TemperatureTemperature Internal EnergyInternal Energy

A A macroscopic statemacroscopic state of an isolated of an isolated system can be specified only if the system can be specified only if the system is in internal thermal system is in internal thermal equilibriumequilibrium

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Work in Thermodynamic Work in Thermodynamic ProcessesProcesses

Work is an important energy Work is an important energy transfer mechanism in transfer mechanism in thermodynamic systemsthermodynamic systems

Heat is another energy transfer Heat is another energy transfer mechanismmechanism

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Work in a Gas CylinderWork in a Gas Cylinder

The gas is contained in The gas is contained in a cylinder with a a cylinder with a moveable pistonmoveable piston

The gas occupies a The gas occupies a volume V and exerts volume V and exerts pressure P on the walls pressure P on the walls of the cylinder and on of the cylinder and on the pistonthe piston

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Work in a Gas Cylinder, Work in a Gas Cylinder, cont.cont.

A force is applied A force is applied to slowly to slowly compress the gascompress the gas The compression The compression

is slow enough for is slow enough for all the system to all the system to remain essentially remain essentially in thermal in thermal equilibriumequilibrium

W = - P W = - P ΔVΔV This is the work This is the work

done done onon the gas the gas

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More about Work on a Gas More about Work on a Gas CylinderCylinder

When the gas is compressedWhen the gas is compressed ΔV is negative ΔV is 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 ΔV is positiveΔV is 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

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Notes about the Work Notes about the Work EquationEquation

The pressure remains constant The pressure remains constant during the expansion or during the expansion or compressioncompression This is called an This is called an isobaricisobaric process process

If the pressure changes, the If the pressure changes, the average pressure may be used to average pressure may be used to estimate the work doneestimate the work done

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PV DiagramsPV Diagrams Used when the Used when the

pressure and volume pressure and volume are known at each step are known at each step of the processof the process

The work done on a gas The work done on a gas that takes it from some that takes it from some initial state to some initial state to some final state is the final state is the negative of the area negative of the area under the curve on the under the curve on the PV diagramPV diagram This is true whether or This is true whether or

not the pressure stays not the pressure stays constantconstant

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PV Diagrams, cont.PV Diagrams, cont.

The curve on the diagram is called the The curve on the diagram is called the pathpath taken between the initial and final statestaken between the 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 Same initial and final states, but different amounts of

work are donework are done

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Other ProcessesOther Processes

IsovolumetricIsovolumetric Volume 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 No heat is exchanged with the

surroundingssurroundings

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Processes for Transferring Processes for Transferring EnergyEnergy

By doing workBy doing work Requires a macroscopic displacement of the point Requires a macroscopic displacement of the point

of application of a forceof application 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 Generally accompanied by measurable

macroscopic variablesmacroscopic variables PressurePressure TemperatureTemperature VolumeVolume

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First Law of First Law of ThermodynamicsThermodynamics

Terms in the equationTerms in the equation QQ

HeatHeat Positive if energy is transferred Positive if energy is transferred toto the system the system

WW WorkWork Positive if done Positive if done onon the system the system

UU Internal energyInternal energy Positive if the temperature increasesPositive if the temperature increases

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First Law of First Law of Thermodynamics, contThermodynamics, cont

The relationship among U, W, and Q The relationship among U, W, and Q can be expressed ascan be expressed as ΔU = UΔU = Uff – U – Uii = Q + W = Q + W

This means that the change in This means that the change in internal energy of a system is equal internal energy of a system is equal to the sum of the energy transferred to the sum of the energy transferred across the system boundary by heat across the system boundary by heat and the energy transferred by workand the energy transferred by work

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Applications of the First Applications of the First Law –Law –Isolated SystemIsolated System

An An isolated systemisolated system does not does not interact with its surroundingsinteract with its surroundings

No energy transfer takes place and No energy transfer takes place and no work is doneno work is done

Therefore, the internal energy of Therefore, the internal energy of the isolated system remains the isolated system remains constantconstant

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Applications of the First Applications of the First Law –Law –Cyclic ProcessesCyclic Processes

A cyclic process is one in which the A cyclic process is one in which the process originates and ends at the process originates and ends at the same statesame state UUff = U = Uii and Q = -W and Q = -W

The net work done per cycle by the The net work done per cycle by the gas is equal to the area enclosed gas is equal to the area enclosed by the path representing the by the path representing the process on a PV diagramprocess on a PV diagram

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Cyclic Process in a PV Cyclic Process in a PV DiagramDiagram

This is an ideal This is an ideal monatomic gas monatomic gas confined in a cylinder confined in a cylinder by a moveable pistonby a moveable piston

A to B is an A to B is an isovolumetric process isovolumetric process which increases the which increases the pressurepressure

B to C is an isothermal B to C is an isothermal expansion and lowers expansion and lowers the pressurethe pressure

C to A is an isobaric C to A is an isobaric compressioncompression

The gas returns to its The gas returns to its original state at point Aoriginal state at point A

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Applications of the First Applications of the First Law –Law –Isothermal ProcessesIsothermal Processes

Isothermal means constant Isothermal means constant temperaturetemperature

The cylinder and gas are in The cylinder and gas are in thermal contact with a thermal contact with a large source of energylarge source of energy

Allow the energy to Allow the energy to transfer into the gas (by transfer into the gas (by heat)heat)

The gas expands and The gas expands and pressure falls to maintain a pressure falls to maintain a constant temperatureconstant temperature

The work done is the The work done is the negative of the heat addednegative of the heat added

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Applications of the First Applications of the First Law – Adiabatic ProcessLaw – Adiabatic Process

Energy transferred by heat is zeroEnergy transferred by heat is zero The work done is equal to the change in The work done is equal to the change in

the internal energy of the systemthe internal energy of the system One way to accomplish a process with One way to accomplish a process with

no heat exchange is to have it happen no heat exchange is to have it happen very quicklyvery quickly

In an adiabatic expansion, the work In an adiabatic expansion, the work done is negative and the internal done is negative and the internal energy decreasesenergy decreases

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Applications of the First Applications of the First Law – Law – Isovolumetric ProcessIsovolumetric Process

No change in volume, therefore no No change in volume, therefore no work is donework is done

The energy added to the system The energy added to the system goes into increasing the internal goes into increasing the internal energy of the systemenergy of the system Temperature will increaseTemperature will increase

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Additional Notes About the Additional Notes About the First LawFirst Law

The First Law is a general equation The First Law is a general equation of Conservation of Energyof Conservation of Energy

There is no practical, macroscopic, There is no practical, macroscopic, distinction between the results of distinction between the results of energy transfer by heat and by energy transfer by heat and by workwork

Q and W are related to the Q and W are related to the properties of state for a systemproperties of state for a system

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The First Law and Human The First Law and Human MetabolismMetabolism

The First Law can be applied to living The First Law can be applied to living organismsorganisms

The internal energy stored in humans The internal energy stored in humans goes into other forms needed by the goes into other forms needed by the organs and into work and heatorgans and into work and heat

The The metabolic ratemetabolic rate ( (ΔU / ΔT) is directly ΔU / ΔT) is directly proportional to the rate of oxygen proportional to the rate of oxygen consumption by volumeconsumption by volume Basal metabolic rate (to maintain and run Basal metabolic rate (to maintain and run

organs, etc.) is about 80 Worgans, etc.) is about 80 W

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Various Metabolic RatesVarious Metabolic Rates

Fig. T12.1, p. 369

Slide 11

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Aerobic FitnessAerobic Fitness

One way to One way to measure a measure a person’s physical person’s physical fitness is their fitness is their maximum maximum capacity to use or capacity to use or consume oxygenconsume oxygen

Fig. T12.2, p. 370

Slide 12

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Efficiency of the Human Efficiency of the Human BodyBody

Efficiency is Efficiency is the ratio of the ratio of the the mechanical mechanical power power supplied to supplied to the the metabolic metabolic rate or total rate or total power inputpower input

F ig . T 1 2 .3 , p . 3 7 0

S lid e 1 3

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Heat EngineHeat Engine

A A heat engineheat engine is a device that is a device that converts internal energy to other converts internal energy to other useful forms, such as electrical or useful forms, such as electrical or mechanical energymechanical energy

A heat engine carries some A heat engine carries some working substance through a working substance through a cyclical processcyclical process

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Heat Engine, cont.Heat Engine, cont.

Energy is Energy is transferred from a transferred from a source at a high source at a high temperature (Qtemperature (Qhh))

Work is done by the Work is done by the engine (Wengine (Wengeng))

Energy is expelled Energy is expelled to a source at a to a source at a lower temperature lower temperature (Q(Qcc))

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Heat Engine, cont.Heat Engine, cont. Since it is a cyclical Since it is a cyclical

process, process, ΔU = 0ΔU = 0 Its initial and final Its initial and final

internal energies are the internal energies are the samesame

Therefore, QTherefore, Qnetnet = W = Wengeng The work done by the The work done by the

engine equals the net engine equals the net energy absorbed by energy absorbed by the enginethe engine

The work is equal to The work is equal to the area enclosed by the area enclosed by the curve of the PV the curve of the PV diagramdiagram

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Thermal Efficiency of a Thermal Efficiency of a Heat EngineHeat Engine

Thermal efficiency is defined as the Thermal efficiency is defined as the ratio of the work done by the engine ratio of the work done by the engine to the energy absorbed at the to the energy absorbed at the higher temperaturehigher temperature

e = 1 (100% efficiency) only if Qe = 1 (100% efficiency) only if Qcc = = 00 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 Second Law of ThermodynamicsThermodynamics

It is impossible to construct a heat It is impossible to construct a heat engine that, operating in a cycle, engine that, operating in a cycle, produces no other effect than the produces no other effect than the absorption of energy from a absorption of energy from a reservoir and the performance of an reservoir and the performance of an equal amount of workequal amount of work Kelvin – Planck statementKelvin – Planck statement Means that QMeans that Qcc cannot equal 0 cannot equal 0

Some QSome Qcc must be expelled to the must be expelled to the environmentenvironment

Means that e cannot equal 100%Means that e cannot equal 100%

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Heat Pumps and Heat Pumps and RefrigeratorsRefrigerators

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 is This process means the heat engine is running as a heat pumprunning as a heat pump A refrigerator is a common type of heat A refrigerator is a common type of heat

pumppump An air conditioner is another example of a An air conditioner is another example of a

heat pumpheat pump

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Summary of the First and Summary of the First and Second LawsSecond Laws

First LawFirst Law We cannot get a greater amount of We cannot get a greater amount of

energy out of a cyclic process than energy out of a cyclic process than we put inwe put in

Second LawSecond Law We can break evenWe can break even

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Reversible and Irreversible Reversible and Irreversible ProcessesProcesses

A A reversiblereversible process is one in which process is one in which every state along some path is an every state along some path is an equilibrium stateequilibrium state And one for which the system can be And one for which the system can be

returned to its initial state along the same returned to its initial state along the same pathpath

An An irreversibleirreversible process does not meet process does not meet these requirementsthese requirements Most natural processes are irreversibleMost natural processes are irreversible Reversible process are an idealization, but Reversible process are an idealization, but

some real processes are good some real processes are good approximationsapproximations

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Carnot EngineCarnot Engine A theoretical engine developed by Sadi A theoretical engine developed by Sadi

CarnotCarnot A heat engine operating in an ideal, A heat engine operating in an ideal,

reversible cycle (now called a reversible cycle (now called a Carnot Carnot CycleCycle) between two reservoirs is the most ) between two reservoirs is the most efficient engine possibleefficient engine possible

Carnot’s TheoremCarnot’s Theorem: No real engine : No real engine operating between two energy reservoirs operating between two energy reservoirs can be more efficient than a Carnot engine can be more efficient than a Carnot engine operating between the same two operating between the same two reservoirsreservoirs

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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 A to B is an isothermal expansionisothermal expansion

The gas is placed in The gas is placed in contact with the high contact with the high temperature reservoirtemperature reservoir

The gas absorbs heat The gas absorbs heat QQhh

The gas does work The gas does work WWABAB in raising the in raising the pistonpiston

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Carnot Cycle, B to CCarnot Cycle, B to C B to C is an adiabatic B to C is an adiabatic

expansionexpansion The base of the The base of the

cylinder is replaced cylinder is replaced by a thermally by a thermally nonconducting wallnonconducting wall

No heat enters or No heat enters or leaves the systemleaves the system

The temperature falls The temperature falls from Tfrom Thh to T to Tcc

The gas does work The gas does work WWBCBC

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Carnot Cycle, C to DCarnot Cycle, C to D

The gas is placed in The gas is placed in contact with the cold contact with the cold temperature reservoirtemperature reservoir

C to D is an C to D is an isothermal isothermal compressioncompression

The gas expels The gas expels energy Qenergy QCC

Work WWork WCDCD is done on is done on the gasthe gas

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Carnot Cycle, D to ACarnot Cycle, D to A D to A is an adiabatic D to A is an adiabatic

compressioncompression The gas is again placed The gas is again placed

against a thermally against a thermally nonconducting wallnonconducting wall So no heat is exchanged So no heat is exchanged

with the surroundingswith the surroundings The temperature of the The temperature of the

gas increases from Tgas increases from TCC to Tto Thh

The work done on the The work done on the gas is Wgas is WCDCD

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Carnot Cycle, PV DiagramCarnot Cycle, PV Diagram

The work done by The work done by the engine is the engine is shown by the shown by the area enclosed by area enclosed by the curvethe curve

The net work is The net work is equal to Qequal to Qhh - Q - Qcc

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Efficiency of a Carnot Efficiency of a Carnot EngineEngine

Carnot showed that the efficiency of Carnot showed that the efficiency of the engine depends on the the engine depends on the temperatures of the reservoirstemperatures of the reservoirs

Temperatures must be in KelvinsTemperatures must be in Kelvins All Carnot engines operating All Carnot engines operating

between the same two between the same two temperatures will have the same temperatures will have the same efficiencyefficiency

h

Cc T

T1e

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Notes About Carnot Notes About Carnot EfficiencyEfficiency

Efficiency is 0 if TEfficiency is 0 if Thh = T = Tcc

Efficiency 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 is lowered and as Tlowered and as Thh is raised is raised

In most practical cases, TIn most practical cases, Tcc is near is near room temperature, 300 Kroom temperature, 300 K So generally TSo generally Thh is raised to increase is raised to increase

efficiencyefficiency

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Real Engines Compared to Real Engines Compared to Carnot EnginesCarnot Engines

All real engines are less efficient All real engines are less efficient than the Carnot enginethan the Carnot engine Real engines are irreversible because Real engines are irreversible because

of frictionof friction Real engines are irreversible because Real engines are irreversible because

they complete cycles in short they complete cycles in short amounts of timeamounts of time

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EntropyEntropy

A state variable related to the Second A state variable related to the Second Law of Thermodynamics, the entropyLaw of Thermodynamics, the entropy

The change in entropy, The change in entropy, ΔS, between ΔS, between two equilibrium states is given by the two equilibrium states is given by the energy, Qenergy, Qrr, transferred along the , transferred along the reversible path divided by the reversible path divided by the absolute temperature, T, of the absolute temperature, T, of the system in this intervalsystem in this interval

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Entropy, cont.Entropy, cont.

Mathematically,Mathematically, This applies only to the reversible path, This applies only to the reversible path,

even if the system actually follows an even if the system actually follows an irreversible pathirreversible path To calculate the entropy for an irreversible To calculate the entropy for an irreversible

process, model it as a reversible processprocess, model it as a reversible process When energy is absorbed, Q is positive When energy is absorbed, Q is positive

and entropy increasesand entropy increases When energy is expelled, Q is negative When energy is expelled, Q is negative

and entropy decreasesand entropy decreases

T

QS r

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More About EntropyMore About Entropy Note, the equation defines the Note, the equation defines the change in change in

entropyentropy The entropy of the Universe increases in all The entropy of the Universe increases in all

natural processesnatural processes This is another way of expressing the Second Law of This is another way of expressing the Second Law of

ThermodynamicsThermodynamics

There are processes in which the entropy of There are processes in which the entropy of a system decreasesa system decreases If the entropy of one system, A, decreases it will be If the entropy of one system, A, decreases it will be

accompanied by the increase of entropy of another system, accompanied by the increase of entropy of another system, B.B.

The change in entropy in system B will be greater than that The change in entropy in system B will be greater than that of system A.of system A.

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Perpetual Motion MachinesPerpetual Motion Machines A perpetual motion machine would operate A perpetual motion machine would operate

continuously without input of energy and continuously without input of energy and without any net increase in entropywithout any net increase in entropy

Perpetual motion machines of the first type Perpetual motion machines of the first type would violate the First Law, giving out more would violate the First Law, giving out more energy than was put into the machineenergy than was put into the machine

Perpetual motion machines of the second Perpetual motion machines of the second type would violate the Second Law, possibly type would violate the Second Law, possibly by no exhaustby no exhaust

Perpetual motion machines will never be Perpetual motion machines will never be inventedinvented

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Entropy and DisorderEntropy and Disorder

Entropy can be described in terms Entropy can be described in terms of disorderof disorder

A disorderly arrangement is much A disorderly arrangement is much more probable than an orderly one more probable than an orderly one if the laws of nature are allowed to if the laws of nature are allowed to act without interferenceact without interference This comes from a statistical This comes from a statistical

mechanics developmentmechanics development

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Entropy and Disorder, Entropy and Disorder, cont.cont.

Isolated systems tend toward greater disorder, Isolated systems tend toward greater disorder, and entropy is a measure of that disorderand entropy is a measure of that disorder S = kS = kBB ln W ln W

kkBB is Boltzmann’s constant is Boltzmann’s constant W is a number proportional to the probability that W is a number proportional to the probability that

the system has a particular configurationthe system has a particular configuration This gives the Second Law as a statement of This gives the Second Law as a statement of

what is most probably rather than what must bewhat is most probably rather than what must be The Second Law also defines the direction of The Second Law also defines the direction of

time of all events as the direction in which the time of all events as the direction in which the entropy of the universe increasesentropy of the universe increases

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Grades of EnergyGrades of Energy

The tendency of nature to move toward a The tendency of nature to move toward a state of disorder affects a system’s state of disorder affects a system’s ability to do workability to do work

Various forms of energy can be Various forms of energy can be converted into internal energy, but the converted into internal energy, but the reverse transformation is never completereverse transformation is never complete

If two kinds of energy, A and B, can be If two kinds of energy, A and B, can be completely interconverted, they are of completely interconverted, they are of the the same gradesame grade

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Grades of Energy, cont.Grades of Energy, cont.

If form A can be completely converted to If form A can be completely converted to form B, but the reverse is never complete, form B, but the reverse is never complete, A is a A is a higher gradehigher grade of energy than B of energy than B

When a high-grade energy is converted to When a high-grade energy is converted to internal energy, it can never be fully internal energy, it can never be fully recovered as high-grade energyrecovered as high-grade energy

Degradation of energyDegradation of energy is the conversion is the conversion of high-grade energy to internal energyof high-grade energy to internal energy

In all real processes, the energy available In all real processes, the energy available for doing work decreasesfor doing work decreases

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Heat Death of the Heat Death of the UniverseUniverse

The entropy of the Universe always The entropy of the Universe always increasesincreases

The entropy of the Universe should The entropy of the Universe should ultimately reach a maximumultimately reach a maximum At this time, the Universe will be at a state of At this time, the Universe will be at a state of

uniform temperature and densityuniform temperature and density This state of perfect disorder implies no This state of perfect disorder implies no

energy will be available for doing workenergy will be available for doing work This state is called the This state is called the heat deathheat death of the of the

UniverseUniverse