ThermodynamicThermodynamic

Zeroth law of Zeroth law of thermodynamicsthermodynamics

If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other.

Temperature ScalesTemperature Scales Thermometers can be calibrated by Thermometers can be calibrated by

placing them in thermal contact with placing them in thermal contact with an environment that remains at an environment that remains at constant temperatureconstant temperature• Environment could be mixture of ice and Environment could be mixture of ice and

water in thermal equilibriumwater in thermal equilibrium• Also commonly used is water and steam Also commonly used is water and steam

in thermal equilibriumin thermal equilibrium

Celsius ScaleCelsius Scale Temperature of an ice-water mixture Temperature of an ice-water mixture

is defined as 0º Cis defined as 0º C• This is the This is the freezing pointfreezing point of water of water

Temperature of a water-steam Temperature of a water-steam mixture is defined as 100º Cmixture is defined as 100º C• This is the This is the boiling pointboiling point of water of water

Distance between these points is Distance between these points is divided into 100 segmentsdivided into 100 segments

Kelvin ScaleKelvin Scale When the pressure of a gas goes to When the pressure of a gas goes to

zero, its temperature is –273.15º Czero, its temperature is –273.15º C This temperature is called This temperature is called absolute absolute

zerozero This is the zero point of the Kelvin This is the zero point of the Kelvin

scalescale• ––273.15º C = 0 K273.15º C = 0 K

To convert: To convert: TTC C = T= TKK – 273.15 – 273.15

Some KelvinSome KelvinTemperaturesTemperatures

Some Some representative representative Kelvin Kelvin temperaturestemperatures

Note, this scale is Note, this scale is logarithmiclogarithmic

Absolute zero has Absolute zero has never been never been reachedreached

Fahrenheit ScalesFahrenheit Scales Most common scale used in the USMost common scale used in the US Temperature of the freezing point is Temperature of the freezing point is

32º32º Temperature of the boiling point is Temperature of the boiling point is

212º212º 180 divisions between the points180 divisions between the points

Comparing Temperature ScalesComparing Temperature Scales

273.159 325

95

C K

F C

F C

T T

T T

T T

Thermal ExpansionThermal Expansion The thermal expansion of an object is a The thermal expansion of an object is a

consequence of the change in the average consequence of the change in the average separation between its constituent atoms separation between its constituent atoms or moleculesor molecules

At ordinary temperatures, molecules At ordinary temperatures, molecules vibrate with a small amplitudevibrate with a small amplitude

As temperature increases, the amplitude As temperature increases, the amplitude increasesincreases• This causes the overall object as a whole to This causes the overall object as a whole to

expandexpand

Linear (area, volume) Linear (area, volume) ExpansionExpansion

For small changes in temperatureFor small changes in temperature

The coefficient of linear expansion, , depends The coefficient of linear expansion, , depends on the materialon the material

Similar in two dimensions (area expansion)Similar in two dimensions (area expansion)

… … and in three dimensions (volume expansion)and in three dimensions (volume expansion)

tLL o

2, tAA o

3,solidsfor tVV o

ExampleExample

A copper telephone wire has essentially no sag between poles 35.0 m apart on a winter day when the temperature is –20.0°C. How much longer is the wire on a summer day when TC = 35.0°C? Assume that the thermal coefficient of copper is constant throughout this range at its room temperature value.

Applications of Thermal Applications of Thermal ExpansionExpansion

1. Thermostats1. Thermostats• Use a Use a bimetallic stripbimetallic strip• Two metals expand differentlyTwo metals expand differently

2. Pyrex Glass2. Pyrex Glass• Thermal stresses are smaller than for ordinary glassThermal stresses are smaller than for ordinary glass

3. Sea levels3. Sea levels• Warming the oceans will increase the volume of the oceansWarming the oceans will increase the volume of the oceans

Unusual Behavior of WaterUnusual Behavior of Water

At the temperature of water increases from 0ºC At the temperature of water increases from 0ºC to 4 ºC, it contracts and its density increasesto 4 ºC, it contracts and its density increases

Above 4 ºC, water exhibits the expected Above 4 ºC, water exhibits the expected expansion with increasing temperatureexpansion with increasing temperature

Maximum density of water is 1000 kg/mMaximum density of water is 1000 kg/m33 at 4 ºC at 4 ºC

Ideal GasIdeal Gas Properties of gasesProperties of gases

• A gas does not have a fixed volume or pressureA gas does not have a fixed volume or pressure• In a container, the gas expands to fill the containerIn a container, the gas expands to fill the container

Ideal gasIdeal gas::• Collection of atoms or molecules that move randomlyCollection of atoms or molecules that move randomly• Molecules exert no long-range force on one anotherMolecules exert no long-range force on one another• Molecules occupy a negligible fraction of the volume of their Molecules occupy a negligible fraction of the volume of their

containercontainer Most gases at room temperature and pressure Most gases at room temperature and pressure

behave approximately as an ideal gasbehave approximately as an ideal gas

MolesMoles It’s convenient to express the amount of It’s convenient to express the amount of

gas in a given volume in terms of the gas in a given volume in terms of the number of moles, nnumber of moles, n

One mole is the amount of the substance One mole is the amount of the substance that contains as many particles as there that contains as many particles as there are atoms in 12 g of carbon-12are atoms in 12 g of carbon-12

massmolarmassn

Avogadro’s HypothesisAvogadro’s Hypothesis Equal volumes of gas at the same Equal volumes of gas at the same

temperature and pressure contain the temperature and pressure contain the same numbers of moleculessame numbers of molecules

• Corollary: At standard temperature and Corollary: At standard temperature and pressure, one mole quantities of all gases pressure, one mole quantities of all gases contain the same number of moleculescontain the same number of molecules

• This number is called NThis number is called NAA• Can also look at the total number of Can also look at the total number of

particles: N = n Nparticles: N = n NAA

Avogadro’s NumberAvogadro’s Number The number of particles in a mole is The number of particles in a mole is

called called Avogadro’s NumberAvogadro’s Number• NNAA=6.02 x 10=6.02 x 102323 particles / mole particles / mole

The mass of an individual atom can The mass of an individual atom can be calculated:be calculated:

Aatom N

massmolarm

Equation of State for an Equation of State for an Ideal GasIdeal Gas

Boyle’s LawBoyle’s Law• At a At a constant temperatureconstant temperature, pressure is , pressure is

inversely proportional to the volumeinversely proportional to the volume Charles’ LawCharles’ Law

• At a At a constant pressureconstant pressure, the temperature , the temperature is directly proportional to the volumeis directly proportional to the volume

Gay-Lussac’s LawGay-Lussac’s Law• At a At a constant volumeconstant volume, the pressure is , the pressure is

directly proportional to the temperaturedirectly proportional to the temperature

Ideal Gas LawIdeal Gas Law

Summarizes Boyle’s Law, Charles’ Law, Summarizes Boyle’s Law, Charles’ Law, and Guy-Lussac’s Lawand Guy-Lussac’s Law

PV = n R TPV = n R T• R is the R is the Universal Gas ConstantUniversal Gas Constant• R = 8.31 J / mole KR = 8.31 J / mole K• R = 0.0821 L atm / mole KR = 0.0821 L atm / mole K

P V = N kP V = N kBB T T• kkBB is is Boltzmann’s ConstantBoltzmann’s Constant• kkBB = R / N = R / NAA = 1.38 x 10 = 1.38 x 10-23-23 J/ K J/ K

Kinetic Theory of GasesKinetic Theory of Gases -- -- AssumptionsAssumptions

The number of molecules in the gas is large and the The number of molecules in the gas is large and the average separation between them is large compared to average separation between them is large compared to their dimensionstheir dimensions

The molecules obey Newton’s laws of motion, but as a The molecules obey Newton’s laws of motion, but as a whole they move randomlywhole they move randomly

The The molecules interact only by short-range forcesmolecules interact only by short-range forces during during elastic collisionselastic collisions

The molecules make elastic collisions with the wallsThe molecules make elastic collisions with the walls The gas under consideration is a pure substance, all the The gas under consideration is a pure substance, all the

molecules are identicalmolecules are identical

Pressure of an Ideal GasPressure of an Ideal Gas The pressure is The pressure is

proportional to the proportional to the number of molecules number of molecules per unit volumeper unit volume and to and to the the average average translational kinetic translational kinetic energyenergy of a molecule of a molecule

2mv

21

VN

23P

Molecular Interpretation of Molecular Interpretation of TemperatureTemperature

TemperatureTemperature is proportional to the is proportional to the average kinetic energy of the moleculesaverage kinetic energy of the molecules

The total kinetic energy is proportional to The total kinetic energy is proportional to the absolute temperaturethe absolute temperature

Tkmv B23

21 2

nRTKEtotal 23

Internal EnergyInternal Energy In a monatomic gas, the KE is the only In a monatomic gas, the KE is the only

type of energy the molecules can havetype of energy the molecules can have

U is the U is the internal energyinternal energy of the gas of the gas In a polyatomic gas, additional possibilities In a polyatomic gas, additional possibilities

for contributions to the internal energy are for contributions to the internal energy are rotational and vibrational energy in the rotational and vibrational energy in the moleculesmolecules

nRTU23

Speed of the MoleculesSpeed of the Molecules Expressed as the Expressed as the root-mean-squareroot-mean-square (rms) (rms)

speedspeed

At a given temperature, lighter molecules At a given temperature, lighter molecules move faster, on average, than heavier move faster, on average, than heavier onesones• Lighter molecules can more easily reach Lighter molecules can more easily reach

escape speed from the earthescape speed from the earth

MTR

mTkv B

rms33

Energy in Thermal ProcessesEnergy in Thermal Processes

Internal Energy vs. HeatInternal Energy vs. Heat Internal EnergyInternal Energy, U, is the energy associated with , U, is the energy associated with

the microscopic components of the systemthe microscopic components of the system• Includes kinetic and potential energy associated with the Includes kinetic and potential energy associated with the

random translational, rotational and vibrational motion random translational, rotational and vibrational motion of the atoms or moleculesof the atoms or molecules

• Also includes the intermolecular potential energyAlso includes the intermolecular potential energy

HeatHeat is energy transferred between a system and is energy transferred between a system and its environment because of a temperature its environment because of a temperature difference between themdifference between them• The system The system QQ is used to represent the amount of energy is used to represent the amount of energy

transferred by heat between a system and its transferred by heat between a system and its environmentenvironment

Units of HeatUnits of Heat

CalorieCalorie• An historical unit, before the connection between An historical unit, before the connection between

thermodynamics and mechanics was recognizedthermodynamics and mechanics was recognized• A A caloriecalorie is the amount of energy necessary to raise the is the amount of energy necessary to raise the

temperature of 1 g of water from 14.5° C to 15.5° C .temperature of 1 g of water from 14.5° C to 15.5° C . A Calorie (food calorie) is 1000 calA Calorie (food calorie) is 1000 cal

JouleJoule 1 cal = 4.186 J1 cal = 4.186 J• This is called the This is called the Mechanical Equivalent of HeatMechanical Equivalent of Heat

BTUBTU (US Customary Unit) (US Customary Unit)• BTU stands for British Thermal UnitBTU stands for British Thermal Unit• A A BTUBTU is the amount of energy necessary to raise the is the amount of energy necessary to raise the

temperature of 1 lb of water from 63° F to 64° Ftemperature of 1 lb of water from 63° F to 64° F

UnitsUnitsSISI Joule (J)Joule (J)CGSCGS Calorie (cal)Calorie (cal)US CustomaryUS Customary BTU (btu)BTU (btu)

Specific HeatSpecific Heat Every substance requires a unique Every substance requires a unique amount amount

of energyof energy per unit mass to change the per unit mass to change the temperature of that substance by 1° Ctemperature of that substance by 1° C• directly proportional to mass (thus, per unit directly proportional to mass (thus, per unit

mass)mass) The The specific heat, c,specific heat, c, of a substance is a of a substance is a

measure of this amountmeasure of this amount

TmQc

UnitsUnits

SISI Joule/kg °C (J/kg °C)Joule/kg °C (J/kg °C)CGSCGS Calorie/g °C (cal/g °C )Calorie/g °C (cal/g °C )

Notes: Heat and Specific HeatNotes: Heat and Specific Heat

Q = m c ΔTQ = m c ΔT• ΔT is always the ΔT is always the final temperaturefinal temperature

minus the minus the initial temperatureinitial temperature• When the When the temperature increasestemperature increases, ΔT , ΔT

and and ΔQ are considered to be positive ΔQ are considered to be positive and energy flows into the systemand energy flows into the system

• When the When the temperature decreasestemperature decreases, ΔT , ΔT and and ΔQ are considered to be negative ΔQ are considered to be negative and energy flows out of the systemand energy flows out of the system

Example1: Example1: How much heat is needed to raise temperature of aluminum by 5°C?

Given:

Mass: m=0.5 kgTemp. T= 5°Specific heat: cAl =900 J/kg°C

Find:

Q=?

JoulesCCkgJkg

TmcQ Al

225059005.0

Heat is related to mass and temperature by

Thus, energy is flowing into the system!

Consequences of Different Consequences of Different Specific HeatsSpecific Heats

WaterWater has a has a highhigh specific heat specific heat compared to compared to landland

On a hot day, the On a hot day, the air above the land air above the land warms fasterwarms faster

The warmer air The warmer air flows upward and flows upward and cooler air moves cooler air moves toward the beachtoward the beach

CkgJc

CkgJc

OH

Si

4186

700

2

What happens at night?

QuestionQuestion

What happens at night?

1. same2. opposite3. nothing4. none of the above

How to determine specific heat?

CalorimeterCalorimeter A technique for determining the A technique for determining the

specific heat of a substance is called specific heat of a substance is called calorimetrycalorimetry

A A calorimetercalorimeter is a vessel that is a is a vessel that is a good insulator that allows a thermal good insulator that allows a thermal equilibrium to be achieved between equilibrium to be achieved between substances without any energy loss substances without any energy loss to the environmentto the environment

CalorimetryCalorimetry Analysis performed using a calorimeterAnalysis performed using a calorimeter Conservation of energy applies to the isolated Conservation of energy applies to the isolated

systemsystem The energy that leaves the warmer substance The energy that leaves the warmer substance

equals the energy that enters the waterequals the energy that enters the water• QQcoldcold = -Q = -Qhothot • Negative sign keeps consistency in the sign Negative sign keeps consistency in the sign

convention of ΔTconvention of ΔT

Example2: Example2: A 0.010-kg piece of unknown metal heated to 100°C and dropped into the bucket containing 0.5 kg of water at

20°C. Determine specific heat of metal if the final temperature of the system is 50°C

Given:

Mass: m1=0.010 kgm2=0.5 kg

Specific heat (water): cW =4186 J/kg°CTemperatures:

T1=100 °CT2=20 °C

Tf=50 °C

Find:

Specific heat =?

0627905.0

205041865.01005001.0

0222

JcCCCkgJkgCCckg

TcmTcmQQ

metal

metal

OHOHOHmetalmetalmetalmetalwater

Conservation of energy: heat lost by metal is the same as heat acquired by water:

Solve this equation:

0 metalwater QQ

CkgJcmetal51025.1

iron

Phase Transitions

ICE WATER STEAM

Add heat

Add heat

These are three states of matter (plasma is another one)

Phase ChangesPhase Changes

A A phase changephase change occurs when the occurs when the physical characteristics of the physical characteristics of the substance change from one form to substance change from one form to anotheranother

Common phases changes areCommon phases changes are• Solid to liquid – meltingSolid to liquid – melting• Liquid to gas – boilingLiquid to gas – boiling

Phases changes involve Phases changes involve a change in a change in the internal energythe internal energy, , but but no change in no change in temperaturetemperature

Latent HeatLatent Heat

During a phase change, the amount of heat is During a phase change, the amount of heat is given asgiven as• Q = m LQ = m L

L is the L is the latent heatlatent heat of the substance of the substance• Latent means hidden or concealedLatent means hidden or concealed

Choose a positive sign if you are adding energy to Choose a positive sign if you are adding energy to the system and a negative sign if energy is being the system and a negative sign if energy is being removed from the systemremoved from the system

Latent heat of fusionLatent heat of fusion is used for melting or is used for melting or freezingfreezing

Latent heat of vaporizationLatent heat of vaporization is used for boiling or is used for boiling or condensingcondensing

Graph of Ice to SteamGraph of Ice to Steam

Problem-solving hints:Problem-solving hints: Use consistent unitsUse consistent units Transfers in energy are given as Transfers in energy are given as Q=mcΔTQ=mcΔT for for

processes with processes with no phase changesno phase changes Use Use Q = m LQ = m Lff or or Q = m LQ = m Lvv if if there is a phase there is a phase

changechange In In QQcoldcold = - Q = - Qhothot be careful of sign, be careful of sign, ΔT = TΔT = Tff - T - Tii

Methods of Heat TransferMethods of Heat Transfer Need to know the rate at which Need to know the rate at which

energy is transferredenergy is transferred Need to know the mechanisms Need to know the mechanisms

responsible for the transferresponsible for the transfer Methods includeMethods include

• ConductionConduction• ConvectionConvection• RadiationRadiation

1. Conduction1. Conduction The transfer can be viewed on an The transfer can be viewed on an

atomic scaleatomic scale• It is an exchange of energy between It is an exchange of energy between

microscopic particles by collisionsmicroscopic particles by collisions• Less energetic particles gain energy Less energetic particles gain energy

during collisions with more energetic during collisions with more energetic particlesparticles

Rate of conduction depends upon the Rate of conduction depends upon the characteristics of the substancecharacteristics of the substance

Conduction exampleConduction example The molecules vibrate The molecules vibrate

about their equilibrium about their equilibrium positionspositions

Particles near the flame Particles near the flame vibrate with larger vibrate with larger amplitudesamplitudes

These collide with adjacent These collide with adjacent molecules and transfer molecules and transfer some energysome energy

Eventually, the energy Eventually, the energy travels entirely through the travels entirely through the rodrod

Conduction can occur only if there is a Conduction can occur only if there is a difference in temperature between two difference in temperature between two parts of the conducting mediumparts of the conducting medium

ConductionConduction The slab allows The slab allows

energy to transfer energy to transfer from the region of from the region of higher temperature higher temperature to the region of to the region of lower temperaturelower temperature

LTTkA

tQP ch

Heat flow Thermal conductivity

ConductionConduction

A is the cross-sectional areaA is the cross-sectional area L = Δx is the thickness of the slab or the L = Δx is the thickness of the slab or the

length of a rodlength of a rod P is in Watts when Q is in Joules and t is P is in Watts when Q is in Joules and t is

in secondsin seconds k is the k is the thermal conductivitythermal conductivity of the of the

materialmaterial• Good conductors have high k values and Good conductors have high k values and

good insulators have low k valuesgood insulators have low k values

Home InsulationHome Insulation Substances are rated by their Substances are rated by their R valuesR values

• R = L / kR = L / k More multiple layers, the total R value is More multiple layers, the total R value is

the sum of the R values of each layerthe sum of the R values of each layer Wind increases the energy loss by Wind increases the energy loss by

conduction in a homeconduction in a home

2. Convection2. Convection Energy transferred by the movement of a Energy transferred by the movement of a

substancesubstance• When the movement results from differences When the movement results from differences

in density, it is called in density, it is called natural conductionnatural conduction• When the movement is forced by a fan or a When the movement is forced by a fan or a

pump, it is called pump, it is called forced convectionforced convection

Convection exampleConvection example Air directly above the Air directly above the

flame is warmed and flame is warmed and expandsexpands

The density of the air The density of the air decreases, and it risesdecreases, and it rises

The mass of air warms The mass of air warms the hand as it moves the hand as it moves byby

Applications:Applications:• RadiatorsRadiators• Cooling automobile Cooling automobile

enginesengines

3. Radiation3. Radiation Radiation does not require physical Radiation does not require physical

contactcontact All objects radiate energy continuously in All objects radiate energy continuously in

the form of electromagnetic waves due to the form of electromagnetic waves due to thermal vibrations of the moleculesthermal vibrations of the molecules

Rate of radiation is given by Rate of radiation is given by Stefan’s LawStefan’s Law

Radiation exampleRadiation example

The electromagnetic waves carry the The electromagnetic waves carry the energy from the fire to the handsenergy from the fire to the hands

No physical contact is necessaryNo physical contact is necessary

Radiation equationRadiation equation P = σAeTP = σAeT44

• P is the rate of energy transfer, in WattsP is the rate of energy transfer, in Watts• σ = 5.6696 x 10σ = 5.6696 x 10-8-8 W/m W/m22 K K44

• A is the surface area of the objectA is the surface area of the object• e is a constant called the e is a constant called the emissivityemissivity

e varies from 0 to 1e varies from 0 to 1• T is the temperature T is the temperature in Kelvinsin Kelvins

Energy Absorption and Energy Absorption and Emission by RadiationEmission by Radiation

With its surroundings, the rate at With its surroundings, the rate at which the object at temperature T which the object at temperature T with surroundings at Twith surroundings at Too radiates is radiates is• PPnetnet = σAe(T = σAe(T44 – T – T44

oo))• When an object is in equilibrium with its When an object is in equilibrium with its

surroundings, it radiates and absorbs at surroundings, it radiates and absorbs at the same ratethe same rate

Its temperature will not changeIts temperature will not change

Example: Example: Determine solar energy over the area of 1 m2. Temperature of Sun’s surface is 6000 K and temperature of

surroundings is 300 K.

Given:

Area: A= 1 m2 Temperatures:

T1=6000 KT2=300 K

Find:

Power =?

Use Stefan’s law:

40

4 TTAPower

sJ

Km

KKAPower

7

41528

44

103.7

103.1111067.5

3006000

Temperature of Sun’s surface Temperature on the Earth

Ideal Absorbers and ReflectorsIdeal Absorbers and Reflectors An An ideal absorberideal absorber is defined as an object is defined as an object

that absorbs all of the energy incident on that absorbs all of the energy incident on itit• e = 1e = 1

This type of object is called a This type of object is called a black bodyblack body• An ideal absorber is also an ideal radiator of An ideal absorber is also an ideal radiator of

energyenergy An An ideal reflectorideal reflector absorbs none of the absorbs none of the

energy incident on itenergy incident on it• e = 0e = 0

Applications of RadiationApplications of Radiation ClothingClothing

• Black fabric acts as a good absorberBlack fabric acts as a good absorber• White fabric is a better reflectorWhite fabric is a better reflector

ThermographyThermography• The amount of energy radiated by an object The amount of energy radiated by an object

can be measured with a thermographcan be measured with a thermograph Body temperatureBody temperature

• Radiation thermometer measures the intensity Radiation thermometer measures the intensity of the infrared radiation from the eardrumof the infrared radiation from the eardrum

Resisting Energy TransferResisting Energy Transfer Dewar flask/thermos bottleDewar flask/thermos bottle Designed to minimize Designed to minimize

energy transfer to energy transfer to surroundingssurroundings

Space between walls is Space between walls is evacuated to minimize evacuated to minimize conduction and convectionconduction and convection

Silvered surface minimizes Silvered surface minimizes radiationradiation

Neck size is reducedNeck size is reduced

Global WarmingGlobal Warming Greenhouse exampleGreenhouse example

• Visible light is absorbed and re-emitted Visible light is absorbed and re-emitted as infrared radiationas infrared radiation

• Convection currents are inhibited by the Convection currents are inhibited by the glassglass

Earth’s atmosphere is also a good Earth’s atmosphere is also a good transmitter of visible light and a good transmitter of visible light and a good absorber of infrared radiationabsorber of infrared radiation