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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