Thermal PhysicsThermal Physics

Topic 3.1 Thermal ConceptsTopic 3.1 Thermal Concepts

Temperature – MacroscopicTemperature – Macroscopic

• At a macroscopic level, temperature is the degree of At a macroscopic level, temperature is the degree of hotness or coldness of a body as measured by a hotness or coldness of a body as measured by a thermometerthermometer

• Temperature is a property that determines the Temperature is a property that determines the direction of thermal energy transfer between two direction of thermal energy transfer between two bodies in contactbodies in contact

• Temperature is measured in degrees Celsius (Temperature is measured in degrees Celsius (ooC) or C) or Kelvin (K)Kelvin (K)– Where Temp in K = Temp in Where Temp in K = Temp in ooC + 273C + 273– Temp in K is known as the absolute temperatureTemp in K is known as the absolute temperature

Thermal EquilibriumThermal Equilibrium

• When 2 bodies are placed in contactWhen 2 bodies are placed in contact• Heat will flow from the body at higher temp to the body Heat will flow from the body at higher temp to the body

with higher temp with higher temp • Until the two objects reach the same temperatureUntil the two objects reach the same temperature• They will then be in They will then be in Thermal EquilibriumThermal Equilibrium• This is how a thermometer worksThis is how a thermometer works

ThermometersThermometers

• A temperature scale is constructed by taking two A temperature scale is constructed by taking two fixed, reproducible temperaturesfixed, reproducible temperatures

• The upper fixed point is the boiling point of The upper fixed point is the boiling point of pure pure water at water at atmospheric pressureatmospheric pressure

• The lower fixed point is the melting point of The lower fixed point is the melting point of pure pure ice ice at at atmospheric pressureatmospheric pressure

• These were then given the values of 100 These were then given the values of 100 ooCC and 0 and 0 ooC C respectively, and the scale between them was respectively, and the scale between them was divided by 100 to give individual degreesdivided by 100 to give individual degrees

Temperature - MicroscopicTemperature - Microscopic

• At a microscopic level, temperature is regarded as a At a microscopic level, temperature is regarded as a measure of the measure of the average kinetic energy per moleculeaverage kinetic energy per molecule associated with its movement associated with its movement in the substancein the substance

Internal EnergyInternal Energy

• The Internal (thermal) energy of a body is the total energy associated with the thermal motions of the particles

• It can comprise of both kinetic and potential energies associated with particle motion

• Kinetic energy arises from the translational and rotational motions

• Potential energy arises from the forces (bonds) between the molecules

HeatHeat• The term The term heatheat represents energy transfer due to a represents energy transfer due to a

temperature differencetemperature difference• Occurs from higher to lower temperature regionsOccurs from higher to lower temperature regions

Methods of Heat TransferMethods of Heat Transfer

• Heat can be transferred from one body to another byHeat can be transferred from one body to another by

– ConductionConduction– ConvectionConvection– RadiationRadiation

Topic 3.2 Thermal Properties of Matter

Thermal Physics

Heat Capacity/Thermal Capacity, CHeat Capacity/Thermal Capacity, C

When substances undergo the same temperature change they can When substances undergo the same temperature change they can store or release different amounts of energystore or release different amounts of energythey have different they have different heat capacitiesheat capacities

Defined as the amount of energy needed to change the Defined as the amount of energy needed to change the temperature of a body by unit temperaturetemperature of a body by unit temperature

C = Q / C = Q / T in JKT in JK-1-1

•Q = thermal energy in joulesQ = thermal energy in joulesT = the change in temperature in KelvinT = the change in temperature in Kelvin

Applies to Applies to aa specific BODY specific BODY

• A body with a high heat capacity will take in thermal energy at a A body with a high heat capacity will take in thermal energy at a slower rate than a substance with a low heat capacity because slower rate than a substance with a low heat capacity because it needs more time to absorb a greater quantity of thermal it needs more time to absorb a greater quantity of thermal energyenergy

• They also cool more slowly because they give out thermal They also cool more slowly because they give out thermal energy at a slower rateenergy at a slower rate

SpecificSpecific HHeaeat Capacity, ct Capacity, c

• Defined as the amount of thermal energy required to change Defined as the amount of thermal energy required to change temperature of 1 kg of the MATERIAL by unit temperature (1K)temperature of 1 kg of the MATERIAL by unit temperature (1K)

• Specific Heat Capacity = Specific Heat Capacity = = = Q / (mQ / (mT) in J kg T) in J kg -1-1 K K-1-1

– where m is the mass of the materialwhere m is the mass of the material

• For an object made of one specific material:For an object made of one specific material: Heat Capacity = m x Specific Heat CapacityHeat Capacity = m x Specific Heat Capacity

• Unit masses of different substanceUnit masses of different substancess contain contain

– different numbers of moleculesdifferent numbers of molecules– of different typesof different types– of different massesof different masses

• If the same amount of internal energy is added to each unit If the same amount of internal energy is added to each unit massmass

– it is distributed amongst the moleculesit is distributed amongst the molecules

• The average energy change of each molecule will be different The average energy change of each molecule will be different for each substancefor each substance

• Therefore the temperature changes will be differentTherefore the temperature changes will be different

• So the specific heat capacities will be differentSo the specific heat capacities will be different

Methods of finding the S.H.CMethods of finding the S.H.C

• Two methodsTwo methods

– DirectDirect– IndirectIndirect

Direct Method - LiquidsDirect Method - Liquids

• Using a calorimeter of known heat capacity Using a calorimeter of known heat capacity

• (or specific heat capacity of the material and the mass of the calorimeter)(or specific heat capacity of the material and the mass of the calorimeter)

• Because: heat capacity = mass x specific heat capacityBecause: heat capacity = mass x specific heat capacity

ThermometerThermometerCalorimeterCalorimeter

Heating coilHeating coilLiquidLiquidInsulationInsulation

StirrerStirrer To joulemeterTo joulemeteror voltmeteror voltmeterand ammeterand ammeter

Calculations - LiquidsCalculations - Liquids

• Electrical energy = V I tElectrical energy = V I t

• Energy gained by liquid = mEnergy gained by liquid = m ll ccll TTll

• Energy gained by calorimeter = mEnergy gained by calorimeter = mcc c ccc TTcc

• Using conservation of energyUsing conservation of energy

• Electrical energy input = thermal energy gained by liquid + thermal Electrical energy input = thermal energy gained by liquid + thermal energy gained by calorimeter energy gained by calorimeter

• V I t = mV I t = mll ccll TTl l + m+ mcc c ccc TTcc

• The only unknown is the specific heat capacity of the liquidThe only unknown is the specific heat capacity of the liquid

Direct Method - SolidsDirect Method - Solids

• Using a specially prepared block of the material Using a specially prepared block of the material • The block is cylindrical and has 2 holes drilled in itThe block is cylindrical and has 2 holes drilled in it

– one for the thermometer and one for the heaterone for the thermometer and one for the heater– Heater hole in the centre, so the heat spreads evenly through the Heater hole in the centre, so the heat spreads evenly through the

blockblock– Thermometer hole, ½ way between the heater and the outside of Thermometer hole, ½ way between the heater and the outside of

the block, so that it gets the averge temperature of the block the block, so that it gets the averge temperature of the block

InsulationInsulation

ThermometerThermometer

Heating coilHeating coilSolidSolid

InsulationInsulation

To joulemeterTo joulemeteror voltmeteror voltmeterand ammeterand ammeter

• V I t = mV I t = mss ccss TTs s

• The only unknown is the specific The only unknown is the specific heat capacity of the solidheat capacity of the solid

Indirect MethodIndirect Method

• Sometimes called the Sometimes called the method of mixturesmethod of mixtures

• In the case of solid, a known mass of solid is heated to a known In the case of solid, a known mass of solid is heated to a known temperature (usually by immersing in boiling water for a period of time)temperature (usually by immersing in boiling water for a period of time)

• Then it is transferred to a known mass of liquid in a calorimeter of Then it is transferred to a known mass of liquid in a calorimeter of known massknown mass

• The change in temperature is recorded and from this the The change in temperature is recorded and from this the specific heat capacity of the solid can be foundspecific heat capacity of the solid can be found

• Energy lost by block = Energy gained by liquid and calorimeterEnergy lost by block = Energy gained by liquid and calorimeter

• mmbb ccbb TTb b = m= mww c cww TTww + m + mcc c ccc TTcc

– the SHC of water and the calorimeter are neededthe SHC of water and the calorimeter are needed

ApparatusApparatus

HeatHeat

ThermometerThermometerBeakerBeakerBoiling WaterBoiling WaterBlockBlock ThermometerThermometer

CalorimeterCalorimeterWaterWaterBlockBlockInsulationInsulation

• In the case of a liquidIn the case of a liquid

• A hot solid of known specific heat capacity is transferred to a A hot solid of known specific heat capacity is transferred to a liquid of unknown specific heat capacityliquid of unknown specific heat capacity

• A similar calculation then occursA similar calculation then occurs

Phases (States) of MatterPhases (States) of Matter

• Matter is defined as anything that has mass and occupies spaceMatter is defined as anything that has mass and occupies space• There are 4 states of matterThere are 4 states of matter• Solids, Liquids, Gases and PlasmasSolids, Liquids, Gases and Plasmas• Most of the matter on the Earth in the form of the first 3Most of the matter on the Earth in the form of the first 3• Most of the matter in the Universe is in the plasma stateMost of the matter in the Universe is in the plasma state

Macroscopic propertiesMacroscopic properties

• Macroscopic properties are all the observable behaviours of that Macroscopic properties are all the observable behaviours of that material such as shape, volume, compressibilitymaterial such as shape, volume, compressibility

• The many macroscopic or physical properties of a substance The many macroscopic or physical properties of a substance can provide evidence for the nature of that substancecan provide evidence for the nature of that substance

Macroscopic Macroscopic CharacteristicsCharacteristics

Microscopic Microscopic CharacteristicsCharacteristics

FluidsFluids

• LiquidsLiquids• Gases Gases • are both fluidsare both fluids• Because they FLOWBecause they FLOW

Arrangement of ParticlesArrangement of Particles

• SolidsSolids

• Closely packed Closely packed • Strongly bonded to neighboursStrongly bonded to neighbours• held rigidly in a fixed positionheld rigidly in a fixed position• the force of attraction between particles gives them PEthe force of attraction between particles gives them PE

• LiquidsLiquids

• Still closely packed Still closely packed • Bonding is still quite strongBonding is still quite strong• NotNot held rigidly in a fixed position and bonds can break and reform held rigidly in a fixed position and bonds can break and reform• PE of the particles is higher than a solid because the distance PE of the particles is higher than a solid because the distance

between the particles is higherbetween the particles is higher

• GasesGases

• Widely spaced Widely spaced • Only interact significantly on closest approach or collisionOnly interact significantly on closest approach or collision• Have a much higher PE than liquids because the particles are furthest apartHave a much higher PE than liquids because the particles are furthest apart

Changes of StateChanges of State

• A substance can undergo changes of state or phase changes at A substance can undergo changes of state or phase changes at different temperaturesdifferent temperatures

• Pure substances have definite melting and boiling points which Pure substances have definite melting and boiling points which are characteristic of the substanceare characteristic of the substance

– When the solid is heated the particles of the solid vibrate at When the solid is heated the particles of the solid vibrate at an increasing rate as the temperature is increasedan increasing rate as the temperature is increased

– The vibrational KE of the particles increasesThe vibrational KE of the particles increases– At the melting point a temperature is reached at which the At the melting point a temperature is reached at which the

particles vibrate with sufficient thermal energy to break from particles vibrate with sufficient thermal energy to break from their fixed positions and begin to slip over each othertheir fixed positions and begin to slip over each other

– As the solid continues to melt more and more particles gain As the solid continues to melt more and more particles gain sufficient energy to overcome the forces between the sufficient energy to overcome the forces between the particles and over time all the solid particles are changed to particles and over time all the solid particles are changed to a liquida liquid

– The PE of the system increases as the particleThe PE of the system increases as the particless move apart move apart

– As the heating continues the temperature of the liquid rises As the heating continues the temperature of the liquid rises due to an increase in the vibrational, rotational and due to an increase in the vibrational, rotational and translational energy of the particlestranslational energy of the particles

– At the boiling point a temperature is reached at which the At the boiling point a temperature is reached at which the particles gain sufficient energy to overcome the inter-particle particles gain sufficient energy to overcome the inter-particle forces and escape into the gaseous state. PE increases.forces and escape into the gaseous state. PE increases.

– Continued heating at the boiling point provides the energy Continued heating at the boiling point provides the energy for all the particles to changefor all the particles to change

Heating CurveHeating CurveSol

id

Liqu

id

Gas

Solid - liquidphase change

Liquid - gasphase change

Temp / oC

Time /min

Changes of StateChanges of State

GASGASSOLIDSOLID LIQUIDLIQUID

Freezing/solidificationFreezing/solidification

vaporisationvaporisation

condensationcondensation

meltingmelting

sublimationsublimation

Thermal energy given outThermal energy given out

Thermal energy addedThermal energy added

Latent HeatLatent Heat

• The thermal energy which a particle absorbs in melting, The thermal energy which a particle absorbs in melting, vaporisingvaporising or or sublimation or gives out in freezing, condensing or sublimating is called sublimation or gives out in freezing, condensing or sublimating is called Latent Heat Latent Heat because it does not produce a change in temperaturebecause it does not produce a change in temperature

• When thermal energy is absorbed/released by a body, the When thermal energy is absorbed/released by a body, the temperature may rise/fall, or it may remain constanttemperature may rise/fall, or it may remain constant

– If the temperature remains constant then a phase change will occur If the temperature remains constant then a phase change will occur as the thermal energy must either increase the PE of the particles as the thermal energy must either increase the PE of the particles as they move further apartas they move further apart

– or decrease the PE of the particles as they move closer togetheror decrease the PE of the particles as they move closer together

DefinitionDefinition

• The quantity of heat energy required to change one kilogram of a The quantity of heat energy required to change one kilogram of a substance from one phase to another, without a change in substance from one phase to another, without a change in temperature is called the temperature is called the SpecificSpecific Latent Heat of TransformationLatent Heat of Transformation

• Specific Latent Heat = Q / m (J kg Specific Latent Heat = Q / m (J kg -1-1))

Types of Latent HeatTypes of Latent Heat

• FusionFusion• VaporisationVaporisation• SublimationSublimation

• The latent heat of fusion of a substance is less than the latent heat The latent heat of fusion of a substance is less than the latent heat of vaporisation or the latent heat of sublimationof vaporisation or the latent heat of sublimation

QuestionsQuestions

• When dealing with questions think about When dealing with questions think about

– where the heat is being given outwhere the heat is being given out– where the heat is being absorbedwhere the heat is being absorbed– try not to miss out any parttry not to miss out any part

Methods of finding Latent HeatMethods of finding Latent Heat

• Using similar methods as for specific heat capacityUsing similar methods as for specific heat capacity• The latent heat of fusion of ice can be found by adding ice to water The latent heat of fusion of ice can be found by adding ice to water

in a calorimeterin a calorimeter

ApparatusApparatus

Block Block of iceof ice

ThermometerThermometer

CalorimeterCalorimeter

WaterWater

Block of iceBlock of ice

InsulationInsulation

• The change in temperature is recorded and from this the latent heat The change in temperature is recorded and from this the latent heat of fusion of the ice can be foundof fusion of the ice can be found

• Energy gained by block melting = Energy lost by liquid and Energy gained by block melting = Energy lost by liquid and calorimetercalorimeter

• mmbb LLbb = m = mww c cww TTww + m + mcc c ccc TTcc

• the SHC of water and the calorimeter are neededthe SHC of water and the calorimeter are needed

Latent Heat of VaporisationLatent Heat of Vaporisation

InsulationInsulation

ThermometerThermometer

Heating coilHeating coilLiquid in CalorimeterLiquid in Calorimeter

To joulemeterTo joulemeteror voltmeteror voltmeterand ammeterand ammeter

• The latent heat of vaporisation of a liquid could be found by an The latent heat of vaporisation of a liquid could be found by an electrical methodelectrical method

• The initial mass of the liquid is recordedThe initial mass of the liquid is recorded• The change in temperature is recorded for heating the liquid to The change in temperature is recorded for heating the liquid to

boilingboiling• The liquid is kept boilingThe liquid is kept boiling• The new mass is recordedThe new mass is recorded• Energy supplied by heater = energy to raise temperature of Energy supplied by heater = energy to raise temperature of

liquid + energy use to vaporise some of the liquidliquid + energy use to vaporise some of the liquid• (The calorimeter also needs to be taken in to account.(The calorimeter also needs to be taken in to account.• V I t = mV I t = mll c cllTTll+ m+ mee LLe e + m+ mcc c cccTTcc

EvaporationEvaporation

• The process of evaporation is a change from the liquid state to the The process of evaporation is a change from the liquid state to the gaseous state which occurs at a gaseous state which occurs at a temperature below the boiling pointtemperature below the boiling point

ExplanationExplanation

• A substance at a particular temperature has a range of particle energiesA substance at a particular temperature has a range of particle energies

• So in a liquid at any instant, a small fraction of the particles will have KE So in a liquid at any instant, a small fraction of the particles will have KE considerably greater than the average valueconsiderably greater than the average value

• If these particles are near the surface of the liquid, they will have If these particles are near the surface of the liquid, they will have enough KE to overcome the attractive forces of the neighbouring enough KE to overcome the attractive forces of the neighbouring particles and escape from the liquid as a gasparticles and escape from the liquid as a gas

• This energy is needed as gases have more PE than liquids.This energy is needed as gases have more PE than liquids.

CoolingCooling

• Now that the more energetic particles have escapedNow that the more energetic particles have escaped• The average KE of the remaining particles in the liquid will be The average KE of the remaining particles in the liquid will be

loweredlowered• Since temperature is related to the average KE of the particlesSince temperature is related to the average KE of the particles• A lower KE infers a lower temperature A lower KE infers a lower temperature

CoolCool

• This is why the temperature of the liquid falls as an evaporative This is why the temperature of the liquid falls as an evaporative cooling takes placecooling takes place

• A substance that cools rapidly is said to be a volatile liquidA substance that cools rapidly is said to be a volatile liquid• When overheating occurs in a human on hot days, the body When overheating occurs in a human on hot days, the body

starts to perspirestarts to perspire• Evaporation of the perspiration cools the body Evaporation of the perspiration cools the body

Factors Affecting The RateFactors Affecting The Rate

• Evaporation can be increased byEvaporation can be increased by– Increasing temperatureIncreasing temperature– (more particles have a higher KE)(more particles have a higher KE)– Increasing surface areaIncreasing surface area– (more particles closer to the surface)(more particles closer to the surface)– Increasing air flow above the surfaceIncreasing air flow above the surface– (gives the particles somewhere to go to)(gives the particles somewhere to go to)

Topic 3.3 Ideal Gases

The MoleThe Mole• The mole is the amount of substance which contains the same number The mole is the amount of substance which contains the same number

of elementary entities as there are in 12 grams of carbon-12of elementary entities as there are in 12 grams of carbon-12

• Experiments show that this is 6.02 x 10Experiments show that this is 6.02 x 102323 particle particles s

• A value denoted by A value denoted by NNAA and called the Avogadro Constant and called the Avogadro Constant (units: mol (units: mol-1-1))

Molar MassMolar Mass• Molar mass is the mass of one mole of the substanceMolar mass is the mass of one mole of the substance

• SI units are kg molSI units are kg mol-1-1

ExampleExample

• Molar mass of Oxygen gas is 32x10Molar mass of Oxygen gas is 32x10-3-3 kg mol kg mol-1-1

• How many moles and how many molecules is 20g of Oxygen?How many moles and how many molecules is 20g of Oxygen?

• 20 x 1020 x 10-3-3 kg / 32 x10 kg / 32 x10-3-3 kg mol kg mol-1-1

0.625 mol0.625 mol

0.625 mol x 6.02 x 100.625 mol x 6.02 x 102323 molecules molecules

3.7625 x 103.7625 x 102323 molecules molecules

Thermal Properties of GasesThermal Properties of Gases

• An ideal gas can be characterized by three An ideal gas can be characterized by three state variablesstate variables

– Pressure 1 Pa (pascal) = 1N/1mPressure 1 Pa (pascal) = 1N/1m22

– Volume mVolume m33 – Temperature KTemperature K

• Experiments use these macroscopic properties of a gas to formulate Experiments use these macroscopic properties of a gas to formulate a number of gas laws. That is historical approach. a number of gas laws. That is historical approach.

• There is another way:There is another way:

• The relationship between them may be deduced from kinetic theory The relationship between them may be deduced from kinetic theory and is called the and is called the ideal gas lawideal gas law::

The Ideal Gas EquationThe Ideal Gas Equation

• PV = nRT = NkTPV = nRT = NkT • Where n is the number of molesWhere n is the number of moles• R is the universal gas constant = 8.31 J molR is the universal gas constant = 8.31 J mol-1-1 K K-1-1

• N is number of moleculesN is number of molecules• k is Boltzman constant = 1.38066 x 10k is Boltzman constant = 1.38066 x 10-23-23 J/K J/K

An Ideal GasAn Ideal Gas

• Is a theoretical gas that obeys the gas lawsIs a theoretical gas that obeys the gas laws• And thus fit the ideal gas equation exactlyAnd thus fit the ideal gas equation exactly

Real GasesReal Gases

• Real gases conform to the gas laws under certain limited conditionsReal gases conform to the gas laws under certain limited conditions• But they condense to liquids and then solidify if the temperature is But they condense to liquids and then solidify if the temperature is

loweredlowered• Furthermore, there Furthermore, there areare relatively small forces of attraction between relatively small forces of attraction between

particles of a real gasparticles of a real gas• This is not the case for an ideal gasThis is not the case for an ideal gas

The Kinetic Theory of GasesThe Kinetic Theory of Gases"the theory of moving molecules";"the theory of moving molecules";

Rudolf Clausius, 1857Rudolf Clausius, 1857•The The ideal gas equationideal gas equation is the result of experimental observations about is the result of experimental observations about the behavior of gases. It describes the behavior of gases. It describes howhow gases behave. gases behave.

•A gas expands when heated at constant pressure A gas expands when heated at constant pressure

•The pressure increases when a gas is compressed at constant The pressure increases when a gas is compressed at constant temperature temperature

•But, But, whywhy do gases behave this way? do gases behave this way?

•What happens to What happens to gas particlesgas particles when conditions such as pressure and when conditions such as pressure and temperature change?temperature change?

•That can be explained with a simple theoretical model known as the That can be explained with a simple theoretical model known as the kinetic molecular theorykinetic molecular theory..

•The kinetic theory relates the macroscopic behaviour of an ideal gas to the The kinetic theory relates the macroscopic behaviour of an ideal gas to the microscopic behaviour of its molecules or atomsmicroscopic behaviour of its molecules or atoms

•This theory is based on the following This theory is based on the following postulates, or assumptionspostulates, or assumptions. .

• Gases consist of tiny particles called atoms or moleculesGases consist of tiny particles called atoms or molecules

• The total number of particles in a sample is very largeThe total number of particles in a sample is very large

• The particles are in constant random motionThe particles are in constant random motion

• The range of the intermolecular forces is small compared to the The range of the intermolecular forces is small compared to the average separationaverage separation

• The size of the particles is relatively small compared with the distance The size of the particles is relatively small compared with the distance between them, so they are treated as pointsbetween them, so they are treated as points

• Collisions of a short duration occur between particles and the Collisions of a short duration occur between particles and the walls of the containerwalls of the container

• Collisions are perfectly elasticCollisions are perfectly elastic• No forces act between the particles except when they collideNo forces act between the particles except when they collide• Between collisions the particles move in straight linesBetween collisions the particles move in straight lines• And obey Newton’s Laws of motionAnd obey Newton’s Laws of motion

• Gas consists of large numbers of Gas consists of large numbers of tiny particles called atoms or tiny particles called atoms or moleculesmolecules that behave like hard, spherical objects in a state that behave like hard, spherical objects in a state of constant, random motion.of constant, random motion.

• The size of the particles is relatively small compared with The size of the particles is relatively small compared with the distance between them, so they are treated as pointsthe distance between them, so they are treated as points

• Collisions of a short duration occur between particles and Collisions of a short duration occur between particles and the walls of the containerthe walls of the container

• No Intermolecular forces act between the particles except when they collide, No Intermolecular forces act between the particles except when they collide, so between collisions the particles move in straight linesso between collisions the particles move in straight lines

• Collisions are perfectly elastic (none of the energy of a gas Collisions are perfectly elastic (none of the energy of a gas particle is lost in collisions)particle is lost in collisions)

• Energy can be transferred between molecules during collisions.Energy can be transferred between molecules during collisions.

• They all obey Newton’s Laws of motionThey all obey Newton’s Laws of motion

Macroscopic BehaviourMacroscopic Behaviour

The large number of particles ensures that the number of particles The large number of particles ensures that the number of particles moving in all directions is constant at any timemoving in all directions is constant at any time

With these basic assumptions we can relate the pressure of a gas With these basic assumptions we can relate the pressure of a gas (macroscopic behaviour) to the behavior of the molecules themselves(macroscopic behaviour) to the behavior of the molecules themselves (microscopic behaviour).(microscopic behaviour).

PressurePressure

• • Pressure is the result of collisions between molecules Pressure is the result of collisions between molecules and the wall of the containerand the wall of the container

• • Focus on one molecule moving toward the wall and examine Focus on one molecule moving toward the wall and examine what happens when on molecule strikes this wall.what happens when on molecule strikes this wall.

Elastic collision – no loss of kinetic Elastic collision – no loss of kinetic energy, so speed remains the same, energy, so speed remains the same, only direction changes. only direction changes. If you can imagine 3-D picture you can If you can imagine 3-D picture you can “see” that only the component of the “see” that only the component of the molecule’s momentum perpendicular to molecule’s momentum perpendicular to the wall changes.the wall changes.

• • Change in momentum implies that there must be a force Change in momentum implies that there must be a force exerted by the wall on the particle.exerted by the wall on the particle. • • That means that there is a force exerted on the wall by that molecule. That means that there is a force exerted on the wall by that molecule.

• • The average pressure on the wall is the average of all The average pressure on the wall is the average of all microscopic forces per unit area:microscopic forces per unit area:

FP =

A• • It can be shown that the pressure on the wall can be expressed as:It can be shown that the pressure on the wall can be expressed as:

21avg3

NP= m(v )

V

• • Now, finally we have the Now, finally we have the pressure in a gas expressed in pressure in a gas expressed in terms of molecular propertiesterms of molecular properties..

• • This is a surprisingly simple result! This is a surprisingly simple result! The macroscopic pressure The macroscopic pressure of a gas relates directly to the average kinetic energy per moleculeof a gas relates directly to the average kinetic energy per molecule ..

• • We got key connection between microscopic behaviour We got key connection between microscopic behaviour and macroscopic observables.and macroscopic observables.

3avg 2KE = kT

• • If we compare the ideal-gas equation of state: PV = NkT, with the If we compare the ideal-gas equation of state: PV = NkT, with the result from kinetic theory: PV = ⅓ N m (vresult from kinetic theory: PV = ⅓ N m (v22))avg avg we find we find

• • The average translational kinetic energy of molecules in a gas The average translational kinetic energy of molecules in a gas is directly proportional to the absolute temperature. is directly proportional to the absolute temperature.

• • The higher the temperature, according to kinetic theory, The higher the temperature, according to kinetic theory, the faster the molecules are moving on the average. the faster the molecules are moving on the average.

• • At absolute zero they have zero kinetic energy. Can not go lower.At absolute zero they have zero kinetic energy. Can not go lower.

• • This relation is one of the triumphs of the kinetic energy This relation is one of the triumphs of the kinetic energy theory.theory.

• • The absolute temperature is a The absolute temperature is a measuremeasure of the of the average kinetic energyaverage kinetic energy of its molecules of its molecules

• • If two different gases are at the same temperature, their molecules If two different gases are at the same temperature, their molecules have the same average kinetic energy, but more massive molecules have the same average kinetic energy, but more massive molecules will have lower average speed. will have lower average speed.

• • If the temperature of a gas is If the temperature of a gas is doubleddoubled, the average kinetic , the average kinetic energy of its molecules is energy of its molecules is doubleddoubled

Absolute TemperatureAbsolute Temperature

• • Although the molecules of gas have an average kinetic energy (and therefore Although the molecules of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds an average speed) the individual molecules move at various speeds • • Some are moving fast, others relatively slowly Some are moving fast, others relatively slowly • • At higher temperatures at greater fraction of the molecules At higher temperatures at greater fraction of the molecules are moving at higher speeds are moving at higher speeds • • For OFor O22 molecules at 300 K, the most probable speed is 390 m/s. molecules at 300 K, the most probable speed is 390 m/s.

• • When temperature increases to 1100 K the most probable speed increases When temperature increases to 1100 K the most probable speed increases to roughly 750 m/s. Other speed occur as well, from speeds near zero to to roughly 750 m/s. Other speed occur as well, from speeds near zero to those that are very large, but these have much lower probabilities.those that are very large, but these have much lower probabilities.

Molecular SpeedMolecular Speed

Application of the "Kinetic Molecular Theory" to the Gas LawsApplication of the "Kinetic Molecular Theory" to the Gas LawsMicroscopic justification of the lawsMicroscopic justification of the laws

Pressure Law (Gay-Lussac’s Law)Pressure Law (Gay-Lussac’s Law)

Effect of a pressure increase at a constant volumeEffect of a pressure increase at a constant volume

Macroscopically:Macroscopically: at constant volume the pressure of a gas is proportional to its temperature:at constant volume the pressure of a gas is proportional to its temperature:

PV = NkT → P = (const) TPV = NkT → P = (const) T

example: a closed jar, or aerosol can, thrown into a fire will explode example: a closed jar, or aerosol can, thrown into a fire will explode due to increase in gas pressure inside. due to increase in gas pressure inside.

Microscopically: Microscopically:

• • As T increases, KE of molecules increase As T increases, KE of molecules increase

• • That implies greater change in momentum when they hit That implies greater change in momentum when they hit the wall of the containerthe wall of the container

• • Thus microscopic force from each molecule on the wall Thus microscopic force from each molecule on the wall will be greater will be greater

• • As the molecules are moving faster on average they As the molecules are moving faster on average they will hit the wall more oftenwill hit the wall more often

• • The total force will increase, therefore the pressure The total force will increase, therefore the pressure will increasewill increase

The Charles’s lawThe Charles’s law Effect of a volume increase at a constant pressureEffect of a volume increase at a constant pressure

Macroscopically:Macroscopically: at constant pressure, volume of a gas at constant pressure, volume of a gas is proportional to its temperature:is proportional to its temperature:

PV = NkT → V = (const) TPV = NkT → V = (const) T

• • An increase in temperature means an increase in the average An increase in temperature means an increase in the average kinetic energy of the gas molecules, thus an increase in speedkinetic energy of the gas molecules, thus an increase in speed

Microscopically:Microscopically:

• • There will be more collisions per unit time, furthermore, the momentum There will be more collisions per unit time, furthermore, the momentum of each collision increases (molecules strike the wall harder) of each collision increases (molecules strike the wall harder)

• • Therefore, there would be an increase in pressure Therefore, there would be an increase in pressure

• • If we allow the volume to change to maintain If we allow the volume to change to maintain constant pressure, the volume will increase with increasing temperatureconstant pressure, the volume will increase with increasing temperature

Boyle - Marriott’s LawBoyle - Marriott’s Law

Effect of a pressure decrease at a constant temperatureEffect of a pressure decrease at a constant temperature

Macroscopically:Macroscopically: at constant temperature the pressure of a gas is inversely proportional at constant temperature the pressure of a gas is inversely proportional to its volume:to its volume:

PV = NkT → P = (const)/VPV = NkT → P = (const)/V

Microscopically:Microscopically:

• • Constant T means that the average KE of the gas molecules Constant T means that the average KE of the gas molecules remains constant remains constant

• • This means that the average speed of the molecules, v, remains This means that the average speed of the molecules, v, remains unchanged unchanged

• • If the average speed remains unchanged, but the volume If the average speed remains unchanged, but the volume increases, this means that there will be fewer collisions with the increases, this means that there will be fewer collisions with the container walls over a given time container walls over a given time

• • Therefore, the pressure will decrease Therefore, the pressure will decrease