Thermal Physics Topic 3 1 Thermal Concepts Temperature

Thermal Physics Topic 3. 1 Thermal Concepts

Temperature – Macroscopic • At a macroscopic level, temperature is the degree of hotness or coldness of a body as measured by a thermometer • Temperature is a property that determines the direction of thermal energy transfer between two bodies in contact • Temperature is measured in degrees Celsius (o. C) or Kelvin (K) – Where Temp in K = Temp in o. C + 273 – Temp in K is known as the absolute temperature

Thermal Equilibrium • When 2 bodies are placed in contact • Heat will flow from the body at higher temp to the body with higher temp • Until the two objects reach the same temperature • They will then be in Thermal Equilibrium • This is how a thermometer works

Thermometers • A temperature scale is constructed by taking two fixed, reproducible temperatures • The upper fixed point is the boiling point of pure water at atmospheric pressure • The lower fixed point is the melting point of pure ice at atmospheric pressure • These were then given the values of 100 o. C and 0 o. C respectively, and the scale between them was divided by 100 to give individual degrees

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

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

Heat • The term heat represents energy transfer due to a temperature difference • Occurs from higher to lower temperature regions Methods of Heat Transfer • Heat can be transferred from one body to another by – – – Conduction Convection Radiation

Thermal Physics Topic 3. 2 Thermal Properties of Matter

Heat Capacity/Thermal Capacity, C w. When substances undergo the same temperature change they can store or release different amounts of energy wthey have different heat capacities w. Defined as the amount of energy needed to change the temperature of a body by unit temperature w. C= Q / T in JK-1 • Q = thermal energy in joules • T = the change in temperature in Kelvin w. Applies to a specific BODY • 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 it needs more time to absorb a greater quantity of thermal energy • They also cool more slowly because they give out thermal energy at a slower rate

Specific Heat Capacity, c • Defined as the amount of thermal energy required to change temperature of 1 kg of the MATERIAL by unit temperature (1 K) • Specific Heat Capacity = = Q / (m T) in J kg -1 K-1 – where m is the mass of the material • For an object made of one specific material: Heat Capacity = m x Specific Heat Capacity

• Unit masses of different substances contain – – – different numbers of molecules of different types of different masses • If the same amount of internal energy is added to each unit mass – it is distributed amongst the molecules • The average energy change of each molecule will be different for each substance • Therefore the temperature changes will be different • So the specific heat capacities will be different

Methods of finding the S. H. C • Two methods – Direct – Indirect

Direct Method - Liquids • Using a calorimeter of known heat capacity • (or specific heat capacity of the material and the mass of the calorimeter) • Because: heat capacity = mass x specific heat capacity To joulemeter or voltmeter and ammeter Stirrer Thermometer Calorimeter Heating coil Liquid Insulation

Calculations - Liquids • Electrical energy = V I t • Energy gained by liquid = ml cl Tl • Energy gained by calorimeter = mc cc Tc • Using conservation of energy • Electrical energy input = thermal energy gained by liquid + thermal energy gained by calorimeter • V I t = ml cl Tl + mc cc Tc • The only unknown is the specific heat capacity of the liquid

Direct Method - Solids • Using a specially prepared block of the material • The block is cylindrical and has 2 holes drilled in it – one for thermometer and one for the heater – Heater hole in the centre, so the heat spreads evenly through the block – Thermometer hole, ½ way between the heater and the outside of the block, so that it gets the averge temperature of the block Insulation To joulemeter or voltmeter and ammeter Thermometer Heating coil Solid Insulation • V I t = ms cs Ts • The only unknown is the specific heat capacity of the solid

Indirect Method • Sometimes called the method of mixtures • 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) • Then it is transferred to a known mass of liquid in a calorimeter of known mass • The change in temperature is recorded and from this the specific heat capacity of the solid can be found • Energy lost by block = Energy gained by liquid and calorimeter • mb cb Tb = mw cw Tw + mc cc Tc – the SHC of water and the calorimeter are needed

Apparatus Thermometer Beaker Boiling Water Block Heat Thermometer Calorimeter Water Block Insulation • In the case of a liquid • A hot solid of known specific heat capacity is transferred to a liquid of unknown specific heat capacity • A similar calculation then occurs

Phases (States) of Matter • • • Matter is defined as anything that has mass and occupies space There are 4 states of matter Solids, Liquids, Gases and Plasmas Most of the matter on the Earth in the form of the first 3 Most of the matter in the Universe is in the plasma state Macroscopic properties • Macroscopic properties are all the observable behaviours of that material such as shape, volume, compressibility • The many macroscopic or physical properties of a substance can provide evidence for the nature of that substance

Macroscopic Characteristics Microscopic Characteristics

Fluids • • Liquids Gases are both fluids Because they FLOW

Arrangement of Particles • Solids • Closely packed • Strongly bonded to neighbours • held rigidly in a fixed position • the force of attraction between particles gives them PE • Liquids • Still closely packed • Bonding is still quite strong • Not held rigidly in a fixed position and bonds can break and reform • PE of the particles is higher than a solid because the distance between the particles is higher • Gases • Widely spaced • Only interact significantly on closest approach or collision • Have a much higher PE than liquids because the particles are furthest apart

Changes of State • A substance can undergo changes of state or phase changes at different temperatures • Pure substances have definite melting and boiling points which are characteristic of the substance – When the solid is heated the particles of the solid vibrate at an increasing rate as the temperature is increased – The vibrational KE of the particles increases – At the melting point a temperature is reached at which the particles vibrate with sufficient thermal energy to break from their fixed positions and begin to slip over each other – As the solid continues to melt more and more particles gain sufficient energy to overcome the forces between the particles and over time all the solid particles are changed to a liquid – The PE of the system increases as the particles move apart

– As the heating continues the temperature of the liquid rises due to an increase in the vibrational, rotational and translational energy of the particles – At the boiling point a temperature is reached at which the particles gain sufficient energy to overcome the inter-particle forces and escape into the gaseous state. PE increases. – Continued heating at the boiling point provides the energy for all the particles to change

Heating Curve So l Liq id Solid - liquid phase change uid G Liquid - gas phase change as Temp / o. C Time /min

Changes of State Thermal energy added sublimation melting SOLID vaporisation LIQUID Freezing/solidification GAS condensation Thermal energy given out

Latent Heat • The thermal energy which a particle absorbs in melting, vaporising or sublimation or gives out in freezing, condensing or sublimating is called Latent Heat because it does not produce a change in temperature • When thermal energy is absorbed/released by a body, the temperature may rise/fall, or it may remain constant – If the temperature remains constant then a phase change will occur as thermal energy must either increase the PE of the particles as they move further apart – or decrease the PE of the particles as they move closer together

Definition • The quantity of heat energy required to change one kilogram of a substance from one phase to another, without a change in temperature is called the Specific Latent Heat of Transformation • Specific Latent Heat = Q / m (J kg -1) Types of Latent Heat • • • Fusion Vaporisation Sublimation • The latent heat of fusion of a substance is less than the latent heat of vaporisation or the latent heat of sublimation

Questions • When dealing with questions think about – where the heat is being given out – where the heat is being absorbed – try not to miss out any part

Methods of finding Latent Heat • Using similar methods as for specific heat capacity • The latent heat of fusion of ice can be found by adding ice to water in a calorimeter Apparatus Block of ice Thermometer Calorimeter Water Block of ice Insulation

• The change in temperature is recorded and from this the latent heat of fusion of the ice can be found • Energy gained by block melting = Energy lost by liquid and calorimeter • mb L b = m w c w T w + m c c c T c • the SHC of water and the calorimeter are needed

• The latent heat of vaporisation of a liquid could be found by an electrical method Latent Heat of Vaporisation Insulation Thermometer To joulemeter or voltmeter and ammeter Heating coil Liquid in Calorimeter

• The initial mass of the liquid is recorded • The change in temperature is recorded for heating the liquid to boiling • The liquid is kept boiling • The new mass is recorded • Energy supplied by heater = energy to raise temperature of liquid + energy use to vaporise some of the liquid • (The calorimeter also needs to be taken in to account. • V I t = ml cl Tl+ me Le + mc cc Tc

Evaporation • The process of evaporation is a change from the liquid state to the gaseous state which occurs at a temperature below the boiling point Explanation • A 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 considerably greater than the average value • If these particles are near the surface of the liquid, they will have enough KE to overcome the attractive forces of the neighbouring particles and escape from the liquid as a gas • This energy is needed as gases have more PE than liquids.

Cooling • Now that the more energetic particles have escaped • The average KE of the remaining particles in the liquid will be lowered • Since temperature is related to the average KE of the particles • A lower KE infers a lower temperature Cool • This is why the temperature of the liquid falls as an evaporative cooling takes place • A substance that cools rapidly is said to be a volatile liquid • When overheating occurs in a human on hot days, the body starts to perspire • Evaporation of the perspiration cools the body

Factors Affecting The Rate • Evaporation can be increased by – Increasing temperature – (more particles have a higher KE) – Increasing surface area – (more particles closer to the surface) – Increasing air flow above the surface – (gives the particles somewhere to go to)

Topic 3. 3 Ideal Gases

The Mole • The mole is the amount of substance which contains the same number of elementary entities as there are in 12 grams of carbon-12 • Experiments show that this is 6. 02 x 1023 particles • A value denoted by NA and called the Avogadro Constant (units: mol-1) Molar Mass • Molar mass is the mass of one mole of the substance • SI units are kg mol-1 Example • Molar mass of Oxygen gas is 32 x 10 -3 kg mol-1 • How many moles and how many molecules is 20 g of Oxygen? • 20 x 10 -3 kg / 32 x 10 -3 kg mol-1 • 0. 625 mol x 6. 02 x 1023 molecules • 3. 7625 x 1023 molecules

Thermal Properties of Gases • An ideal gas can be characterized by three state variables – Pressure 1 Pa (pascal) = 1 N/1 m 2 – Volume m 3 – Temperature K • Experiments use these macroscopic properties of a gas to formulate a number of gas laws. That is historical approach. • There is another way: • The relationship between them may be deduced from kinetic theory and is called the ideal gas law:

The Ideal Gas Equation • • • PV = n. RT = Nk. T Where n is the number of moles R is the universal gas constant = 8. 31 J mol-1 K-1 N is number of molecules k is Boltzman constant = 1. 38066 x 10 -23 J/K An Ideal Gas • Is a theoretical gas that obeys the gas laws • And thus fit the ideal gas equation exactly Real Gases • Real gases conform to the gas laws under certain limited conditions • But they condense to liquids and then solidify if the temperature is lowered • Furthermore, there are relatively small forces of attraction between particles of a real gas • This is not the case for an ideal gas

The Kinetic Theory of Gases "the theory of moving molecules"; Rudolf Clausius, 1857 • The ideal gas equation is the result of experimental observations about the behavior of gases. It describes how gases behave. • A gas expands when heated at constant pressure • The pressure increases when a gas is compressed at constant temperature • But, why do gases behave this way? • What happens to gas particles when conditions such as pressure and temperature change? • That can be explained with a simple theoretical model known as the kinetic molecular theory. • The kinetic theory relates the macroscopic behaviour of an ideal gas to the microscopic behaviour of its molecules or atoms • This theory is based on the following postulates, or assumptions.

• Gases consist of tiny particles called atoms or molecules • The total number of particles in a sample is very large • The particles are in constant random motion • The range of the intermolecular forces is small compared to the average separation • The size of the particles is relatively small compared with the distance between them, so they are treated as points • Collisions of a short duration occur between particles and the walls of the container • Collisions are perfectly elastic • No forces act between the particles except when they collide • Between collisions the particles move in straight lines • And obey Newton’s Laws of motion

• Gas consists of large numbers of tiny particles called atoms or molecules that behave like hard, spherical objects in a state of constant, random motion. • The size of the particles is relatively small compared with the distance between them, so they are treated as points • Collisions of a short duration occur between particles and the walls of the container • No Intermolecular forces act between the particles except when they collide, so between collisions the particles move in straight lines • Collisions are perfectly elastic (none of the energy of a gas particle is lost in collisions) • Energy can be transferred between molecules during collisions. • They all obey Newton’s Laws of motion

Macroscopic Behaviour § The large number of particles ensures that the number of particles moving in all directions is constant at any time § With these basic assumptions we can relate the pressure of a gas (macroscopic behaviour) to the behavior of the molecules themselves (microscopic behaviour).

Pressure • Pressure is the result of collisions between molecules and the wall of the container • Focus on one molecule moving toward the wall and examine what happens when on molecule strikes this wall. Elastic collision – no loss of kinetic energy, so speed remains the same, only direction changes. If you can imagine 3 -D picture you can “see” that only the component of the molecule’s momentum perpendicular to the wall changes. • Change in momentum implies that there must be a force exerted by the wall on the particle. • 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 microscopic forces per unit area: • It can be shown that the pressure on the wall can be expressed as: • Now, finally we have the pressure in a gas expressed in terms of molecular properties. • This is a surprisingly simple result! The macroscopic pressure of a gas relates directly to the average kinetic energy per molecule. • We got key connection between microscopic behaviour and macroscopic observables.

• If we compare the ideal-gas equation of state: PV = Nk. T, with the result from kinetic theory: PV = ⅓ N m (v 2)avg we find • The average translational kinetic energy of molecules in a gas is directly proportional to the absolute temperature. • The higher the temperature, according to kinetic theory, the faster the molecules are moving on the average. • At absolute zero they have zero kinetic energy. Can not go lower. • This relation is one of the triumphs of the kinetic energy theory.

Absolute Temperature • The absolute temperature is a measure of the average kinetic energy of its molecules • If two different gases are at the same temperature, their molecules have the same average kinetic energy, but more massive molecules will have lower average speed. • If the temperature of a gas is doubled, the average kinetic energy of its molecules is doubled Molecular Speed • Although the molecules of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds • Some are moving fast, others relatively slowly • At higher temperatures at greater fraction of the molecules are moving at higher speeds • For O 2 molecules at 300 K, the most probable speed is 390 m/s. • 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 those that are very large, but these have much lower probabilities.

Application of the "Kinetic Molecular Theory" to the Gas Laws Microscopic justification of the laws

Pressure Law (Gay-Lussac’s Law) Effect of a pressure increase at a constant volume Macroscopically: at constant volume the pressure of a gas is proportional to its temperature: PV = Nk. T → P = (const) T example: a closed jar, or aerosol can, thrown into a fire will explode due to increase in gas pressure inside.

Microscopically: • As T increases, KE of molecules increase • That implies greater change in momentum when they hit the wall of the container • Thus microscopic force from each molecule on the wall will be greater • As the molecules are moving faster on average they will hit the wall more often • The total force will increase, therefore the pressure will increase

The Charles’s law Effect of a volume increase at a constant pressure Macroscopically: at constant pressure, volume of a gas is proportional to its temperature: PV = Nk. T → V = (const) T

Microscopically: • An increase in temperature means an increase in the average kinetic energy of the gas molecules, thus an increase in speed • There will be more collisions per unit time, furthermore, the momentum of each collision increases (molecules strike the wall harder) • Therefore, there would be an increase in pressure • If we allow the volume to change to maintain constant pressure, the volume will increase with increasing temperature

Boyle - Marriott’s Law Effect of a pressure decrease at a constant temperature Macroscopically: at constant temperature the pressure of a gas is inversely proportional to its volume: PV = Nk. T → P = (const)/V

Microscopically: • Constant T means that the average KE of the gas molecules remains constant • This means that the average speed of the molecules, v, remains unchanged • If the average speed remains unchanged, but the volume increases, this means that there will be fewer collisions with the container walls over a given time • Therefore, the pressure will decrease