Thermal Physics

 The term heat represents energy transfer due to a Thermal Physics temperature difference  Occurs from higher to lower temperature regions Topic 3.1 Thermal Concepts ♦ Temperature – Macroscopic Topic 3.2 Thermal Properties of Matter

 At a macroscopic level, temperature is the degree of ♦ Heat Capacity/Thermal Capacity, C hotness or coldness of a body as measured by a thermometer  When substances undergo the same temperature change they can store or release different amounts of energy  Temperature is a property that determines the direction of thermal energy transfer between two bodies in contact  They have different heat capacities o  Temp is measured in degrees Celsius ( C) or Kelvin (K)  Defined as the amount of energy needed to change the  T(K) = T(oC) + 273 temperature of a body by unit temperature (1K)  Temperature in K is known as the absolute temperature  C = Q / DT (JK-1) ♦ Thermal Equilibrium o Q = thermal energy in joules o DT = the change in temperature in Kelvin  When 2 bodies are placed in contact  Thermal energy will flow from the body with lower temp  Applies to a specific BODY to the body with higher   Until the two objects reach the same temperature A body with a high heat capacity will take in thermal  They will then be in Thermal Equilibrium energy at a slower rate than a substance with a low heat  This is how a thermometer works capacity because it needs more time to absorb a greater quantity of ♦ Thermometers o thermal energy  They also cool more slowly because they give out thermal  A temperature scale is constructed by taking two fixed, reproducible temperatures energy at a slower rate  The upper fixed point is the boiling point of pure water at ♦ atmospheric pressure Specific Heat Capacity, c  The lower fixed point is the melting point of pure ice at  Defined as the amount of thermal energy required to atmospheric pressure change temperature of 1 kg of material by unit o  These were then given the values of 100 C and temperature (1K). 0oC respectively, and the scale between them was -1 -1 divided by 100 to give individual degrees  c = Q / (mDT) (J kg K ) • Q = thermal energy in joules ♦ Temperature - Microscopic • DT = the change in temperature in Kelvin • m = the mass of the material  At a microscopic level, temperature is regarded as a measure of the average kinetic energy per molecule  For an object made of one specific material: in a substance o Heat Capacity = m x Specific Heat Capacity

♦ Internal Energy  Unit masses of different substances contain  The Internal energy of a body is the total energy associated • different numbers of molecules with the thermal motions of the particles • of different types  Is the total of the kinetic energy due to the motion of • of different masses molecules of a substance and the total potential energy associated with the vibrational and electric energy of  If the same amount of internal energy is added to each atoms within molecules or crystals. It includes the energy unit mass in all the chemical bonds, and the energy of the free, • it is distributed amongst the molecules conduction electrons in metals.  The average energy change of each molecule will be  It can comprise of both kinetic and potential energies different for each substance associated with particle motion  Therefore the temperature changes will be different  Kinetic energy arises from the translational and rotational  So the specific heat capacities will be different motions  Potential energy arises from the intermolecular forces ♦ Methods of finding the S.H.C between the molecules  Two methods ♦ Heat  Direct 2  Energy gained by solid = m c DT s s s  V I t = m c DT  Indirect s s s  The only unknown is the specific heat capacity of the solid ♦ Direct Method – SHC of Liquids

 Using a calorimeter of known heat capacity  (or specific heat capacity of the material and the mass of ♦ Indirect Method the calorimeter)  Because: heat capacity = mass x specific heat capacity

 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 – to be in thermal equilibrium with water)  Then it is transferred to a known mass of liquid in a calorimeter of known mass ♦ Calculations - Liquids  The change in temperature is recorded and from this the specific heat capacity of the solid can be found  Electrical energy = V I t  Energy lost by block = Energy gained by liquid and  Energy gained by liquid = m c DT calorimeter l l l  m c DT = m c DT + m c DT  Energy gained by calorimeter = m c DT b b b w w w c c c c c c the SHC of water and the calorimeter are needed  Using conservation of energy  Electrical energy input = thermal energy gained by liquid + thermal energy gained by calorimeter  V I t = m c DT + m c DT l l l c c c  The only unknown is the specific heat capacity of the liquid

♦ Direct Method – SHC of Solids

 Using a specially prepared block of the material  The block is cylindrical and has 2 holes drilled in it • one for the thermometer and one for the heater  In the case of a liquid • Heater hole in the centre, so the heat spreads evenly through  A hot solid of known specific heat capacity is transferred to the block a liquid of unknown specific heat capacity • Thermometer hole, ½ way between the heater and the outside  A similar calculation then occurs of the block, so that it gets the average temperature of the block ♦ 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 ♦ Calculations - Solids  The many macroscopic or physical properties of a substance can provide evidence for the nature of that  Again using the conservation of energy substance  Electrical Energy input is equal to the thermal energy gained by the solid ♦ Macroscopic Characteristics  Electrical energy = V I t 3

Characteristics Solid Liquid Gas • At the melting point a temperature is reached at which the Shape Definite Variable Variable particles vibrate with sufficient thermal energy to break from Volume Definite Definite Variable their fixed positions and begin to slip over each other Almost Very Slightly Highly Compressibility Incompressible Compressible Compressible • As the solid continues to melt more and more particles gain Diffusion Small Slow Fast sufficient energy to overcome the forces between the particles Comparative and over time all the solid particles are changed to a liquid High High Low Density ♦ Microscopic Characteristics • 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.

♦ Fluids • Continued heating at the boiling point provides the energy for all the particles to change  Liquids  Gases ♦ Heating Curve

♦ 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 ♦ Changes of State • 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 ♦ Latent Heat

♦ Changes of States  The thermal energy which a particle absorbs in melting,  A substance can undergo changes of state or phase changes at vaporising or sublimation or gives out in freezing, different temperatures condensing or sublimating is called Latent (“hidden”) Heat because it does not produce a change in temperature  Pure substances have definite melting and boiling points which are characteristic of the substance  When thermal energy is absorbed/released by a body, the temperature may rise/fall, or it may remain constant • When the solid is heated the particles of the solid vibrate at an • If the temperature remains constant then a phase change will increasing rate as the temperature is increased occur as the thermal energy must either increase the PE of the • The vibrational KE of the particles increases particles as they move further apart • or decrease the PE of the particles as they move closer together 4

♦ 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  The initial mass of the liquid is recorded  Fusion  The change in temperature is recorded for heating the  Vaporisation liquid to boiling  Sublimation  The liquid is kept boiling  The new mass is recorded  The latent heat of fusion of a substance is less than the  Energy supplied by heater = energy to raise temperature of latent heat of vaporisation or the latent heat of liquid + energy use to vaporise some of the liquid sublimation  (The calorimeter also needs to be taken in to account.)

 V I t = m c DT + m L + m c DT ♦ Questions l l l e e c c c ♦ Evaporation  When dealing with questions think about  The process of evaporation is a change from . where the heat is being given out the liquid state to the gaseous state which . where the heat is being absorbed occurs at a temperature below the boiling point . try not to miss out any part ♦ Explanation ♦ Methods of finding Latent Heat  A substance at a particular temperature has a range of  Using similar methods as for specific heat capacity particle energies  The latent heat of fusion of ice can be found by adding ice  So in a liquid at any instant, a small fraction of the particles to water in a calorimeter 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 ♦ Cooling

 Now that the more energetic particles have escaped  The average KE of the remaining particles in the liquid will be lowered  The change in temperature is recorded and from this the  Since temperature is related to the average KE of the latent heat of fusion of the ice can be found particles  Energy gained by block melting = Energy lost by liquid and  A lower KE infers a lower temperature calorimeter  This is why the temperature of the liquid falls as an  m L = m c DT + m c DT b b w w w c c c evaporative cooling takes place  the SHC of water and the calorimeter are needed  A substance that cools rapidly is said to be a volatile liquid  The latent heat of vaporisation of a liquid could be found  When overheating occurs in a human on hot days, the by an electrical method body starts to perspire  Evaporation of the perspiration cools the body ♦ Latent Heat of Vaporisation ♦ Factors Affecting The Rate

 Evaporation can be increased by

• Increasing temperature • (more particles have a higher KE) • Increasing surface area 5

• (more particles closer to the surface) Rudolf Clausius, 1857 • Increasing air flow above the surface  The ideal gas equation is the result of experimental • (gives the particles somewhere to go to) observations about the behavior of gases. It describes how gases behave. Ideal Gases • A gas expands when heated at constant pressure • The pressure increases when a gas is compressed at ♦ The Mole constant temperature

 The mole is the amount of substance which contains the  But, why do gases behave this way? same number of elementary entities as there are in 12  What happens to gas particles when conditions such as grams of carbon-12 pressure and temperature change? 23  Experiments show that this is 6.02 x 10 particles  That can be explained with a simple theoretical model  A value denoted by N called the Avogadro constant A known as the kinetic molecular theory. -1 (units mol )  The kinetic theory relates the macroscopic behaviour of an ideal gas to the microscopic behaviour of its molecules or atoms

♦ Molar Mass  This theory is based on the following postulates, or assumptions.  Molar mass is the mass of one mole of the substance -1  SI units are kg mol ♦ The Kinetic Molecular Theory Postulates ♦ Example -3 -1  Molar mass of Oxygen gas is 32x10 kg mol  Gas consists of large numbers of molecules (or atoms, in  If I have 20g of Oxygen, how many moles do I have and the case of the noble gases) that behave like hard, how many molecules? spherical objects in a state of constant, random motion. -3 -3 -1  20 x 10 kg / 32 x10 kg mol  The size of the particles is much smaller than the distance  \ 0.625 mol between them, so they are treated as points 23  \ 0.625 mol x 6.02 x 10 molecules  Collisions of a short duration occur between particles and 23 the walls of the container  \ 3.7625 x 10 molecules  No intermolecular forces act between the particles except ♦ Thermal Properties of Gases when they collide, so between collisions the particles move in straight lines  An ideal gas can be characterized by three state variables  Collisions are perfectly elastic (none of the energy of a gas • Pressure 1 Pa (Pascal) = 1 N/1m2 particle is lost in collisions) • Volume m3 1 liter = 10-3 m3  Energy can be transferred between molecules • Temperature K during collisions.  Experiments use these macroscopic properties of a gas to  They all obey Newton’s Laws of motion formulate a number of gas laws. That is historical approach. There is another way: ♦ Macroscopic behaviour  The relationship between them may be deduced from kinetic theory of gasses and is called the ideal gas law:  The large number of particles ensures that the number of particles moving in all directions is constant at any time PV = nRT = NkT  With these basic assumptions we can relate the pressure of a gas (macroscopic behaviour) to the behavior of the • n = number of moles: n = N/NA molecules themselves (microscopic behaviour). • R = universal gas constant = 8.3145 J/mol K • N = number of molecules ♦ Pressure • k = Boltzmann constant = 1.38066 x 10-23 J/K  Pressure exerted by the gas on the walls is due to ♦ The Kinetic – Molecular Theory of Gasses collisions of the molecules with the walls of the container.  Focus on one molecule moving toward the wall and "the theory of moving molecules"; examine what happens when on molecule strikes this wall. 6

 For O2 molecules at 300 K, the most probable speed is 390 Elastic collision – no loss of kinetic energy, so m/s. When temperature increases to 1100 K the most speed remains the same, only direction probable speed increases to roughly 750 m/s. Other speed changes. occur as well, from speeds near zero to those that are very If you can imagine 3-D picture you can “see” large, but these have much lower probabilities. that only the component of the molecule’s momentum perpendicular to the wall changes.  Application of the "Kinetic Molecular Theory" to

 Change in momentum implies that there must be a force the Gas Laws exerted by the wall on the particle.  Microscopic justification of the laws  That means that there is a force exerted on the wall by that molecule. ♦ Pressure Law (Gay-Lussac’s Law)  The average pressure on the wall is the average of all  Effect of a pressure increase at a constant volume microscopic forces per unit area:  Macroscopically: at constant volume the pressure of a  It can be shown that the pressure on the wall can be gas is proportional to its temperature: expressed as: PV = NkT → P = (const) T

.  example: a closed jar, or aerosol can, thrown into a fire will  Now, finally we have the pressure in a gas expressed in explode due to increase in gas pressure inside. terms of molecular properties.  This is a surprisingly simple result! The macroscopic  Microscopically: pressure of a gas relates directly to the average kinetic energy per molecule.  As T increases, KE of molecules increase  We got key connection between microscopic behaviour  That implies greater change in momentum when they hit and macroscopic observables. the wall of the container  Thus microscopic force from each molecule on the wall will  If we compare the ideal-gas equation of state: PV= NkT be greater 2 with the result from kinetic theory: PV = ⅓ N m(v )avg ,  As the molecules are moving faster on average they will hit we find the wall more often  The total force will increase, therefore the pressure will

increase  The average translational kinetic energy of molecules in a gas is directly proportional to the absolute temperature. ♦ The Charles’s law

 The higher the temperature, according to kinetic theory,  Effect of a volume increase at a constant pressure the faster the molecules are moving on the average.  At absolute zero they have zero kinetic energy. Can not go  Macroscopically: at constant pressure, volume of a gas lower. is proportional to its temperature:  This relation is one of the triumphs of the kinetic energy. PV = NkT → V = (const) T ♦ Absolute Temperature  Microscopically:  The absolute temperature is a measure of the average kinetic energy of its molecules  An increase in temperature means an increase in the  If two different gases are at the same temperature, their average kinetic energy of the gas molecules, thus an molecules have the same average kinetic energy, but more increase in speed massive molecules will have lower average speed.  There will be more collisions per unit time, furthermore,  If the temperature of a gas is doubled, the average kinetic the momentum of each collision increases (molecules energy of its molecules is doubled strike the wall harder)  Therefore, there would be an increase in pressure  If we allow the volume to change to maintain constant ♦ Molecular Speed pressure, the volume will increase with increasing temperature  Although the molecules in a sample of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds ♦ Boyle-Marriott’s Law  Some are moving fast, others relatively slowly  At higher temperatures at greater fraction of the  Effect of a pressure decrease at a constant temperature molecules are moving at higher speeds  Macroscopically: at constant temperature the pressure 7

of a gas is inversely proportional to its volume: PV = NkT → 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