Physics Unit 5 Revision Siobhan Parish Radioactivity Chapter 9 Discovery of the nucleus Rutherford’s experiment 1. Alpha particles had the same speed as otherwise slow α particles would be deflected more than the Evacuated faster ones on the same initial path metal container 2. Container must be evacuated or Thin α would be stopped by air α source metal foil θ molecules 3. Alpha source must have a long half-life or later readings would Observe Moveable be lower than earlier ones due to microscope Fluorescent radioactive decay screen Discovery of the nucleus Rutherford found: • Most α particles went through the foil • ~ 1 in 2000 were deflected • ~ 1 in 10000 were deflected more than 90◦ Rutherford concluded: • Nucleus at the centre of the atom contained most of its mass • Nucleus was very small • Nucleus is positively charged The discovery of the nucleus • The greater deflection is because the electrostatic force of repulsion between the alpha particle and the nucleus increases with decreased separation between them • The smaller deflection means the alpha particle is further away from the nucleus Discovery of the nucleus • The size of the nucleus • 1 in 10000 α particles scattered >90˚for n layers of atoms in the foil, (n≈104). Therefore there’s a 1 in 10000n chance of deflection • Chance = = •= = • d = = ≈ 10-15 Properties of radiation • Marie Curie discovered the nature of radioactive materials • Showed how radioactive compounds could be separated and identified • Henri Becquerel discovered that uranium could be used to produce X-Ray images- saw that it could penetrate paper and blacken photographic film • Marie found radium to be >1,000,000 more radioactive than uranium Mag field into diagram α (+ charged) Properties of radiation γ (uncharged) β (- charged) Rutherford found that radiation: • Ionised air making it conduct electricity- made a detector which could measure the radiation from its ionising effect • Was of two types: alpha (easily absorbed) and beta (more penetrating). A third type, gamma, is even more penetrating and was discovered a year later Properties of radiation Ionisation • The chamber contains air at atmospheric pressure • Ions created in the chamber are attracted to the Source oppositely charged electrode where they Grid are discharged Wall • Electrons pass through the pA as a Ionisation electrode chamber result of ionisation in the chamber • Current proportional to the number Insulator Central electrode of ions per second pA Picoammeter Properties of radiation • α radiation causes strong ionisation. If the source is moved away from the top of the chamber ionisation ceases beyond a certain distance because α radiation has a range in air of no more than a few centimetres • β radiation has a weaker ionising effect than α. Range in air is up to a metre or more. Produces fewer ions per mm along it’s path • γ radiation has the weakest ionising effect, because photons carry no charge Properties of radiation Cloud chambers • Contains air saturated with a vapour at a very low temperature • Due to ionisation alpha and beta particles going through the cloud chamber leave visible tracks of minute condensed vapour droplets • Air space is supersaturated • The ions produced trigger the formation of droplets Properties of radiation • Alpha particles produce straight tracks that radiate from the source and are easily visible • Tracks from a given isotope are all of the same length showing alpha particles have the same range • Beta particles produce wispy tracks that are easily deflected as a result of collisions with air molecules • Tracks are not as easily seen as alpha tracks as beta particles are less ionising Properties of radiation • A Geiger tube and counter can be used to test absorption by different materials • Each particle of radiation that enters the tube is registered by the counter as a single count • Number of counts in a given time is used to measure count rate- number of counts divided by time taken • Before this count rate due to background radiation must be calculated Absorber Geiger tube Source in sealed container Radioactive emissions To scaler counter Properties of radiation • The count rate is then measured with the source at a fixed distance from the tube without any absorber present- background count rate is taken away from this figure to give the TRUE count rate from the source • Count rate then measured with the absorber at a fixed position between source and the tube • True count rates with and without the absorber present can then be compared Properties of radiation • The effect of the thickness of the absorber can be compared by using absorbers of different thickness of the same material The graph shoes a set of measurements for the absorption of β radiation by aluminium (logarithmic scale) Properties of radiation The Geiger tube • Sealed metal tube containing argon gas • Thin mica window at the end allow α & β radiation to enter • Metal rod down the middle is at positive potential • Tube wall connected to negative terminal of power supply and is earthed • When ionising radiation enters the tube it ionises the gas atoms along its track Properties of radiation • Negative ions attracted to rod and positive ions to the wall • Ions accelerate and collide with other gas atoms producing more ions • More ions created in the same way so many are created and discharged at electrodes in a short time • Pulse of charge passes round the circuit through a resistor causing a voltage pulse across R (single count) Properties of radiation • Time taken for the tube to regain its nonconducting state after an ionising particle to enter it is usually of the order 0.2ms • Another particle entering the tube in this time won’t cause a voltage pulse • Count rate shouldn’t be greater than 1/0.2ms Rod Thin mica window High voltage unit + + - Incoming particle Tube wall R To pulse counter About α, β and γ radiation α radiation • Composed of two protons and two neutrons • Same as helium nucleus • This was discovered by Rutherford • 4x heavier than the nucleus of a hydrogen atom About α, β and γ radiation α radiation • α particles collected as a gas in a glass tube fitted with two electrodes • When a voltage is applied to the electrodes the gas conducted electricity and Discharge emitted light produced here High voltage unit + • Using a spectrometer Glass chamber can see that the tube is 0 Mercury to Thin walled filled with helium compress α glass tube gas About α, β and γ radiation β radiation • Consists of fast-moving electrons • Proved by measuring the deflection of a beam of particles using electric and magnetic fields • Measured the specific charge, found to be the same as electrons • Created from a nucleus with too many neutrons • Positron is emitted from an unstable nucleus with too many protons About α, β and γ radiation γ radiation • Photons with a wavelength with order 10-11m or less • Discovery made by using a crystal to diffract a beam of γ radiation in a similar way to a beam of light in a diffraction grating I= About α, β and γ radiation Inverse square law for γ radiation Intensity, I, of the radiation is the energy per second passing normally through unit area • For a point source emitting n γ photons per second of energy hf, enerfy per second = nhf • At a distance r from the source all the photos pass through area 4πr2, constant = nhf/4πr2 so I equals above equation About α, β and γ radiation • I varies with the inverse square of distance, r • The experimental set up below shows how this is verified Geiger tube γ source d0 γ source Sphere of radius, r d Tube γ photons entering tube Photons emitted in all directions To scaler counter Photons emitted in all directions About α, β and γ radiation α radiation β radiation γ radiation Nature 2 protons + 2 neutrons β- = electron β+ = positron Photon of energy of order MeV Range in air Fixed range depending on energy Up to about 1m Follows inverse square law Deflection in magnetic field Easily deflected Opposite direction to α; less easily deflected Not deflected Absorption Stopped by paper or thin metal foil Stopped by ~ 5mm of aluminium Stopped by several cms of lead Ionisation Produces about 104 ions per mm in air at standard pressure Produces about 100 ions per mm in air at standard pressure Very weak ionising effect Energy of each particle/photon Constant for a given source Varies up to a maximum for a given source Constant for a given source About α, β and γ radiation • emission α • XY+α β- emission • X Y + β- + e β+ emission • X Y + β+ + νe Electron capture • X + e- Y + ν e A γ photon is emitted if a nucleus has excess energy after it has emitted a α or βparticle Dangers of radioactivity Ionising radiation affects living cells because: • It can destroy cell membranes which causes cells to die • Can damage vital molecules such as DNA directly or indirectly by created ‘free radical’ ions. Damaged DNA can cause cells to divide and grow uncontrollably There’s no evidence of the existence of a threshold level where cells will not be damaged Dangers of radioactivity • If using equipment that produces ionising radiation a film badge must be worn • Badge contains a strip of photographic film in a light-proof wrapper • Different areas of the film are covered by absorbers of different thicknesses • The amount of exposure to each form of radiation is estimated by the blackening of the film • If the badge is overexposed the worker cannot continue working with the equipment Dangers of radioactivity • Dose of radiation is measured by the energy absorbed by unit mass of matter from the radiation • Same dose of different types of radiation has different effects • Alpha particles produce more ions per mm than gamma so it is more damaging • Alpha radiation is more damaging inside the body because it can’t penetrate the dead skin cells outside the body Dangers of radioactivity Dose equivalent is the energy that would need to be absorbed per unit mass of matter from 250k of X-Radiation to have the same effect as a certain dose of ionising radiation, units: Sv (sievert) Recommended limit of radiation exposure is 15mSv per year Reality is much lower at the average radiation exposure being exposed to 2mSv per year Dangers of radiation • All subjected to background radiation due to cosmic radiation and radioactive material in rocks, soil and in the air 310 10 8 3 800 37 0 380 500 Air (e.g. radon gas) Medical Ground and buildings Food and drink Cosmic ray s Nuclear weapons Air trav el Nuclear power Dangers of radiation Storage of radioactive materials • Should be in lead-lined containers. Most produce gamma radiation as well as alpha and beta • Lead lining of containers must be thick enough to contain gamma radiation to about the background level • Regulations require the containers are kept under ‘lock and key’ and records are kept of contents Dangers of radiation Using radioactive materials • No source should come into contact with the skin • Solid sources transferred using handling tools such as tongs or a glove-box/robots. Ensures that it is kept as far as practical from the skin and beyond range of alpha/beta radiation • Liquid/gas should be in sealed containers Radioactive decay The half life, T1/2, of a radioactive isotope is the time taken for the mass of the isotope to decrease to half the initial mass • Curve of the graph is a decay curve • Mass of initial isotope decreases gradually as the number of nuclei of the isotope decrease • Mass of the isotope decreases with time at a slower and slower rate. Decrease • exponentially Radioactive decay • After n half lives from the start: 0.5nm0 • Decreases exponentially because radioactive decay is random • Number of nuclei that decay in a time is proportional to the number of nuclei remaining Radioactive decay The activity, A, of a radioactive isotope is the number of nuclei of the isotope that disintegrate per second, units: Bq • Activity is proportional to mass of the isotope • Activity decreases with time • For a radioactive source of activity A that emits particles or photons of the same energy E, the energy per second or Power of the source = AE Theory of radioactive decay • Every nucleus of a radioactive isotope has an equal probability of undergoing radioactive decay in a given time • The number of nuclei that disintegrate in a certain time interval depends only on the number of nuclei present • Number of nuclei that disintegrate is ΔN, it’s proportional to: - N, number of nuclei of X remaining at time, t - the duration of the time interval Δt Theory of radioactive decay Decay constant, λ, is the probability of an individual nucleus decaying per second units: s-1 • Number of nuclei that decay, ΔN = -λNΔt • Needs a minus sign because ΔN is a decrease • Rate of disintegration = ΔN/Δt = -λN • The rate of disintegration is also the activity, A, so the above equation is the end result • The solution of the equation is: N = N0e-λt Theory of radioactive decay • Graph of number of nuclei against t represents the equation N = N0e-λt • The mass of a radioactive isotope can be found using the equation: m = m0e-λt because mass is proportional to number of nuclei • The activity of a sample of N nuclei of an isotope is in accordance to equation: A = A0e-λt • Corrected count rate is proportional to the activity so: C = C0e-λt Theory of radioactive decay • • • • The graph of lnN against t is a straight line The y-intercept = lnN0 The gradient = The N = N0e-λt equation can also be written in the form lnN = lnN0 – t • The longer the half life of a substance, the smaller the decay constant because the probability of decay per second is smaller Radioactive isotopes in use Carbon dating • Living plants and trees contain a small amount percentage of the radioactive isotope of carbon because of cosmic rays knocking out neutrons from nuclei • Measuring the activity of carbon in dead wood enables the age of it to be calculated, provided the activity of the same mass of living wood is known Radioactive isotopes in use Argon dating • Rocks contain trapped argon gas because of the decay of the radioactive isotope of potassium • This happens when its nucleus captures an inner shell electron • A proton in the nucleus changed into a neutron and a neutrino is emitted (electron capture) 40 • Can also decay by 20 β- emission to form the calcium isotope Ca. This is 8x more likely than electron capture Radioactive isotopes in use Radioactive tracers • A radioactive tracer is used to follow the path of a substance through a system. It should: - have a half life stable enough for the necessary measurements to be made, short enough to decay quickly after use - emit α or β radiation so it can be detected outside the flow path Radioactive isotopes in use Application Method Tracer Detecting underground pipe leaks Tracer injected into flow- detector on surface used to detect leakage Contains β emitter or a γ emitter as α radiation would be absorbed by the pipes Modelling oil reservoirs to improve oil recovery Water containing tracer injected into reservoir at high pressure, monitor breakthrough of isotope Tritiated water 3H2O, a β emitter with a half-life of 12 years Investigating uptake of fertilisers by plants Watered with solution containing fertiliser. Measure radioactivity of leaves to determine uptake Fertiliser contains phosphorous a β emitter with a half-life of 14 days Monitoring uptake of iodine by thyroid gland Drink solution containing sodium iodide. Activity of patient’s thyroid compared to identical sample 24 hours later Solution of sodium iodide contains iodine a β emitter with a half life of 8 days Decay modes • An N-Z graph shows the neutron number against the proton number for all known isotopes • Stable nuclei lie along a bely curving upwards with an increasing neutron-proton ratio from the origin Decay modes • For light isotopes (Z = 0-20) stable nuclei follow straight line N = Z • As Z increases beyond 20 stable nuclei have more neutrons than protons. The neutron/proton ratio increases. Extra neutrons help to bind the nucleons without introducing repulsive electrostatic forces Decay modes • α emitters occur above the stability belt beyond Z=60. Have more neutrons than protons but are too large to stable. Strong nuclear force between the nucleons is unable to overcome electrostatic force of repulsion between protons • β- occur to the left of the stability belt where isotopes are neutron-rich • β+ occur to the right of the stability belt where isotopes are proton-rich. Electron capture also happens in this region Decay modes • A nucleus that emits an alpha particle loses two neutrons and two protons so moves diagonally downwards to the left, across two grid squares • A nucleus that emits a beta minus particle loses a neutron and gains a proton so moves diagonally downwards to the right across one grid square • A nucleus that emits a beta plus particles loses a proton and gains a neutron so moves diagonally upwards to the right across one grid square Decay modes • An unstable nucleus may undergo a series of isotopic changes involving alpha or beta emission before it becomes stable • Naturally occurring isotopes decay through a series of such changes with one or more of the changes having a long half life. This is why some isotopes have not decayed completely • Radioactive series are represented on the N-Z graphs by a sequence of ‘decay arrows’ Decay modes • After an unstable nucleus emits an α or β particle/undergoes electron capture, it might emit a γ photon • Happens is the ‘daughter’ nucleus is formed in an excited state • This state is usually short lived and the nucleus moves its ground state • This can be represented by an energy level diagram Decay modes Technetium generator • Used in hospitals to produce a source that only emits γ radiation • Some form in an excited state after alpha or beta emission and stay in this state long enough to be separated from the parent isotope • The long-lived excited state is a metastable state • Nuclei of Tc isotope Tc 99-43 form in a metastable state after beta minus emission from nuclei of molybdenum- half life of 67h • Tc 99-43(m) has a half life of 6h and returns to ground state by γ emission Decay modes • Technetium generator consists of an ion exchange column containing ammonium Molybdenate exposed to neutron radiation beforehand to make some of the Mo nuclei unstable • Solution of sodium chloride passed through the column causes some chlorine ions to exchange with Pertechnate ions not Mo ions, so solution that emerges contains Tc 99-43(m) Decay modes Uses of Tc 99-43(m) • Monitoring blood flow through the brain using external detectors. Sodium pertechnate solution is first administered intravenously • Gamma camera images internal organs and bones by detecting where γ photons have been emitted by Tc 99-43(m) Nuclear radius • When a beam of high-energy electrons is directed at a thin solid sample of an element • The incident electrons are diffracted by the nuclei of the atoms in the foil • Beam is produced by accelerating electrons through a pd of the order of a hundred million volts • Electrons are diffracted by the nuclei because the de Broglie wavelength of high energy electrons is 10-15m; about the same as the diameter of the nucleus Nuclear radius Electron beam θ Thin metal sample in a vacuum Amplifier and meter Detector Detector reading • A detector is used to measure the number of electrons per second diffracted through different angles θmin Angle of diffraction Nuclear radius • Scattering of beam electrons is due to chargesame as alpha scattering but electrons are attracted not repelled by the nuclei. Causes intensity to decrease as angle increases • Diffraction of beam electrons by each nucleus causes intensity maxima and minima to be superimposed on the effect above • Happens provided the de Broglie wavelength of the electrons in the beam is no longer than the dimensions of the nucleus Nuclear radius • Superimposed intensity variations are similar to concentric bright and dark fringes in a monochromatic light diffraction grating • Angle of the first minimum from the centre θmin, is measured and used to calculate the diameter of the nucleus- provided wavelength of the incident electrons is known Nuclear radius • The radius, R, of different nuclides can be measured by using samples of different elements • Graph of lnR against lnA gives a straight line with gradient 1/3 and y-intercept r0 • Graph of R against A1/3 gives a straight line through the origin with gradient • Graph of R3 against A gives a straight line through the origin with gradient r0 V= Nuclear radius V= V= • Nuclear volume, V, is proportional to the mass of the nucleus- therefore density is constant and independent of the radius • Can conclude that nucleons are separated by the same distance regardless of the size of the nucleus and are therefore evenly separated inside the nucleus • In the volume formula above, m = Au where 1u = 1 atomic mass unit = 1.661 x 10-27kg Nuclear Energy Chapter 10 E = mc2 Energy and mass • Calculate the increase in mass of a car of 1000kg which gains 450kg • E = mc2 • m=E m = 450 x 103 m = 5 x 1012 c2 3.0 x 108 Energy and mass Energy changes in reactions • Alpha decay Momentum is conserved- momentum bef0re equals momentum after • Beta decay Beta particles have variable KE, the neutrino carries the rest of the energy Energy and mass Energy changes in reactions • Electron capture e- + X Y + v + X-Ray. Neutrino carries charge and conserves lepton number. X-Ray from outer shells as inner shell ‘vacancy’ is filled • Strong nuclear force F = Q1Q2 E= Fxs 4πε0r2 Binding energy • Binding energy of the nucleus is the work done to separate the nucleus into its constituent neutrons and protons • SNF pulls neutrons and protons together and energy is released • Mass decreases by Δm, the mass defect • Δm = (Σ mass of n + p) – mass of nucleus Binding energy • Binding energy = Δmc2 Bi- atomic mass 212 and atomic number 83 has a nucleus mass of 211.80012u. Calculate binding energy of nucleus in MeV • Δm = (83 x 1.00728) + (129 x 1.00867) – 211.80012 = 1.92255u • Binding energy = 1.92255 x 931.3 = 1790MeV Binding energy Alpha particle tunnelling • Two protons and two neutrons come together in the nucleus • They lose binding energy which becomes KE of alpha particle • KE < PE required to escape coulomb barrier (electrostatic force) • Alpha particle can act as a wave & so there is a small probability that it can ‘tunnel’ through the coulomb barrier Binding energy Nuclear stability • An unstable nucleus requires more binding energy than an a stable nucleus. Higher the binding energy per nucleon, the more stable the nucleus because it takes more energy to pull it apart • Fusion Small nuclei join together to make a larger more stable nucleus, energy is released • Fission Large unstable nucleus splits into smaller more stable fragments and energy is released Fission and fusion Induced fission • Looking to make new heavier elements/nuclei by firing neutrons at U-235, but lighter elements were found • Uranium had split AND • Energy released • 2 or 3 neutrons were given off chain reaction Fission and fusion Fusion reactors produce large amounts of power for short periods of time Energy is released by fusing deuterium and tritium to produce nuclei of helium isotope and neutrons Neutrons absorbed by lithium surrounding the reactor vessel. Reaction produces tritium used in main reaction Plasma is contained in steel container and heated by a large current. Magnetic field stops plasma touching side. Energy released per second more than is needed to heat plasma The thermal nuclear reactor Pressurised Water Reactor Fuel rods U-238 (non-fissionable) enriched with 2-3% U-235 (fissionable) Control rods Absorb neutrons to keep constant Water Moderator and coolant Moderator Slow fission neutrons down to allow further fission- collide with moderator atoms Critical mass Fissionable materials must be greater than a minimum mass for chain reaction to occur The thermal nuclear reactor Comparing Pressurised Water Reactor to Advanced Gas Reactor PWR AGR Fuel Uranium oxide in zirconium alloy cans Uranium oxide in stainless steel cans Moderator Water Graphite Coolant Water Carbon dioxide gas Coolant temp /K 600 900 Power output /MW 700 1300 The thermal nuclear reactor Safety features • Thick steel vessel • Containment building • Emergency shut-down system • Remote handling devises for sealed fuel rods The thermal nuclear reactor Radioactive waste Examples Disposal High Level Fuel rods, U-235 and Pu- Sealed containers in 239 trenches/underground caverns Intermediate Level Radioactive material with low activity Stored in drums & encased in concrete. Stored in buildings with reinforced concrete Low Level Lab equipment and protective clothing Sealed in metal drums & buried in trenches Thermal Physics Chapter 11 Internal energy and temperature Energy transfer between two objects takes place if: • One object exerts a force on the other one causing it to move • Heat transfer is energy transfer due to a temperature difference (conduction, convection or radiation) Internal energy and temperature The internal energy of an object due to its temperature is also called it’s thermal energy Internal energy of an object changes as a result of: • Heat transfer by radiation to or from the object • Work done by the object, including electricity If the internal energy of an object is constant, either: • No heat/energy transfer due to radiation • Heat/energy transfer and work done ‘balance each other out Internal energy and temperature • Internal energy of a lamp filament increases when the lamp is switched on because of work done by the electricity supply pushing electrons through the filament • When it reaches its operating temperature, heat transfer to the surroundings takes place and it radiates light • Work done by the electricity supply pushing electrons through the filament is balanced by heat transfer and light radiated from the filament Internal energy and temperature • In a solid atoms and molecules are held to each other by forces due to the electrical charges of the nucleons. Molecules in a solid vibrate randomly about fixed positions- the higher the temperature the more the molecules vibrate. If the temp is raised sufficiently the solid melts because the molecules break free from each other. The energy supplied to melt a solid raises the potential energy of the molecules Internal energy and temperature • In a liquid the molecules move at random in contact with each other. Forces between the molecules are not strong enough to hold them in fixed positions. The energy supplied to a liquid to raise its temperature, its kinetic energy increases • In a gas the molecules move about randomly further apart than in a liquid The internal energy of an object is the sum of the random distribution of the kinetic and potential energies of its molecules Internal energy and temperature Thermal equilibrium is when no overall heat transfer occurs between two objects at the same temperature Temperature in ˚C = absolute temp in kelvins – 273.15 The triple point of water, 273.16K is the temperature at which ice, water and water vapour are in thermal equilibrium Internal energy and temperature An object at absolute zero has minimum Gas internal energy pressure Absolute zero -273˚C 0K 0˚C 273K 100˚C 373K No object can have a temperature below absolute zero ΔQ= mc(T2 – T1) Specific heat capacity The temperature rise of an object when it is heated depends on: • The mass of the object • The amount of energy supplied to it • The substance or substances which the object is made The specific heat capacity, c, of a substance is the energy needed to raise the temperature of unit mass of the substance by 1K without change of state units: Jkg-1K-1 c= Specific heat capacity The inversion tube experiment • The gravitational potential energy of an object falling in the tube is converted into internal energy when it hits the bottom of a tube • The tube is inverted each time the spheres hit the bottom of the tube. • The temperature of the lead shot is measured initially and after a certain number of inversions n= number of inversions; L= length of tube; T= temp change c= Specific heat capacity Specific heat capacity of a metal A thermometer is used to measure the temperature change- water or oil acts as the thermal contact Terminal Tx Terminal TY Rheostat A Thermometer Tx Heater Solid Heater Insulation V TY = (m1c1) x (mcalccal Specific heat capacity •Specific heat capacity of a liquid • Electrical energy supplied = IVt • Energy needed to heat liquid = m1 x c1 x Lid • Energy needed to heat the calorimeter = mcal x ccal x Stirrer Tx Calorimeter TY Insulation Heater Liquid Change of state • Density of a gas is less than the density of the same substance as a liquid or solid molecules are separated by large distances in a gas • Atoms in a solid are locked together by strong force bonds and so solids cannot flow like a liquid or a gas. In a liquid or gas they are not locked together because they have too much kinetic energy Change of state Solid or liquid heated = more kinetic energy Solid heated at its melting point: atoms vibrate so much they break free from each other. Energy needed to melt a solid at its melting point is the latent heat of fusion • Latent heat because no temperature change happens even though the solid is being heated • Fusion because the solid ‘fuses’ into a liquid as it melts Change of state Liquid heated at its boiling point: molecules gain enough energy to overcome the bonds that hold them together; form bubbles of vapour in the liquid. This is the latent heat of vaporisation • Latent heat released when a vapour condensesvapour molecules slow down as the vapour is cooled- move slowly enough for the force bonds to pull molecules together to form a liquid • If solid vaporises directly when heated it’s known as sublimation Change of state DEFINITIONS Specific latent heat of fusion, lf: energy needed to change the state of unit mass of the substance from solid to liquid without change of temperature, units: Jkg-1 Specific latent heat of vaporisation: energy needed to change the state of unit mass of the substance from liquid to vapour without change of temperature, units: Jkg-1 Change of state Graph showing what will happen if a pure solid is heated to its melting point and beyond Liq uid Temp, T Melting point l id So ΔT Δt Time, t Assuming no heat loss occurs during heating, and energy is transferred at a constant rate P If solid has a larger specific heat capacity than liquid the liquid will heat up faster Gases Chapter 12 The experimental gas laws Pressure of a gas is the force per unit area that the gas exerts normally on a surface, it depends on temperature, volume and mass, units: Pa or Nm-2 IN ALL GAS CALCULATIONS TEMPERATURE MUST BE IN KELVINS The experimental gas laws Boyle’s law Measured how pressure of a fixed mass of gas varies with volume. On a graph plotting 1/V gives a straight line Pressure T3 >T2 >T1 T3 T2 T1 Volume The experimental gas laws Charles’ law Measured the volume of a fixed mass of gas at constant pressure varies with absolute temperature- leads to the idea of absolute zero. No matter how much gas is used, if the gas is an ideal gas, it’s volume would be zero at absolute zero Volume 273 373 Temp,K The experimental gas laws The pressure law • Diagram shows how pressure of a fixed mass of gas at constant volume can be measured at different temperatures • On a graph of pressure against temperature in kelvins, it Pressure gives a straight line through gauge Dry Water air the origin bath Heater The ideal gas law • Molecules in a gas move at random with different speeds • When molecules collide they bounce off each other/the surface without loss of speed • Pressure of gas on a surface is due to the gas molecules hitting the surface • Each impact causes a tiny force on the surface • Overall result is that the gas exerts a measurable pressure on the surface The ideal gas law • The effect of individual molecules in a gas can be seen if smoke particles are observed using a microscope • Their motion is called Brownian motion • Motion of each particle is due to it being bombarded unevenly at random by individual molecules • They’re subjected to a force due to the impacts which changes its magnitude and direction The ideal gas law Brownian motion Observer Path of one smoke particle Microscope Smoke in glass cell Field of view Smoke particles Lamp Lens The ideal gas law • The Avogadro constant • The Avogadro constant, NA, is the number of atoms in exactly 12g of the value of NA is: 6.023 x 1023 • One atomic mass unit, u, 1/12th of the mass of a atom: 1u = 1.661 x 1027kg The ideal gas law Molar mass • A mole of a substance is the quantity of the substance that contains NA particles • Number of moles in a certain quantity of a substance is its molarity • The molar mass is the mass of 1 mole of the substance 1. Number of moles in mass MS of a substance = MS/M where M is the molar mass of the substance 2. Number of molecules in MS = NAMS/M The ideal gas law • ideal gas is a gas that obeys Boyle’s law- the An three gas laws can be combined to make One mole of any ideal gas, the value of pV/T is equal to 8.31Jmol-1K-1 • This value is the molar gas constant, R • For n moles of an ideal gas, the ideal gas equation is above The ideal gas law • Using the ideal gas equation • MS of a substance is equal to its molar mass, M x the number of moles, n • The density of an ideal gas of molar mass = nM/V = pM/RT • Density of an ideal gas at constant pressure, is inversely proportional to its temperature pV nR • Substituting the number of moles, n, in the equation pV=nRT with gives the equation above T The kinetic theory of gases Explaining Boyle’s law: the pressure of a gas is increased by reducing its volume because the gas molecules travel less distance between impacts due to the reduced volume. More impacts per second so pressure is greater Explaining the pressure law: the pressure of a gas is increased by raising its temperature. Average speed if the molecules is increased by raising the temperature- impacts are harder and more frequent The kinetic theory of gases Molecular speeds • Molecules in an ideal gas have a continuous spread of speeds • Speed of an individual molecule changes when it collides with another gas molecule • This is providing the distribution and temperature stay the same • Above equation shows the root mean square speed of the molecules where N is the number of molecules The kinetic theory of gases • If the temperature of a gas is raised the molecules move faster on average • Root mean square speed of the molecules increases • Distribution curve becomes flatter and broader No. of molecules Low temp High temp Speed, v The kinetic theory of gases Assumptions 1. Molecules move with Random continuous motion 2. Molecules do not Attract each other 3. The collide Elastically 4. The Duration of the collisions are negligible compared to the time between collisions 5. The Volume of one molecule is negligible compared to the volume of the whole gas Really Angry Eels Don’t Vote y The kinetic theory of gases Proof of • 1) Ft = 2mu1 ∴ F = 2) Time between collisions = Combining equations = 3) Pressure, p = p for one molecule = 4) For N molecules p = + +…+ p= + +…+) =) p= or or 5) Combining these equations by adding together means 3p = ( + + ) + + = ∴ 3p = 6) pV = 1/3Nm z x
