A2 Physics Notes by Mr. Seo

• These notes cover A2 Physics, created by Mr. Seo, revision 1.20

Contents Overview

• Temperature is covered starting on page 2
• Thermal Properties of Materials is covered starting on page 16
• Ideal Gases are covered starting on page 23
• Motion in a Circle is covered starting on page 29
• Oscillations are covered starting on page 39
• Gravitational Field is covered starting on page 50
• Electric Field is covered starting on page 58
• Capacitance is covered starting on page 70
• Magnetic Field is covered starting on page 80
• Electromagnetic Induction is covered starting on page 105
• A.C. is covered starting on page 119
• Quantum Physics is covered starting on page 137
• Nuclear Physics is covered starting on page 156
• Electricity and Electronics is covered starting on page 167
• Medical Imaging is covered starting on page 188
• Communication is covered starting on page 219

Temperature

• Property of an object that determines which way heat flows between it and another object
• When two bodies (A and B) at different temperatures are in thermal contact, heat flows from the higher to the lower temperature until they equalize
• Two bodies are in thermal equilibrium when there is no net heat transfer and they have the same temperature

Thermal Equilibrium

• Thermal equilibrium occurs when both bodies have the same temperature and no net heat transfer occurs between them

Thermometric Property

• Physical property that varies significantly with temperature

Examples of Thermometric Properties

• Length of the liquid is used in liquid-in-glass thermometers
• Resistance is used in resistance thermometers
• Pressure is used in gas thermometers
• Voltage is used in thermocouple thermometers

Establishing a Temperature Scale

• Choose a thermometric substance (solid, liquid, or gas)
• Select the thermometric parameter X (length, pressure, resistance, or e.m.f.)
• Choose two fixed points to define the temperature scale (melting point of ice and boiling point of water)
• Assumes the thermometric parameter X varies uniformly or linearly with temperature, θ.

Empirical Temperature Scales

• Scales constructed this way are empirical temperature scales
• This scale is known as an empirical centigrade scale

Liquid-in-glass Thermometer

• The thermometric parameter, X, is the length of mercury/ethanol column, l
• Thermometer calibrations occur by marking the mercury column's length when measuring two fixed points 0°C & 100°C
• Divide the interval between the marks on the scale into 100 equal divisions
• The defining equation is θ = (lt-l₀) / (l₁₀₀-l₀) × 100°C, where l₀ = column length at the ice point and l₁₀₀ = column length at the steam point

Platinum-Resistance Thermometer

• Electrical resistance of a pure metal increases with temperature
• The thermometric parameter X = electrical resistance, R, of the platinum wire
• Fine platinum winds on an insulating material strip inside a porcelain tube
• During use, the thermometer is one arm of a Wheatstone bridge
• For accurate measurements, the lead resistance between the bridge and the platinum is compensated for by connecting dummy leads in the other arm of the bridge
• With the porcelain tube in the body whose temperature you require, the variable resistor Rv is adjusted until the meter reads zero, indicating the bridge is balanced

Platinum-Resistance Thermometer Pros

• Wide measurement range
• Accurate readings

Platinum-Resistance Thermometer Cons

• Bulky so it won't measure small objects accurately
• Large heat capacity means it is not sensitive to rapid temperature changes

Thermistor Thermometer/Resistance Thermometer

• The resistance is found using the formula R=V/I, with ammeter and voltmeter measurements
• It can always be used in this method
• Resistance is directly found from the ohmmeter
• It cannot always be used due to the maximum range being 20000 Ω

Thermistor Thermometer Advantages

• Low heat capacity
• More sensitive to rapid temperature changes

Thermistor Thermometer Disadvantage

• Not as accurate

Constant Volume Gas Thermometer

• Advantage: Most accurate, with any small temperature change causing a significant pressure change
• Disadvantage: High heat capacity, longer time to achieve thermal equilibrium and cannot measure rapidly fluctuating temperatures, also the thermometer is bulky
• The thermometric parameter, X = Pressure of a fixed gas mass at constant volume, P
• Place the bulb (hence the contained air) in the fluid being measured
• Increased temperature increases gas pressure, pushing mercury down tube X and up tube Y
• Then adjust tube Y's height to restore the mercury level back to its original position at reference mark A
• Raising tube Y restores the mercury to reference mark A, restoring the gas volume to the original value
• Gas pressure, P = Atmospheric pressure + Pressure from the mercury height difference in tubes X & Y
• If using mm of mercury (mm Hg) as the unit of pressure, then P = h + PA ; PA is atmospheric pressure (mm Hg)
• The equation to calculate temperature is θ = (Pθ – P₀)/(P₁₀₀ - P₀) × 100°C, where P₀, P₁₀₀ and Pθ are the gas pressures at 0°C, 100°C and θ°

Thermocouple Thermometer

• The number of electrons flowing from A to B is greater than B to A
• There is a net flow of electrons, producing current
• Where there is current, there must be potential difference
• Current flows from higher to lower potential difference
• The voltmeter measures the e.m.f.
• The greater the temperature difference, the larger the e.m.f. generated

Thermocouple Thermometer Conclusions

• In a thermocouple thermometer, e.m.f (voltmeter reading) is proportional to both junctions (A & B)'s temperature difference, NOT the absolute temperature

Thermocouple Thermometer Advantages

• Computer connectivity provides direct readings without calculation
• Lowest heat capacity
• Requires no power supply

Thermocouple Thermometer Formula

• θ = (Eθ-₀) / (E₁₀₀-₀) × 100°C, where E₀-₀ is the e.m.f set up between the junctions at 0°C
• E₁₀₀-₀ the e.m.f set up between the junctions at 100°C and 0°C

Absolute Thermodynamic Scale Facts

• Theoretical temperature scale that is based on the laws of Thermodynamics
• Absolute as it is independent of thermometric properties
• Identical to the ideal gas scale

Ideal Gas

• For an ideal gas, PV/T=constant, PV α T

###Ideal Gas Requirements

• High temperature
• Low pressure

Absolute Thermodynamic Scale details

• Since PV varies linearly with T, we can obtain values of T by measuring P and V
• The Constant Volume Gas Thermometer measures temperature on this scale
• Because volume is constant, P α T

Thermometric Properties

• All thermometric properties do not vary linearly with temperature
• Thermometric properties vary differently with temperature
• Correspond only at the ice point and steam point

Absolute Thermodynamic Scale

• PaT with V=constant
• As temperature decreases, pressure decreases
• With a centigrade scale in use, say pressure decreases when temperature decreases
• When using the Kelvin scale, pressure is directly proportional to temperature

Determination of Temperature Details

• When pressure is zero, kinetic energy of the molecules is at absolute zero
• Temperature is called absolute zero (the lowest temperature possible)

Absolute Zero

• Extrapolating to the temperature intercept when P=0, one finds that T= -273.15°C
• A new scale was introduced that takes this point at 0, and the unit used is Kelvin (K)
• Since the thermometer, when measuring the triple point of water, measures 0.01°C on this empirical scale, the new Kelvin scale will define the triple point of water as 273.16K

Kelvin Scale Details

• The boiling point of water is defined as 373.15K (100°C on the centigrade scale)
• The melting point of ice is 273.15K (0°C)
• This absolute scale makes the temperature difference between the ice point and steam point exactly 100, similar to the previous centigrade scale
• The thermodynamic scale is defined from two fixed points: Absolute zero (OK), and the triple point of water

Triple Point of Water

• It is the only temperature at which ice, water and water vapor are in thermal equilibrium at 273.16K = 0.01°C
• Rate of water freezing to ice = the rate of ice melting to water, the rate of water vaporizing to vapor = rate of vapor condensing to water

Absolute Scale Formula

• In order to measure temperature with the constant volume gas thermometer on the absolute scale: T = (P/Ptr) × 273.16K
• A temperature interval of 1 Kelvin is defined as 1K = (1/273/16) × Thermodynamic temperature of triple point of water

Celsius Scale

• The Celsius scale results from an arithmetical adjustment to the thermodynamic scale measured in Kelvin
• The value, t (°C) is given by subtracting 273.15 from the thermodynamic temperature, T, measured in Kelvin
• t = T - 273.15 ; where t is in °C and T is in Kelvin
• This has made the Celsius scale similar to the centigrade, based on thermodynamic temperature, where the centigrade version uses the ice point and steam point as its two fixed points

Liquid-in-glass thermometer properties

• Temp Range (°C): -39 to 356
• Thermometric property is length of mercury (or ethanol) column in a glass tube
• Advantages: Simple to use, Direct reading, Portable, Cheap
• Disadvantages: Limited range, Fragile, Slow response, Relatively large heat capacity, Not very accurate

Constant volume gas

• Temp Range (°C): -270 to 1500
• Thermometric property is pressure of a fixed mass of gas at constant volume
• Advantages: Very wide range, Extremely accurate, Very sensitive to small changes
• Disadvantages: Bulky, No direct reading calculation required, Very slow to use and not suitable for rapidly changing temperature

Platinum Resistance

• Temp Range (°C): -200 to 1200
• Thermometric property is electrical resistance of a platinum coil
• Advantages: Wide range, Very accurate, Sensitive
• Disadvantages: Unsuitable for rapidly varying temperatures because of large heat capacity, Needs a power supply and bulky when used with Wheatstone bridge

Resistance (Thermistor)

• Temp Range (°C): -50 to 300
• Thermometric property is resistance of a thermistor
• Advantages: Reasonably fast response because of small heat capacity
• Disadvantages: Not very accurate, Needs a power supply, voltmeter and ammeter, Limited range

Thermocouple

• Temp Range (°C): -250 to 1500
• Thermometric property is electrical motive force across the junction of 2 dissimilar metals
• Advantages: Wide range, Quite accurate, Fast response because of small heat capacity
• Disadvantages: Has to use sensitive electrical equipment to ensure accurate measurement

Empirical Scale

• Based on the experimental observation of variations of a particular thermometric property with temperature
• It assumes the thermometric parameter X varies linearly with temperature
• 2 fixed points are chosen, such as in the Centigrade scale where the fixed points are the ice point and steam point with arbitrary values of 0°C and 100°C, respectively
• The equation for the Centigrade Scale is t = (Xt - X₀) / (X₁₀₀ - X₀) × 100°C

Thermodynamic Scale

• Based on the ideal gas equation : PV = nRT
• For a constant volume, V, the thermometric parameter, P α T is not assumed
• Because there is a natural zero, only 1 fixed point must be chosen. This is the triple point of water, with an arbitrary value of 273.16K
• The equation is T= (P/Ptr)× 273.16K

Thermal Properties of Materials

• The kinetic model is based on matter is made up of tiny particles, particles attract each other and can move about

Differences in States of Matter

• Solid: very close spacing of particles, long-range ordering, vibrational and rotational motion
• Liquid: close spacing, short-range ordering, restricted translational motion
• Gas: very far apart, total disorder, free and random motion

Internal Energy Definition

• The sum of all the random and microscopic potential and kinetic energy of all the molecules in the body
• Internal energy of ideal gas is only kinetic energy given there are no intermolecular forces

Internal Kinetic Energy

• The total energy of all the atoms and molecules due to their motion
• Internal kinetic energy is directly proportional to temperature in Kelvin

Internal Potential Energy

• The total energy of all the atoms and molecules due to their intermolecular forces
• Internal potential energy depends on Separation.

Kinetic and Potential Energy relationship

• If separation increases, potential energy increases
• Separation decreases, potential energy decreases

Bonds and Potential Energy

• If bonds break, potential energy goes up
• If bonds form, potential energy goes down

Heating of a Solid

• Section I : Solid at room temperature below melting point, heat increases temperature until it increases to the melting point
• Increased temperature increases the kinetic energy
• Mean molecular separation increases slightly and has a slight increase in potential energy

Heating of Solid - Section II

• Heating doesn't cause ay further increase once the solid increases to the melting point
• The heat causes a phase change from solid to liquid, called latent heat of fusion
• That supplied latent heat increases the internal energy by significantly increasing the separation of the molecules
• Latent heat overcomes the forces holding molecules in a regular crystalline lattice, enabling breakage to occur
• The solid structure breaks, giving greater molecular mobility and disorder to the liquid state
• Kinetic energy doesn't increase thus the temperature stays constant

Heating of Solid - Section III

• The solid has become a liquid
• The temperature increases to the boiling point from the temperature rise
• The supplied heat energy increases the liquid kinetic and potential energy
• Temperature increases from rising kinetic energy

Heating of Solid - Section IV

• Vaporization occurs throughout the liquid once the boiling point is reached
• Continued heating does not raise the temperature further
• Latent heat of vaporization supplies at a constant temperature to cause a phase change to vapor

Latent Heat of Vaporization

• Heat can be used in 2 ways: Increase the potential energy by increasing the separation between molecules or do work to expand the molecules into the atmosphere
• The kinetic energy does not increase, temperature remains the same

Heating of Solid - Section V

• Continued heating of the gas produces a rise in temperature
• The heat energy supplied increases the kinetic energy and potential energy of the gas
• Heat Capacity is energy needed per unit temperature rise and its unit is J K⁻¹

Specific Heat Capacity

• The unit is J kg⁻¹ K⁻¹
• Specific heat capacity is the heat energy needed per unit mass per unit temperature rise

Latent Heat

• The unit of latent heat is J and L = Q
• Latent heat of fusion changes a substance from solid to liquid at a constant temperature
• Latent heat of vaporation required to phase change a substance from liquid to gas at a constant temperature

Specific Latent Heat

• The unit is J kg⁻¹ and l=Q/m
• The specific heat of fusions is the energy per unit mass required to change the phase of a substance from solid to liquid at its constant temperature
• The specific latent heat of vaporation changes the substance energy per unit mass from liquid to gas at a constant temperature

Note on Latent Heat

• The specific latent heat of vaporization is greater than the specific latent heat of fusion because there is a larger increase in volume that causes a larger increase in the potential energy of the molecules
• Work is also done to expand against the pressure of the atmosphere

Specific Heat Capacity Examples

• Cylindrical metal blocks with appropriate holes get insulated by polystyrene to prevent loss
• Put oil in the holes.
• The starting temperature is taken, while heater current and voltage get measured too
• Heating is done for a time, and the final temperature is recorded

Liquid Specific capacity examples

• Heat liquid in the calorimeter
• Stir to assist in evenness
• The starting temperature is taken, heater current and voltage get measured
• Energy supplied by the heater gets gained by the liquid inside the calorimeter and stirrer in loss with surroundings

Measuring vapors

• With the liquid boiling, steady current (I1) and voltage (V1) is run by the coil
• The vapor passes through the container holes in the test liquid to a condenser
• The vapor is continuously collected for a time, measured and repeated a few times
• Using a new current heater (I2) and voltage (V2), the mass vapor gets run during the test, mass (m2) gets measured

The First Law of Thermodynamics

• The heat loss H is in each case as it remains unchanged (at boiling point), while the factors that affect losses is exposure, time and temperature differences
• Increase in system internal energy equals amount of heat absorbed and done to the system

Sign of Heat (Q)

• If heat (Q) is absorbed it is +ve
• If heat (Q) is given off by the system it is -ve

Sign of Work Done (W)

• If work (W) is done on the system if it is +ve
• If work (W) is done by the system it is -ve

Sign of Change in Internal Energy (U)

• If energy (U) is gained U is +ve
• If energy (U) is lost U is -ve

Thermodynamic Note

• System internal energy depends on the values of P, V and T
• Internal energy does not depend on the processes in order to reach a thermodynamic state

Ideal gas

• Ideal gas obeys the equation PV=nRT at all values of P, V and T
• A real gas approaches an ideal gas at high temperature and low pressure

Gas Laws

• Boyle
• pressure
• Charles

Boyle Law

• PX T = constant
• PV = constant

Pressure Law

• P α T; V = constant
• P/T = constant

Charles Law

• V α T; P = constant
• V/T = constant

The General Gas Law

• PV/T = constant
• The relation ships are measured in Kelvins