#### 5.1 Thermal physics

Temperature, matter, specific heat capacity and specific latent heat, heat transfer and change of phase . Experimental work to investigate specific heat capacity of materials. How Newton’s laws can be used to model the behaviour of gases

#### Temperature

You will cover:

- thermal equilibrium
- absolute scale of temperature (i.e. the thermodynamic scale) that does not depend on property of any particular substance
- temperature measurements both in degrees Celsius (°C) and in kelvin (K)
- T(K) ≈ θ(°C) + 273

## A Level Maths Papers

(48 Reviews) £9.99#### Solid, liquid and gas

You will cover:

- solids, liquids and gases in terms of the spacing, ordering and motion of atoms or molecules
- simple kinetic model for solids, liquids and gases
- Brownian motion in terms of the kinetic model of matter and a simple demonstration using smoke particles suspended in air.
- internal energy as the sum of the random distribution of kinetic and potential energies associated with the molecules of a system
- absolute zero (0 K) as the lowest limit for temperature; the temperature at which a substance has minimum internal energy
- increase in the internal energy of a body as its temperature rises
- changes in the internal energy of a substance during change of phase; constant temperature during change of phase.

#### Thermal properties of materials

You will cover:

- specific heat capacity of a substance; the equation E = mcΔθ
- Estimating specific heat capacity, using method of mixture.
- an electrical experiment to determine the specific heat capacity of a metal or a liquid
- using an electrical method to determine the specific heat capacity of a metal block and a liquid,
- an electrical experiment to determine the specific latent heat of fusion and vaporisation E = mL
- techniques and procedures used for an electrical method to determine the specific latent heat of a solid and a liquid

#### Ideal gases

You will cover:

- amount of substance in moles; Avogadro constant N
_{A}equals 6.02 × 10^{23}mol^{-1} - model of kinetic theory of gases

large number of molecules in random, rapid motion

particles (atoms or molecules) occupy negligible volume compared to the volume of gas

all collisions are perfectly elastic

the time of the collisions is negligible compared to the time between collisions

negligible forces between particles except during collision - explanation of pressure in terms of Newtonian theory.
- the equation of state of an ideal gas pV = nRT, where n is the number of moles
- techniques and procedures used to investigate PV = constant (Boyle’s law) and P/T = constant
- an estimation of absolute zero using variation of gas temperature with pressure
- the equation pV = ⅓ Nmc
^{2̅}where N is the number of particles (atoms or molecules) and c^{2}is the mean square speed - root mean square (r.m.s.) speed; mean square speed
- the Boltzmann constant; k = R/N
_{A} - pV = NkT; ½mc
^{2̅}= 3/2kT - internal energy of an ideal gas

#### 5.2 Circular motion

Objects travelling at constant speed in circles, e.g. planets, artificial satellites, charged particles in a magnetic field, etc.

Centripetal force and acceleration.

#### Kinematics of circular motion

You will cover:

- the radian as a measure of angle
- period and frequency of an object in circular motion
- angular velocity ω = 2π/T or ω = 2πf

#### Centripetal force

- a constant net force perpendicular to the velocity of an object causes it to travel in a circular path
- constant speed in a circle; v = ωr
- centripetal acceleration a = v
^{2}/r ; a = ω^{2}r - centripetal force; F = mv
^{2}/r; F =mω^{2}r - techniques and procedures used to investigate circular motion using a whirling bung.

#### Oscillations

Atoms vibrating in a solid, a bridge swaying in the wind, the motion of pistons of a car and the motion of tides. Simple harmonic motion, forced oscillations and resonance.

#### Simple harmonic oscillations

You will cover:

- displacement, amplitude, period, frequency, angular frequency and phase difference
- angular frequency ω = 2π/T or ω = 2πf
- simple harmonic motion; defining equation a = –ω
^{2}x - techniques and procedures used to determine the period/frequency of simple harmonic oscillations
- solutions to the equation a = –ω
^{2}x

e.g. x = Acosωt or x = Asinωt - velocity v = ± ω √(A
^{2}– x^{2}) hence v_{max}= ωA - the period of a simple harmonic oscillator is independent of its amplitude (isochronous oscillator
- graphical methods to relate the changes in displacement, velocity and acceleration during simple harmonic motion.

#### Energy of a simple harmonic oscillator

You will cover:

- energy during simple harmonic motion
- energy-displacement graphs for a simple harmonic oscillator

#### Damping

You will cover:

- free and forced oscillations
- the effects of damping on an oscillatory system
- observe forced and damped oscillations for a range of systems
- resonance; natural frequency
- amplitude-driving frequency graphs for forced oscillators
- practical examples of forced oscillations and resonance

## A Level Maths Papers

(48 Reviews) £9.99#### 5.4 Gravitational fields

Newton’s law of gravitation, planetary motion and gravitational potential and energy.

Predict the motion of orbiting satellites, Geostationary satellites, planets and why some objects in our Solar system have very little atmosphere.

#### Point and spherical masses

You will cover:

- gravitational fields are due to objects having mass
- modelling the mass of a spherical object as a point mass at its centre
- gravitational field lines to map gravitational fields
- gravitational field strength; g = F/m
- the concept of gravitational fields as being one of a number of forms of field giving rise to a force

#### Newton’s law of gravitation

You will cover:

- Newton’s law of gravitation; F = –GMm/r
^{2}for the force between two point masses - gravitational field strength g = –GM/r
^{2}for a point mass - gravitational field strength is uniform close to the surface of the Earth and numerically equal to the acceleration of free fall

#### Planetary motion

You will cover:

- Kepler’s three laws of planetary motion
- the centripetal force on a planet is provided by the gravitational force between it and the Sun
- the equation T
^{2}= (4π^{2}/GM) r^{3} - the relationship for Kepler’s third law T
^{2}∝ r^{3}applied to systems other than our solar system - geostationary orbit; uses of geostationary satellites

#### Gravitational potential and energy

You will cover:

- gravitational potential at a point as the work done in bringing unit mass from infinity to the point; gravitational potential is zero at infinity
- gravitational potential V
_{g}= –GM/r at a distance r from a point mass M; changes in gravitational potential - force-distance graph for a point or spherical mass; work done is area under graph
- gravitational potential energy E = mV
_{g}= –GMm/r at a distance r from a point mass M - escape velocity.

#### 5.5 Astrophysics and cosmology

Stars, Wien’s displacement law, Stefan’s law, Hubble’s law and the Big Bang.

#### Stars

You will cover:

- planets, planetary satellites, comets, solar systems, galaxies and the universe
- formation of a star from interstellar dust and gas in terms of gravitational collapse, fusion of hydrogen into helium, radiation and gas pressure
- evolution of a low-mass star like our Sun into a red giant and white dwarf; planetary nebula
- characteristics of a white dwarf; electron degeneracy pressure; Chandrasekhar limit
- evolution of a massive star into a red super giant and then either a neutron star or black hole; supernova
- characteristics of a neutron star and a black hole
- Hertzsprung-Russell (HR) diagram as luminositytemperature plot; main sequence; red giants; super red giants; white dwarfs.

#### Electromagnetic radiation from stars

You will cover:

- energy levels of electrons in isolated gas atoms
- the idea that energy levels have negative values
- emission spectral lines from hot gases in terms of emission of photons and transition of electrons between discrete energy levels
- the equations hf = ΔE and hc/λ = ΔE
- different atoms have different spectral lines which can be used to identify elements within stars and absorption line spectrum
- transmission diffraction grating used to determine the wavelength of light
- the condition for maxima d sinθ = nm, where d is the grating spacing
- use of Wien’s displacement law λ
_{max}∝ 1/T to estimate the peak surface temperature (of a star) - luminosity L of a star; Stefan’s law L = 4πr
^{2}σ T^{4}where σ is the Stefan constant - use of Wien’s displacement law and Stefan’s law to estimate the radius of a star.

#### Cosmology

You will cover:

- distances measured in astronomical unit (AU), light-year (ly) and parsec (pc)
- stellar parallax; distances the parsec (pc)
- the equation
*p*= 1/d , where*p*is the parallax in seconds of arc and d is the distance in parsec - the Cosmological principle; universe is homogeneous, isotropic and the laws of physics are universal
- Doppler effect; Doppler shift of electromagnetic radiation
- Doppler equation Δλ/λ ≈ Δf/f ≈ v/c for a source of electromagnetic radiation moving relative to an observer
- Hubble’s law; v ≈ H
_{o}d for receding galaxies, where H_{o}is the Hubble constant - model of an expanding universe supported by galactic red shift
- Hubble constant H
_{o}in both kms^{–1}1 Mpc^{–1}and s^{–1}units - Big Bang Theory
- experimental evidence for the Big Bang theory from microwave background radiation at a temperature of 2.7 K
- the idea that the Big Bang gave rise to the expansion of space-time
- estimation for the age of the universe; t ≈ H
_{o}^{ –1} - evolution of the universe after the Big Bang to the present
- current ideas; universe is made up of dark energy, dark matter, and a small percentage of ordinary matter.

## A Level Maths Home Study Kit

(1 Reviews) £24.99- All of the major A Level Maths topics covered
- Practice questions and answers on every topic

- Revision for the NEW A Level Maths Course
- All exam boards e.g. AQA, OCR, Edexcel, WJEC.