UNIT ONE FORMULAE AND DEFINITIONS

A

Guide

To

CAPE PHYSICS

UNIT # 12014

UNIT ONE FORMULAE AND DEFINITIONS

MODULE 1: MECHANICS

base quantitybase unit

MassmKilogramkg

LengthlMetrem

TimetSeconds

Thermodynamic temperature or absolute temperatureTKelvinK

Electric current IAmpereA

Luminous intensitylvCandelaCd

Amount of substancenMolemol

namesymbolmultiple

TeraT1 x 1012

GigaG1 x 109

MegaM1x 106

Kilok1x 103

namesymbolsub-multiple

Centic1x 10-2

Millim1x 10-3

Micro1x 10-6

Nanon1x 10-9

Picop1x 10-12

MODULE ONE: FORMULAE

COMPONENTS

x component vx = v cos

y component vy = v sin N.B. If the angle is made with the horizontal

Angle of resultant = tan-1 ytot

Xtot(Do not take sign into account)

Sign of X and Y totals determine direction Y = tan-1 x

Resultant magnitude = square root of (xtot 2 + ytot 2)

MOTION

velocity = Distance/time (n.b. This formula however is only valid for constant velocity motion!!!!!! i.e. ZERO acceleration). Average speed = total distance Total time

Average velocity = total displacement

Total time acceleration = a = v - u t v = u + at

u-: initial velocityt-: time

s = ut + at2 v-: final velocity

s = (u+v)t

s-: displacement

v2 = u2 +2as

a-: accelerationProjectile Motion

Projected horizontally

X-Displacement vx = s/t

Y-Displacement y= - gt2 vy = -gt

Trajectory

y= - (g/2u2) s2Projected at an angle to the horizontal

X-Displacement vx = s/t

Y-Displacement y= tv sin - at2 vy = usin - gt

Trajectory

y = - (1/2 g/v2cos2 )s2 + (tan )s

Projectile formulae for projection at angle and coming back to same horizontal level Time of flight = 2usin g

Maximum height = u2sin2 2g

Time to reach maximum height = vsin g

NEWTONS LAWS

F = d(mv) dt

If m is constant, F = m(dv) = ma

dt

F = ma

If velocity is constant, F = v(dm) dt

law of conservation of linear momentum :m1 u1 + m2u2 +m3u3= m1 v1 + m2v2 +m3v3IMPULSE

I = p = mv mu = F t since F = p t

Impulse = force x time

I =

ELASTIC COLLISIONS

The relative speed of approach = The relative speed of separation

For elastic collisions only (w.r.t. velocity

m1u12 + m2u22 = m1v12 + m2v22 (1)

u1 u2 = v2 v1 (2).CIRCULAR MOTION 2 radians = 360o radians = 180 o angular displacement = s/r(s = arc length of circle)

s= r ( must be radians)

To convert degrees to radians =(/360) x 2(where is in degrees and is in radians) i.e. 1 radian = 57.30 Angular velocity, =

v = r

= 2/T

= 2f

a = v

a = r2 a = v2/r

F= m v

F = mr2 F = mv2/r

T = 1/f

Horizontal Circular motionT = mv2/rVertical Circular motion

At the top of the motion T + W = mv2/r T = mv2/r W

T is a minimum At the bottom of the motion T = W + mv2/r

T is a maximumAt the side

T = mv2/rConical Pendulum Tsin = mv2/rwhere T = tension, W = weight of pendulum,

W= Tcos v = velocity, r = radius tan = v2/rgGravitational fields g=F/m2 F = GMm2/r2

g = -GM/r2

(where g is the gravitational field strength) Gravitational Force and Circular motion GMm2/r2 = m2v2/r = m2r2 T2 = 4 2r3 / GM = -GM/rGeostationary Satellites

= 2 T = 2 / (24 x 60 x 60 ) = 7.27 x 10-5 rad s-1 (where T is the period of the earth in seconds)

UPTHRUST/VISCOUS DRAG U = gV = gA(h2 h1) where = density of FLUID, g = gravitational force, A = area

(h2 h1) = height difference

At limiting friction P = Fmax (where P => force applied, F => frictional forces)

Limiting Friction = N ( => coefficient of friction, N => normal reaction force)

Along an Incline

N = W cos

F = N= W sin

Viscous drag, F = 6rv = kv2 ( for a sphere falling through a viscous liquid)MOMENTS

Moment of F = F x d The principle of moments states thatFor a system in equilibrium

Sum of clockwise moments = Sum of anti-clockwise moments

The second law of equilibrium states that

Sum of forces in one direction = Sum of forces in the exact opposite direction Torque of a couple = F d

ENERGY

W = Fs cos

Work done = Energy converted

Ek = m v2 Ep= mgh

Elastic potential/strain energy = kx2 Efficiency = Useful work done /total work done x 100

P = Fv P = E/tERRORS

When X = A B

Absolute error = A + B

Fractional error = A + B A B

% error = A + B x 100%

A B

When X = AB or A/B

% error = A + B x 100

A B

absolute error = X x %error

When X = AnBm or An/Bm

% error = [(n x A/A) + (m x B/B)] x 100%

MODULE ONE : DEFINITIONS A base quantity is one which cannot be expressed as a combination of other quantities

A derived quantity is one which can be expressed as a combination of base quantities e.g. speed=distance/time

An equation is homogeneous if the base units on either side of the equation are the same

The relative atomic mass or the r.a.m. of an element is the mass relative to carbon- 12 where the mass of 1 carbon-12 atom is exactly 12

Avogadros constant is the number of atoms in 12 g of carbon -1

i.e. NA = 6.023 x 1023 atoms per mole One mole of a substance is the r.a.m in grams

A scalar quantity has magnitude only it obeys an arithmetic law of addition

A vector quantity has both magnitude and direction it obeys a geometric law of addition

The equilibrant is the single force required to close the polygon (The magnitude of the resultant but in the opposite direction.

The displacement is the distance travelled in a specific direction ( vector ) The speed ( v / m/s) is the distance travelled per unit time (scalar ) The velocity ( v / m/s ) is the distance travelled per unit time in a specific direction (vector ) . Uniform speed means that in every second the body is travelling the same distance The average speed is the total distance divided by the total time.

Average velocity is the total displacement divided by the total time The acceleration ( a / m/s2 ) is the rate of change of velocity with time. (vector ) Uniform or constant acceleration means that the velocity is changing by the same amount in every second

A deceleration is another way of saying a negative acceleration i.e. when the velocity is decreasing

Newton's first law states that a body will remain at rest or moving with constant velocity unless constrained to do otherwise by some resultant force

Newton's second law states that the rate of change of linear momentum is proportional to the resultant force

A Newton is the force acting when a mass of one kilogram accelerates at 1 ms-2 When more than one force is acting , the F in the equation F=ma is the resultant force When a body has no net force acting it is either stationary or moving with uniform velocity

Newton' third law states that when a body A exerts a force on a body B, then body B exerts an equal and opposite force on body A The linear momentum (p/kgms-1) of a body is the product of the mass and the velocity of a body. It quantifies the ease or the difficulty to change the state of motion of a body.

The law of conservation of linear momentum states that the total momentum in a system remains constant once no external force is acting The impulse is the change in momentum

A collision is perfectly elastic if kinetic energy is conserved The angular displacement in radians is the angle moved through by the object

Angular Velocity (/rads-1) is the rate of change of angular displacement.

The gravitational field is the region around a mass (m1) in which another mass (m2) experiences a force.

Newtons law of universal gravitation states that

(i)the force of attraction between two given masses is inversely proportional to the square of the distance apart

(ii)the force is proportional to the product of the mass

The geostationary satellite is one that remains over a fixed point on the body it is orbiting and thus has the same period as the body

Archimedes principle states that a body wholly or partially submerged experiences an upthrust equal to the weight of the fluid displaced. The upthrust originates from the pressure difference occurring at different depths in the fluid

Friction is a force that opposes motion.

Gravitational field strength the force that a unit mass would experience at that point in the gravitational field.

Viscous or drag force is the frictional force which exists due to the relative motion between the fluid and the body moving through it (viscous drag ). Terminal velocity is the constant velocity at which a body falls when there is no acceleration since net force is zero because the viscous drag equals to the weight .

A body is in equilibrium when :

1. The linear acceleration of the centre of gravity is zero and no resultant force is acting on the c.g

2. The angular or rotational acceleration of the c.g. is zero and there is no resultant torque

The Moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force

The Centre of gravity is the single point through which the weight appears to act

When a body is uniform the centre of gravity is in the middle

The reaction force always acts at the pivot

A couple is a pair of forces equal in magnitude but anti-parallel and separated by a distance d

Work is the product of the force and the displacement in the direction of the force

Energy is the capacity to do work

Kinetic energy is the energy a body possesses by virtue of its motion

Potential energy is energy a body possesses by virtue of its position or state

Gravitational potential energy is energy a body possesses due to its position in a gravitational field Electrical potential energy is potential energy due to a charged bodys position in an electric field

The elastic potential energy or strain energy is the p.e. stored in a wire due to deforming forces

Internal Energy (U) is the sum of the kinetic and potential energy of molecules in a substance .

Power is the rate of doing work

A thermistor is a device whose resistance varies with temperature.

A systematic error causes a set of measurements to spread a bout a value other than the true value.

A random error is one that has an equal chance of being positive or negative

A reading is accurate if it is close to the true value of the reading

A reading is precise if it there is a small degree of uncertainty with the answer being given too many significant figures.

MODULE 2 : WAVES

MODULE TWO: FORMULAE f = 1/T frequency

v = f- speed

PHASE DIFFERENCE = 2 - phase difference where t is the time difference between particles

= 2 - phase difference where x is the path difference between particles

For constructive interference

= 0, 2, 4

x = , 2, 3.n For destructive instructive interference

= , 3, 5

x = /2, 3/2, 5/2(2n+1) /2 I = P/A = E/At- intensity

I = ka2 - intensity

WAVES IN STRINGS

L = /2

f0 = v/2L

fundamental/first harmonic

L =

f1 = 2f0 = v/L

1st overtone/second harmonic

L = 3/2

f2 = 3f0 = 3v/2L

2nd overtone/third harmonic

WAVES IN PIPES

One end open

L = /4

f0 v/4L

fundamental/first harmonic

L =3/4 f1 = 3F0 = 3v/4L 1st overtone/second harmonic

L = 5/4 f2 = 5F0 = 5v/4L

2nd overtone/third harmonic Two ends open

L = /2

f0 = v/2L

fundamental/first harmonic

L =

f1 = 2f0 = v/L

1st overtone/second harmonic

L = 3/2

f2 = 3f0 = 3v/2L

2nd overtone/third harmonic correct determination of with end-correction

L1 = /4 + e

L2 = 3/4 + e

L2 - L1 = /2

= v depth mapping formula

= = = = 1n2

REFLECTION AND REFRACTION Absolute refractive index n= cv/cm n1 sin 1 = n2 sin 2 refraction equation(where n1 and n2 are the refractive indices of the respective materialsFor sound:

Total internal reflection occurs going from air to material

n1 sin 1 = n2 sin 2

sin c = ng/na sin c = ang

For light:

Total internal reflection occurs going from material to air

n1 sin 1 = n2 sin 2

sin c = 1 x sin 90sin c = 1/ angDIFFRACTION

N.B. DIFFRACTION FORMULAE APPLY FOR TWO SOURCE INTERFERENCEFor Constructive interference

For 1st order

= d sin

For 2nd order

2 = d sin

where n = order of diffraction

For nth order

d= slit spacing

n = d sin

angle made with zero orderFor destructive interference

(n - 1) = dsin

INTERFERENCEIf a is small and D is large.

= - interference formula

where a => distance between apertures, x => separation between adjacent bright (or dark) fringes,

D => distance between two screens.

EAR AND EYE

intensity intensity level

intensity level = 10 lg I/I0 [intensity level measures in decibels (db)]

1/f = 1/u + 1/v lens formula (f = focal length, u = object distance, v = image distance)

Magnification=image height/object height= image distance/ object distance 1/f = 1/u + 1/f= power of lens in dioptres = ______1_________

focal length in metres

Radius of curvature/2 = focal length

Near point: 25cm

Far point: infinity with respect to the length/size of eye

SIMPLE HARMONIC MOTION

x0 max displacement

x displacement

v0 max velocity

v velocity

angular frequency

a acceleration

a0 max acceleration

T period

l length of period

g gravitational acceleration

m mass

k spring constant

density of fluid

Simple Pendulum T =

Mass on Spring T =

Oscillating in a fluid T =

For all SHM a= 2x

v = (x02 x2)(formula for an eclipse)

v0 = x0

a0 = x02 Ekmax = Epmax = m2x02 Ek = m2x02 m2x2 Ep = m2x2 Etotal = Ek + Ep[Dont assume that halfway through the motion Etotal = Ek + Ep]When t = 0, x = 0 (eqm. position, sine graph)

x = x0sint

v = x0cost

a = -x02sint

Ek = m2x02cos2t

Ep = m2x02sin2t

When t = 0, x = x0 (max position, cosine graph)

x = x0cost

v = - x0sint

a = -x02cost

Ek = m2x02sin2t

Ep = m2x02cos2t

MODULE TWO: DEFINITIONS Simple Harmonic motion Motion of a body such that the acceleration is proportional to the displacement and opposite in direction Damped oscillations A system is damped when energy of the system is lost to its surroundings resulting in a reduction in amplitude Critical Damping when displaced, the system returns to equilibrium in the shortest time possible. A heavily damped system never returns to equilibrium position

Resonance is the maximum amplitude response of a specimen when the driver frequency is equal or close to the natural frequency of the specimen.

A forced oscillation is one that is being supplied with energy from an external source (called a driver)

A wave is a means of transferring energy from one point to another through the vibration of some system.

Mechanical waves are ones which require a medium e.g. sound, water

Displacement is defined as the distance moved (in a specified direction) by a particle from its mean position.

Amplitude is the maximum displacement of the particle in the direction of the vibration.

Wavelength ( ) is the distance between 2 consecutive points that are vibrating in phase.

Period (T) refers to the time taken for a particle on the wave to make 1 complete vibration or for the wave to travel a distance of 1 wavelength.

Frequency (f) refers to the number of vibrations completed by the particle in 1 second or the number of wavelengths travelled by the wave in 1 second. (f = 1/T)

Frequency does not change unless the source changes

Speed (or velocity) refers to the rate at which the wave energy is travelling in the direction of propagation. i.e. a distance of m in T s. This yields speed

v = /T , hence v = f

The Phase of a wave that which determines the displacement of a wave relative to the amplitude

The Phase difference between 2 particles is the fraction of a cycle by which one particle is vibrating after (behind) the other.

When two points are in phase they have the same displacement at any given point in time.

When two points are antiphase they have the same magnitude of displacement but opposite direction

Two waves are said to be coherent if there is a constant phase difference between them at a specific location where the waves meet. i.e. one wave is always ahead/behind the other by the same fraction of a cycle at that point.

The intensity I of a wave is defined as the power distributed per unit area. The intensity of a wave is also proportional to the square of the amplitude of the wave.

A transverse wave is defined as one in which the displacement is perpendicular to the direction of travel.

A longitudinal wave is defined as one where the vibration of the source or responding medium is parallel to the direction of travel of the wave.

A polarized wave is defined as one in which there is only ONE direction of vibration perpendicular to the direction of travel. (This leads to the wave motion being constricted to one plane, leading to the term plane polarized wave) A progressive wave is one where energy travels outward from the source.) A stationary wave is formed when two coherent progressive waves travel in opposite directions in the same medium at the same time In a stationary wave, the energy is confined to the area between 2 points

Nodes Points on a stationary wave where the net displacement is always zero

Antinodes Points of maximum amplitude on a stationary wave

The fundamental frequency is the lowest frequency of sound possible for a system End-correction (e) is the distance between tuning fork and the top of tube

First harmonic is the fundamental frequency. Overtones are multiples of the fundamental frequency. 1st Law of reflection states that the angle of incidence and the angle of reflection are equal

2nd Law of reflection states that the incident wave, the reflected wave and the normal are all in the same plane.

Refraction is the bending of a wave as it crosses the boundary between two media due to change in wave speed Laws of Refraction:

1. The incident wave, the refracted wave and the normal are all in the same plane

The ratio of bending as a wave travels from one fixed medium to another is a constant (for those media) and is given by speed in medium 1 / speed in medium 2, called the refractive index.

The Refractive Index (n) is the ratio of the velocities as it travels between two media.(This is a constant for wave energy travelling towards this specific boundary) The Refractive Index of a material (n) is the ratio of the velocity in air/vacuum to the velocity in the material.

A medium is defined as being rare if it allows a wave to pass through quickly, and dense if it slows down the wave.

Conditions for total internal reflection are:

1. The wave must be travelling from dense to rare therefore refractive index < 1.

2. The angle of incidence must be greater than the critical angle.

Diffraction is the spreading of the wave energy (over a larger area) as the wave encounters a gap comparable to that of its wavelength in the medium in which it is travelling.

A diffraction grating consists of a material with many openings or slits. Diffraction occurs at each slit changing plane waves to circular waves. Interference occurs between circular waves to produce diffraction pattern 1st order diffraction is produced by secondary waves in phase by virtue of being 1 wavelength out of phase

2nd order diffraction occurs when the 1st and 3rd wave fronts of adjacent slits reinforce each other and have a path difference of 2 Interference is the superposition of wave trains from coherent sources resulting in re-enforcement of the waves at some points and cancellation at others.

The principle of superposition which states: the resultant displacement at any point in a medium where two or more waves interfere, is given by the vector sum of the individual displacements of each wave at that point is used to predict the effect of the waves.

Conditions for interference

Without pattern

1. Waves must be of same type

2. They must meet at a point

3. Waves must be unpolarized or polarized in same direction

With pattern

1. Coherence

2. Same Frequency

E.M. Waves (of which light is a member) are defined as waves constituted by electric and magnetic vectors vibrating perpendicular to each other.

All of these waves have a speed of 3 108 m/s in a vacuum.

Increasing

Frequency

increasing wavelengthVisible spectrum

Increasing

wavelength

increasing frequency

Electromagnetic spectrum

Intensity of sound is the power per unit area being delivered by a source of sound Frequency Response is the audible range of frequencies detected by ear, taking into consideration the threshold intensities.

Subjective objectivepitch frequency loudness intensity quality number of overtones (depends on the harmonics) The threshold of hearing is the smallest sound intensity which can be heard by the ear and is generally taken as 1.010-12Wm-2 at 1kHz. (The threshold of hearing varies with frequency. For low frequencies, much below 1kHz, higher intensities are required.) The sensitivity of the ear is its ability to detect the smallest fractional change I of the intensity I. Thus, sensitivity depends on the ratio and a smaller discernable relative change in intensity implies a greater sensitivity. Loudness is the subjective response of the ear to intensity and changes in intensity. Loudness is not proportional to intensity. Noise is disturbance caused by discordant or disagreeable sounds. Again this is subjective. One mans noise is another mans music

Principal axis is the line which passes through the centre of the lens of Curvature of the lens surface. It is the point that is equidistant from any two points on lens surface.

The Principal focus is the point on the principal axis of lens to which rays of light which are parallel converge after refraction on the surface of the lens.

The near point of the eye is the closest position to the eye at which the eye can focus the image on to the retina. Normal near point has a value of 25cm. The far point of the normal eye is taken to be at infinity, i.e. very distant objects may be focused with the normal eye.

Accommodation( The ability of the eye to focus on objects of both near and far distances by changing the focal length of power of the eye lens Depth of field-Range of distances for object by which we can see image clearly

Depth of focus- Range of image distances where the image is seen clearly

Short sight (myopia) is caused either by the inability of the eye to allow the lens to relax enough to become sufficiently low powered, or by the eyeball being too long so that the distance from the lens to the retina is too large. When a person is said to be short-sighted, it means that only objects which are close to the eye can be focused.

Long sight (hypermetropia) is caused either by the inability of the eye to make the lens thicker and hence more powerful, or by the eye being too short such that the distance from the lens to the retina is too short. A person having long sight is a person who can only focus clearly on objects which are a long distance away from the eye.

Converging/convex lens ( lens thicker in middle than at edges. Converges rays to a point.

Diverging/concave lens ( thicker around edges than in the middle. Refracts rays so that it appears to have come from a point. A person with astigmatism has difficulty in focusing light rays from objects in different planes at the same time.

Cataract- The clouding of the lens as it gets too stiff to accommodate.

MODULE 3: THERMAL AND MECHANICAL PROPERTIES OF MATTER

Formulae empirical formulaXU-XL/ tU-tL = X-XL/ -tL / 100 = X-XL/ XU-XL theoretical scale= (273.16K/Ptr ) x P where P(pressure

Ptr ( pressure at the Triple point of water heat capacityE = C specific heat capacityE = mc latent heat of fusionE=mLf latent heat of vapourizationE=mLv temperature gradient(T1 T2)/ LEquivalent thickness

k1/x1 = k2/x2

rate of flow of energyQ/t =-kA ( T1 T2 ) /L total energy radiated per seconddQ/dt = P = AT4where:T is the absolute temperature (in Kelvin)A the surface area of the body the Stefan-Boltzmann constant = 5.6696 x10-8 Wm-2K-4. ideal gas and Thermodynamicsp pressure of a gas in PaV volume of a gas in m3T thermodynamic temperature in Kn no. of molesN- Number of molecules

NA- Avogadros numberR molar gas constant = 8.31 Jmol-1k-1

k- Boltzmann constant

m- Mass of a molecule

M-mass of entire gas

MM- Molar mass

crms -root mean square speed

- mean square speed

n=N/NA k=R/NA pV = nRT p (V = nR(T at constant pressure

V ( p = nR( T at constant volume

pV = NkT = ( u12 + u22 + u32 + .un2)/N P = m (1/3 N ) /V P = (1/3 ) Ek = 3/2nRT (Ek of the whole substance) Ek =3/2 kT (Ek of one molecule) ( Ek = 3/2nR( T = 3RT/Mm Crms = (3RT/Mm) (U = (Q + (W

COMPRESSION ON ( + BY ( - EXPANSION

ON ( -

BY ( +

for constant volume:

for constant pressure:(U = (Q + (W

(U = (Q - p(V(W = 0

(Q = (U + p(V(U = (Q = nCVM(T

nCPM(T = (U + p(V

nCPM(T = nCVM(T + p(V

for an ideal gas:(U = nR(T = nCVM(TCVM = 3/2 RCPM = CVM + R

= 5/2 R = m/v P = F/A P = g h F = k e E = / = Fl /Ae

MODULE 3: THERMAL AND MECHANICAL PROPERTIES OF MATTER

DEFINITION SHEET

If two bodies in thermal contact have the same temperature then there is no net transfer of heat in either direction and the two bodies are said to be in thermal equilibrium.

A thermometric property is any physical property which varies continuously with temperature and can be used to measure temperature.

An empirical centigrade scale is one which is formulated from experimental results. The scale is divided into one hundred equal parts and numbers are assigned.

Sensitivity of an instrument is the ability of the instrument to respond to small changes Accuracy depends on how well the instrument can give you a value close the true value.

Response Time is how quickly the instrument (thermometer) responds to changes (in temperature).

The Triple point of free water is that unique temperature at which water exists in the solid, liquid and gas phases in equilibrium.

The internal energy is the sum of the potential and kinetic energy of the molecules in a system.

Temperature is a measure of the average kinetic energy of the molecules.

Melting is the process of a solid changing to a liquid and it occurs at one temperature. The melting point of a substance is a single temperature at which the substance changes from solid to liquid.

Boiling is the process by which all molecules of a liquid are provided with enough energy to go into the gaseous state. It occurs at one fixed temperature called the boiling point.

The heat capacity (C; JK-1) of a substance is the amount of heat required to raise the temperature of the body by 1K.

The specific heat capacity (c; Jkg-1K-1) of a substance is the amount of heat required to increase the temperature of unit mass of a substance by 1oC/ 1K (unit temperature).

The latent heat of fusion (Lf; Jkg-1) of a substance is the heat required to change the unit mass, from solid to liquid without a change in temperature.

The latent heat of vaporization (Lv; Jkg-1) of a substance is the heat required to change the unit mass from liquid to gas without a change in temperature.

Evaporation is the process by which molecules of a liquid escape and go into the gaseous state without ever reaching its boiling point. Evaporation occurs at all temperatures below the boiling point.

Thermal waste is the name given to any form of emission that is at a higher temperature than the atmosphere.

Heat treatment is the controlled heating and cooling of materials in order to deliberately alter their mechanical properties.

Thermal Conduction occurs when energy travels through a solid by way of vibrations through the system. Neighbouring atoms are set into increased vibration one after another. In metals, free electrons traveling among the atoms also gain extra energy and travel a little faster as the temperature increases.

Temperature gradient is the temperature difference per unit thickness of block.

The rate of flow of energy is the quantity of thermal energy Q (kilojoules) transmitted per second and is the same for two bodies in thermal contact For two bodies with the same rate of heat transfer, the one with the smaller thermal conductivity has the higher temperature gradient and visa-versa. Convection is the movement whereby the kinetic energy of molecules increases as more thermal energy is added to the fluid which then expands and becomes less dense and due to the effect of gravity, rises up through the more dense fluid which then falls to take its place. Radiation- the transfer of electromagnetic waves, generally by infrared radiation, which carry thermal energy along with it. This thermal energy is converted to kinetic energy and thus, temperature rises.

Greenhouse effect- the absorption of short-wavelength thermal radiation but prevention of removing the re-emitted long-wavelength radiation, resulting in temperature rise.

An ideal gas is one which obeys the ideal gas formula pV=nRT.( An ideal gas has no intermolecular forces, p.e.= 0, behaves as point molecules, collides elastically. Thus obeys all assumptions of the kinetic theory of gases.) CM Molar Heat Capacity is the amount of energy needed to raise the temperature of 1 mole of a substance by 1K.

CVM is the heat required to increase the temperature of 1 mole of a substance by 1K at constant volume.

CPM is the heat required to increase the temperature of 1 mole of a substance by 1K at constant pressure.

The first law of thermodynamics states that the increase in internal energy is equal to the sum of the heat supplied to the system and the work done on the system.

Work done is the areas under the p against V graph.

Isothermal change( temperature remains constant

Adiabatic change( no heat is given to or lost from the system

Isovolumetric change( volume remains constant, no work done

Isobaric change( pressure remains constant Density is the ratio of the mass of a substance to its volume.

Pressure is the force acting normally per unit area

Spacing is the relative distance between molecules.

Ordering is the degree or extent to which we can repeat the structure throughout the body.

Motion of molecules may be of three types- Vibrational- Translational- Rotational

The load (F) is the force applied that causes the deformation.

The extension (e) is the difference between the new length and the original length.

Hookes Law states that the extension is proportional to the applied force as long as the elastic limit is not exceeded. The elastic limit is the point before which the body is elastic (goes back to its original length when deforming forces are removed) and after which the body has a permanent set (body does not go back to its original length)

Tensile strength/ stress (/Pa) is defined as the force per unit cross sectional area. Ultimate tensile stress or ultimate tensile strength (UTS) is the tensile stress at which the material breaks. It is also the maximum stress which the material can withstand.

Tensile strain is defined as the extension per unit length (no unit)

Youngs modulus (E) is the ratio of the stress to the strain of a material

When a body is stretched and the stretching force is removed and it goes back to its original length, then it is said to exhibit elastic behaviour. When a body is stretched and the stretching force is removed and it does NOT go back to its original length, it will have a permanent set. A ductile material is one which has a large plastic region where a small increase in stress causes a large increase in strain energy, e.g. copper.

A brittle material does not behave plastically (it does not have a plastic region). It always returns to its original length when deforming forces are removed. i.e. it is elastic up to its breaking point e.g. glass, iron, concrete. It always obeys Hookes law. Crystalline solid- one which has a regular arrangement and long range order

Non-crystalline/amorphous- one which has no regularity in its internal arrangement.

Polymers- long molecules of atoms joined together like links in a chain

Polymeric material e.g. rubber. There is no region where Hookes law is obeyed. It is very elastic and usually goes back to its original length. It can also withstand high strain stretching to five times its original length. On loading, energy is supplied and since the unloading curve is lower, the energy recovered is less. The difference causes an increase in internal energy. There is usually an increase in temperature since the average kinetic energy of molecules is increased.

Breaking point(the stress at which the material breaks Yield Point- the point at which plastic deformation starts EMBED PBrush

R

O

Y

G

B

I

V

X

G

U

V

I

M

R

In doing experiments to determine specific heat capacity and latent heat,

IVt= mc and IVt=mL

P= A(T14 - T24)

(net rate of absorption/emission of energy)

For the volume of the gas, i.e. the work done

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