HKAL Physics Essay writing : Matters
Chapter 7 Properties Of Matter
7.1.1Spring model for the bonding of molecules inside a solid.
(a)Force must be applied to extend a solid, thus it is somehow held together, thus attractive force exists between atoms.A solid is hard to compress which shows that if we try to push atoms still closer, some kind of repulsive force results.
(b)When a moderate applied force on a solid is removed, it restores to its original shape which reflects the restoring behaviour of ‘springs’.
7.1.2Experiment to measure the extension of a wire
Long wires A and B should be of same material andsimilar length attached to the same rigid supportto allow for any temperature changes or movementof support. In taking measurement of the extension of wire Buntil the bubble in the spirit level indicatesthat it is level.Change in micrometer readinggives the extension.
Glass is strong as a large breaking stress is required to break it.
Glass is stiff as a large stress only gives a small strain.
Glass is brittle as it shows no plastic deformation.
(b)Copper, rubber and glass
Frinitially and stress/strain varieslinearly initially for all materials
(i)Copper contains impurities and dislocationsoccur in lattice, so slip of atom planes occurs later.
(ii)Rubber on stretching rubber becomes rapidly moreordered (X-ray crystal pattern) with molecular chains untwisted eventually no more untwisting possible even though loadincreased.
(iii) Glass is brittle and cannot flow like copper, high stresses occur across the surface cracksand it quickly breaks.
7.1.4Model of a Solid
(a)Force – separation graph
Most solids are crystalline with molecules formedof atoms at ‘fixed’ separations in a lattice.The separations r0 are very close (< 1 moleculardiameter) and if atom nearer a repulsive forcepredominates while farther away force is predominantly attractive. The atoms at anyparticular temperature vibrate about this meanseparation r0. At higher temperatures there isasymmetrical vibration with the displacementgreater on the extension side - hence solidexpands.
(b)Potential – separation graph
(i)Before applying a force molecules are inequilibrium position separatedby a distancer = r0. The net force between them is zeroand the potential energy at R is a minimum.
(ii)On application of extension force, molecules movefurther apart against an increasing attractionforce and over a limited range PQ the extension force (Hooke’s Law).
(iii)A further increase of this force produces anon-linear variation of extension (QS) and atS the material starts to yield, with slipping ofmolecular (ion) planes, ultimately the wirebreaking with molecules free at ends of broken wires and the potential energy ~ 0.(Work needs to be done to overcome attractionforce throughout.)
(iv)On application of a compression force the moleculesare moved closer (PT) and there must now be arepulsive force acting since when force is removedthe length of block recovers its original value -and reverts back to a condition of minimum potentialenergy (R).(Work is done by the molecular repulsive force.)
(c)Relationship between the two graphs
Clearly solids show a resistance to deformation and (1) whenextended by an extension force and the force is removedrevert back to original indicating long range attractive forces between atoms while (2) when compressed and compression force is removedrevert back, also to original dimensionsindicating short range repulsive forces between atoms.
Figure 1Figure 2
Resultant force between atoms is given by the addition ofthese two forces as in fig. 1 and the potential energy infig. 2. Relationship is given by F = .
(d)Thermal expansion of solids
The curve of potential energy against interatomic separation is as follows:
At a certain temperature, the atoms (with total energy E1) vibrate betweenA and B with mean separation r1.
At a higher temperature, the K.E. and thus the total energy of the atoms increases.
Atoms (with energy E2) vibrate between C and D with increased mean separation r2 ( > r1), as the vibration is asymmetrical with the displacement greater on the extension side – solid expands.
7.2.1Steady flow and turbulent flow
Liquid elements which start at a given point always follow the same path and have the same velocity at each point on the path.
Liquid elements which start at a given point take random paths and their velocities vary in magnitude and direction.
7.2.2Velocity gradient in a pipe
Consider a cross-section of the pipe, the liquid layer touching the pipe wall is always stationary due to adhesive force between the liquid molecules and pipe wall. The velocity of liquid is greatest at the centre.Internal friction exists between liquid layers with different velocities because of intermolecular forces.So velocity falls off gradually as the pipe wall is approached.
P - pressure, v - velocity, h - vertical height – all these parameters varying from PQ,
Work done in moving fluid PR is P1A1l1
QS is P2A2l2
net work done per unit volume is (P1 - P2)
similarly K.E. increase per unit volume is ½(v22 - v12)
P.E. gained per unit volume is g(h2 - h1)from conservation of energy,
P1 - P2 = ½(v22 - v12) + g(h2 - h1),
i.e.Bernoulli's equation P + hg + ½v2 = a constant
(b)Source of error
Liquid - due to viscosity the velocity of theliquid at any particular cross-section of the tubewill vary from a maximum at the centre to zero onthe sides of tube. Even if the cross-section and the height remainedconstant the pressure would drop due to energydissipation against viscous force.
Gases - this fluid is compressible so that thedensity would vary with the pressure P -affecting the ‘gh’ term in the equation.
Ball experiences a sideways force and motion due tothe unequal pressures on the opposite sides of theball. This follows from Bernoulli's equation: At same height level P + ½v2 = a constant.
Thus where speed of air (v) is decreased force (P)is increased.
Air-flow over the sail takes a longer path/greater velocity resulting in a decrease in pressure by Bernoulli’s principle. Pressure difference between the two sides of the sail gives a force normal to the sail, which can be resolved into component F producing forward motion.
Gas pipe narrows down at P - increases the rate offlow (v) of the gas. According to Bernoulli'sequation pressure in this region will be reduced andso air will be sucked in producing a mixture ofgas and air for the Bunsen burner.
P + hg + ½v2 = a constant
The static pressure, Ps is given by Ps = P + ghor Ps= P, if the flow is horizontal.
The dynamic pressure (due to movement of liquid) is ½v2, i.e.PT - Ps = ½v2, and
N.B.The velocity of flow varies across tube,being maximum along central axis. If theopen end is offset from the axis by0.7 radius, then value of v is theaverage flow velocity.
Chapter 8 Heat and Gas
8.0.1Melting and vaporization
(a)When ice changes to water at 0, the energy absorbed from the environment is used for overcoming the intermolecular forces of the water molecules in ice so that its potential energy increases during the change of state.
(b)When the temperature of water changes from 0 to 100, the energy absorbed from the environment becomes the kinetic energy of the water molecules and therefore the temperature increases.
(c)When water changes to steam at 100, the energy absorbed from the environment is used for separating the water molecules against their intermolecular forces (&/or atmospheric pressure) so that its potential energy increases during the change of state.
8.0.2Skin Burnt by vapor
Skin burnt by 100 steam is more severe than 100 water because the latent heat of the vaporisation of water is very large and this latent heat is given off when steam changes back to water.
188.8.131.52Macroscopic Point of View
(a)Ideal gas is a gas that obeys the ideal gas equation ( = constant or pV = nRT) or Boyle’s Law under all temperatures and pressures.
(b)Real gas behaves like ideal gas under high temperatures AND low pressures.
(a)Thermometers possess a particular physical propertywhich varies with temperature e.g. pressure,electrical resistance.
(b)Values of this property are measured at tworeproducible temperatures :
(i)ice point, 0 °C - P0, say.
(ii)water boiling point, 100 °C - P100, say.
(c)It is, then, assumed that an intermediate temperature is measured as = .
184.108.40.206Difference of Temperature Scales
(a)We assume a linear relation between thephysical property andtemperature.
(b)Relations may vary fordifferent thermometers. e.g. compare gas thermometer/thermocouple
(i)thermocouple - linear relation gives temperature e while measured property (e.m.f.) Pt givestemperature c.
(b)gas thermometer property Pg would, of course, givetemperature c.
(a)Temperature measurements should agree at the fixedpoints 0 °C and 100 °C.
(b)However in-between these temperatures the readingsof the different thermometers may differ if thelinear relation, physical property temperature does not hold good for oneor both of the thermometers.
8.1.3Measurement of Temperature
220.127.116.11Constant Volume Gas Thermometer
(a)Bulb A containing a gas is placed in location.
(b)As temperature increases gas expands pushing mercury down in B and up in C.
(c)Tube C is raised to bring mercury back to referencelevel R in B, i.e. gas remains at constant volume.
(d)Gas pressure, p = hg + atmospheric pressure
(e)For an ideal gas, PV = RT, PT if V constant.
(f)Temperature defined as ,
where P100 and P0 are the measured pressures at thefixed ‘known’ temperatures of 100 °C (boiling point)and 0 °C (freezing point) for water – thermometercalibrated at these temperatures.
(g)When P is plotted against °C a straight line graphis produced, which if extended to reach the °C axisresults in a value of 0 = -273 °C - the absolute zeroof temperature (no temperature lower is possible).
(a)For measuring a steady temperature.
(b)Properties : large thermal capacity,and cannot react rapidly enough to follow varyingtemperatures.
(c)No current through G, .
(d)Dummy leads at same temperatures as leads to R.
(e) compensate for changes in resistance as varies.
(a)For measuring a rapidly changing temperature.
(b)Properties : small thermal capacity, and canreact rapidly (establishing thermal equilibrium) soas to follow varying temperatures.
(c)No current in G - length AC e.m.f. R must be highresistance to give low p.d. AB.
(d)Better arrangement : Cu connecting wires at same temperature and thereforeon connection with potentiometer thermal e.m.f.s sameand cancel.
8.2Kinetic Theory Model
(a)Molecules move about in random directions colliding withother molecules fairly frequently due to their finite size.
(b)Thus inspite of their relative fast speeds - say AA’the molecules, in fact, take a long time to travel from,say, AB.
(a)Molecule A travels to A’ rapidly with high average speed.
(b)However to travel from A to B it has to suffer many collisions and changes of directionresulting in a slow diffusion rate.
8.2.2Definition of Ideal Gas
(a)Molecules have insignificant volumes, i.e. they are effectively points in the space.
(b)Collisions are the only interactions between molecules, and between molecules and the walls of the container. (or molecules move freely without intermolecular forces)
(c)All collisions are perfectly elastic.
(a)Gas consists of molecules moving randomly within contained space.
(b)Collisions between molecules and of molecules withcontainer are perfectly elastic.
(c)The volume occupied by the molecules is negligiblecompared with the whole volume occupied by the gas .
(d)The intermolecular forces are negligible, exceptduring collisions.
(e)Collision duration times are negligible compared with times spent between collisions.
(f)The pressure exerted by a gas on its container is dueto the force exerted by molecules rebounding from thesurface of the container, and it is measured by the average rate of change ofmomentum of the molecules per unit surface area.
Alternative Description (Assumptions of Kinetic Theory)
(a)Intermolecular forces are negligible,except in collisions.
(b)Volume occupied by molecules is negligible,compared with volume of gas.
(c)All collision between moleculesand with the wall of container are elastic (no energy loss).
(d)Time of contact during collisions is negligible compared with time between collision.
8.2.3Pressure from Kinetic Theory
(a)A gas molecule on colliding with a container wall suffers a change of momentum and hence must be acted on by a force.
(b)By Newton’s third law of motion, the container wall must have had a force exerted on it by the molecule, hence pressure.
(a)Pressure of a gas arises from the momentum change suffered by each gas molecule in colliding elastically with the wall of the container.
8.2.4Temperature from Kinetic Theory
(a)Temperature is associated with the average kinetic energy of the moleculesin the gas.
(b)If the gas is compressed, the wall will be moving inward, a molecule collides with the wall would therefore rebound with an increased speed, and hence the gas temperature would rise because the average kinetic energy of the molecules has increased.
or(If the gas is compressed, the wall will be moving inward, work is done on the gas and hence the gas temperature would rise because the average kinetic energy of the molecules has increased.)
(a)Temperature of an ideal gas is a measure of the mean kinetic energy of the gas molecules. (In fast mean K.E. of the gas molecules is proportional to the absolute temperature of the gas.)
8.2.5Root Mean Square Speed
18.104.22.168Equation of State and Kinetic Theory Equation
(a)The equation of state can be written as pV = nRT, and
(b)the kinetic theory equation of an ideal gas can be written as , where
(c)n – number of moles, R – universal gas constant, T – absolute temperature,
N – number of molecules, m – mass of a molecule and – mean square speed.
(a)Two identical vessels containing hydrogen and oxygen respectively are at the same temperature and pressure.
(b)According to Avogadro’s law, the gases have the same number of molecules.
(As p, V and T are the same, n is the same according to pV = nRT.)
AspV = = nRT, = = .
(c)Therefore the average molecular kinetic energy is the same in both cases since T is the same (or p, V and N are the same).
As = , . (mHmo)
(d)As the molecular mass of hydrogen is smaller than that of oxygen, the mean square speed of the hydrogen is higher than that of the oxygen molecules since their average molecular kinetic energy is the same.
8.3.1The non-applicable of the Kinetic Theory
22.214.171.124At High Pressure
(a)At high pressures, the molecules become closer.
(b)So the actual volume of the molecules becomes more important compared with the measured volume occupied by the gas.
or(The available volume in which the molecules can move is less than the measured volume.)
126.96.36.199At Low Temperature
(a)At low temperatures, the molecular kinetic energy is lower than that at high temperature (or molecules move more slowly than they do at higher temperatures).
(b)The weak attractive forces (intermolecular P.E.) between the molecules become more significant (or interaction time between molecules become longer).
or(The impact/pressure would be reduced by the weak attractive forces on any molecules moving towards the container walls.)
8.3.2P – V Characteristics
Ideal GasReal Gas
(a)For an ideal gas pV = RT and for a constanttemperature T, p (pressure) 1/V (volume).
(b)For a real gas :
(i)the volume occupied by the molecules cannot beconsidered negligible and
(ii)the attractive forces between molecules may causetwo or molecules to combine together effectivelyreducing the effective number of molecules and the resulting pressure.
[Van der Waal’s equation results : (p + a/V2)(V - b) = RT ] (optional)
(iii)At high pressures, where molecules are near togetherdeparture from ideal gas behaviour is most serious and
(iv)at low temperatures, gases liquefy and this can be caused by an increase of pressure for temperatures below the critical temperature, causing a departure from the expected ideal gasbehaviour.
8.4.1Heat, Work and Internal Energy
188.8.131.52Definition of Heat
(a)Heat is a measure of energy transferred from a body at a highertemperature to one at a lower temperature. This has the effect of increasing the kinetic energyof the atoms/molecules.
or(Heat is the energy that flows by conduction, connection or radiation from one body to another due to a temperature difference between them.)
184.108.40.206Definition of Work and Internal Energy
Work is the energy that is transferred from one system to another by a force moving its point of application in its own direction.
220.127.116.11Definition of Internal Energy
(a)Internal energy includes potentialenergy, which depends upon the intermolecular forces.
(b)However there is a considerable contribution to theinternal energy of P.E. due to the interatomic bonds.
(c)K.E. and P.E. contributions roughly equal.
or(The (molecular) energy (either kinetic energy, potential energy or both) in an object at a certain state is the internal energy of the object.)
18.104.22.168Internal Energy for a Gas and a Solid
(a)In a gas the intermolecular forces are smallsince molecules are free to move and on average are widely separated -internal energy almost entirely K.E.
(b)In a solid intermolecular forces are large sinceatoms are close and these vibrate about their equilibrium positions.
22.214.171.124Energy in a Steam Engine
Chemical energy in fuel is transferred to internal energy of steam in the heating process. The steam then turns the turbine by doing work on it.
8.4.2First Law of Thermodynamics
126.96.36.199Definition the First Law of Thermodynamics
(a)Quantitatively, the first law of thermodynamics can be stated as : ΔQ = ΔU + ΔW
(b)In words : The amount of thermal energy transferred into a system equals thechange/increase in the internal energy of that system plus the work done bythe system.
188.8.131.52First Law of Thermodynamics and the Law of Conservation of Energy
(a)They are consistent with each other, for example,
(i)energy transfer can be achieved through work or heat. When work (W) is done on the object, say, by rubbing a metal bar with a cloth, or heat (Q) is transferred to the object, say, by heating the metal bar with a burner, its temperature would increase as a result of internal energy increase (ΔU > 0 and K.E. T).
(ii)Hence the first law of thermodynamics U = Q + W, which relates the change in internal energy and the total energy transfer, is consistent with the law of conservation of energy.
(b)Not all processes which satisfy the principle of conservation of energy will occur spontaneously.
(a)Situation : a compressed gas in a hollow, steel cylinder expands and lifts a weight; it cools in the process and is then heated by conduction through the cylinder.
(i)With the system defined as the gas inside the cylinder, ΔW is positive (i.e. –ΔW is negative) since work is done by the system to raise the weight.
(ii)The internal energy then decreases (ΔU is negative) as (-ΔW) is negative and ΔQ is zero.
(iii)Heat is conducted into the gas through the cylinder, so ΔQ is positive.
(iv)The overall change in internal energy, ΔU, is determined by combining ΔQ and (-ΔW). Since ΔQ is positive and (-ΔW) is negative, ΔU may be positive, negative or zero.