Download HKAL Physics Essay writing : Matters Chapter 7 Properties Of Matter

HKAL Physics Essay writing : Matters
Chapter 7 Properties Of Matter
7.1 Solids
7.1.1
Spring 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’.
7.1.2
Experiment to measure the extension of a wire
(a) Setup
A
attached to rigid
support
B
1M
Test wire
1M
variable load
(b) Precautions
Long wires A and B should be of same material and similar length attached to the same rigid
support to allow for any temperature changes or movement of support. In taking measurement
of the extension of wire B until the bubble in the spirit level indicates that it is level. Change in
micrometer reading gives the extension.
7.1.3
Stress-strain curves
(a) Glass
Stress
Strain
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.
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(b) Copper, rubber and glass
stress
Copper
glass
rubber
strain
F  r initially and stress/strain varies linearly initially for all materials
(i) Copper contains impurities and dislocations occur in lattice, so slip of atom planes occurs
later.
(ii) Rubber on stretching rubber becomes rapidly more ordered (X-ray crystal pattern) with
molecular chains untwisted eventually no more untwisting possible even though load
increased.
(iii) Glass is brittle and cannot flow like copper, high stresses occur across the surface cracks
and it quickly breaks.
7.1.4
Model of a Solid
(a) Force – separation graph
Resultant force
Repulsion
Force
Separation
of atoms
r0
Attraction
Most solids are crystalline with molecules formed of atoms at ‘fixed’ separations in a lattice.
The separations r0 are very close (< 1 molecular diameter) and if atom nearer a repulsive force
predominates while farther away force is predominantly attractive. The atoms at any
particular temperature vibrate about this mean separation r0. At higher temperatures there is
asymmetrical vibration with the displacement greater on the extension side - hence solid
expands.
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(b) Potential – separation graph
V
V
F = -dV/dr
repulsive r < r0
T equilibrium
P
0
r = r0
r
r0
Q S
attractive r > r0
R
(i)
Before applying a force molecules are in equilibrium position separated by a distance r =
r0. The net force between them is zero and the potential energy at R is a minimum.
(ii) On application of extension force, molecules move further apart against an increasing
attraction force and over a limited range PQ the extension  force (Hooke’s Law).
(iii) A further increase of this force produces a non-linear variation of extension (Q  S) and
at S the material starts to yield, with slipping of molecular (ion) planes, ultimately the
wire breaking with molecules free at ends of broken wires and the potential energy ~ 0.
(Work needs to be done to overcome attraction force throughout.)
(iv) On application of a compression force the molecules are moved closer (P  T) and there
must now be a repulsive force acting since when force is removed the length of block
recovers its original value - and reverts back to a condition of minimum potential energy
(R). (Work is done by the molecular repulsive force.)
(c) Relationship between the two graphs
Clearly solids show a resistance to deformation and (1) when extended by an extension force
and the force is removed revert back to original indicating long range attractive forces between
atoms while (2) when compressed and compression force is removed revert back, also to
original dimensions indicating short range repulsive forces between atoms.
+
Resultant force
Potential
Energy
V
Repulsion
Force
F
A
r0
Separation
of atoms r
B
Attraction
0
r0
Separation
of atoms r
E0
_
Figure 1
Figure 2
Resultant force between atoms is given by the addition of these two forces as in fig. 1 and the
potential energy in fig. 2.
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Relationship is given by F = 
dV
.
dr
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(d) Thermal expansion of solids
The curve of potential energy against interatomic separation is as follows:
potential
energy U
Interatomic
separation r
0
E2
r2
C
E1
D
A
r1
B
At a certain temperature, the atoms (with total energy E1) vibrate between A 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 Fluid Dynamics
7.2.1
Steady flow and turbulent flow
(a) Steady 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.
(b) Turbulent flow
Liquid elements which start at a given point take random paths and their velocities vary in
magnitude and direction.
7.2.2
Velocity 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.
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7.2.3
Bernoulli’s equation
(a) Derivation
 (const.)
A2
P2
Y
 (const.)
Q
X
S
l2
high velocity v2
Streamlines
A1
P1
R
P
l1
low velocity v1
P - pressure, v - velocity, h - vertical height – all these parameters varying from P  Q,
 - density.
P  R is P1A1l1
Q  S is P2A2l2
net work done per unit volume is (P1 - P2)
Work done in moving fluid
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 + hg + ½v2 = a constant
(b) Source of error
Liquid - due to viscosity the velocity of the liquid at any particular cross-section of the tube
will vary from a maximum at the centre to zero on the sides of tube. Even if the cross-section
and the height remained constant the pressure would drop due to energy dissipation against
viscous force.
Gases - this fluid is compressible so that the density  would vary with the pressure P affecting the ‘gh’ term in the equation.
7.2.4
Typical Examples
(a) Spinning Ball
Force on ball
Speed of air flow increases
pressure reduced
Spin
Motion
of ball
Speed of air flow decreases
pressure increased
Ball experiences a sideways force and motion due to the unequal pressures on the opposite sides of
the ball. This follows from Bernoulli's equation: At same height level P + ½v2 = a constant.
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Thus where speed of air (v) is decreased force ( P) is increased.
(b) Yacht Sailing
Wind
Yacht
Force on sail
F
S
Sail
Fast moving air
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.
(c) Bunsen Burner
mixture
P
Gas pipe narrows down at P - increases the rate of flow (v) of the gas. According to Bernoulli's
equation pressure in this region will be reduced and so air will be sucked in producing a mixture of
gas and air for the Bunsen burner.
(d) Pitot Tube
Static
pressure
tube Ps
Pitot tube
(gives total
pressure) PT
v
P + hg + ½v2 = a constant
The static pressure, Ps is given by Ps = P + gh or Ps = P, if the flow is horizontal.
The dynamic pressure (due to movement of liquid) is ½v2, i.e. PT
-
Ps
=
½  v2,
and
v  [2(PT  Ps ) / ]
1/ 2
N.B. The velocity of flow varies across tube, being maximum along central axis. If the open end is
offset from the axis by 0.7  radius, then value of v is the average flow velocity.
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Chapter 8 Heat and Gas
8.0 Background Knowledge
8.0.1
Melting and vaporization
(a) When ice changes to water at 0 C , 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 C to 100 C , 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 C , 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.
8.0.2
Skin Burnt by vapor
Skin burnt by 100 C steam is more severe than 100 C 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.
8.1 Boyle’s Law
8.1.1
Ideal Gas
8.1.1.1
Macroscopic Point of View
(a) Ideal gas is a gas that obeys the ideal gas equation (
pV
= constant or pV = nRT) or Boyle’s
T
Law under all temperatures and pressures.
(b) Real gas behaves like ideal gas under high temperatures AND low pressures.
8.1.2
Temperature Scales
8.1.2.1
Definition
(a) Thermometers possess a particular physical property which varies with temperature e.g.
pressure, electrical resistance.
(b) Values of this property are measured at two reproducible 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  =
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P  P0
 100 .
P100  P0
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8.1.2.2 Difference of Temperature Scales
(a) We assume a linear relation between the physical property and temperature.
(b) Relations may vary for different thermometers. e.g. compare gas thermometer/thermocouple
Pc
(i)
t

P
(ii)
Pg
c
0
e 100

thermocouple - linear relation gives temperature e while measured property (e.m.f.) Pt
gives temperature c.
(b) gas thermometer property Pg would, of course, give temperature c.
(i)
Alternative Description
(a) Temperature measurements should agree at the fixed points 0 °C and 100 °C.
(b) However in-between these temperatures the readings of the different thermometers may differ
if the linear relation, physical property  temperature does not hold good for one or both of the
thermometers.
8.1.3
8.1.3.1
Measurement of Temperature
Constant 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 reference level R in B, i.e. gas remains at constant
volume.
(d) Gas pressure, p = hg + atmospheric pressure
(e) For an ideal gas, PV = RT, P  T if V constant.
(f)
Temperature defined as

P P
  0 ,
100 P100  P0
where P100 and P0 are the measured pressures at the fixed ‘known’ temperatures of 100 °C
(boiling point) and 0 °C (freezing point) for water – thermometer calibrated at these
temperatures.
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P
P0
0
 °C
-273
(g) When P is plotted against  °C a straight line graph is produced, which if extended to reach
the  °C axis results in a value of 0 = -273 °C - the absolute zero of temperature (no
temperature lower is possible).
8.1.3.2
Resistance Thermometer
(a) For measuring a steady temperature.
(b) Properties : large thermal capacity, and cannot react rapidly enough to follow varying
temperatures.
Leads to platinum
wire
P
Mica spacers
Dummy
leads
mica
Q
G
S
Platinum wire
Dummy
leads
R
Silica tube
(a)
(b)
(c) No current through G, R 
P
S.
Q
(d) Dummy leads at same temperatures as leads to R.
(e)  compensate for changes in resistance as  varies.
8.1.3.3 Thermocouple
(a) For measuring a rapidly changing temperature.
(b) Properties : small thermal capacity, and can react rapidly (establishing thermal equilibrium) so
as to follow varying temperatures.
to potentiometer
R
R1
R2
A
C
G
Cu
Cu
Pt-Rh
Pt
G
ice
water
E1
0 OC
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B
 OC
ice
water
unknown
temperature t
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(c) No current in G - length AC  e.m.f. R must be high resistance to give low p.d. AB.
(d) Better arrangement : Cu connecting wires at same temperature and therefore on connection
with potentiometer thermal e.m.f.s same and cancel.
8.2 Kinetic Theory Model
8.2.1
Diffusion Speed
(a) Molecules move about in random directions colliding with other molecules fairly frequently
due to their finite size.
(b) Thus inspite of their relative fast speeds - say A  A’ the molecules, in fact, take a long time to
travel from, say, A  B.
Alternative Description
(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 direction
resulting in a slow diffusion rate.
B
A’
A
8.2.2
Definition 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.
Alternative Description
(a) Gas consists of molecules moving randomly within contained space.
(b) Collisions between molecules and of molecules with container are perfectly elastic.
(c) The volume occupied by the molecules is negligible compared with the whole volume
occupied by the gas .
(d) The intermolecular forces are negligible, except during collisions.
(e) Collision duration times are negligible compared with times spent between collisions.
(f) The pressure exerted by a gas on its container is due to the force exerted by molecules
rebounding from the surface of the container, and it is measured by the average rate of change
of momentum of the molecules per unit surface area.
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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 molecules and with the wall of container are elastic (no energy loss).
(d) Time of contact during collisions is negligible compared with time between collision.
8.2.3
Pressure 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.
Alternative Description
(a) Pressure of a gas arises from the momentum change suffered by each gas molecule in colliding
elastically with the wall of the container.
8.2.4
Temperature from Kinetic Theory
(a) Temperature is associated with the average kinetic energy of the molecules in 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.)
Alternative Description
(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.)
8.2.5
Root Mean Square Speed
8.2.5.1
Equation 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 pV 
1
Nmc 2 , where
3
(c) n – number of moles, R – universal gas constant, T – absolute temperature,
N – number of molecules, m – mass of a molecule and c 2 – mean square speed.
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8.2.5.2 Example
(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.)
As pV =
1
1
3nRT
3 pV
Nmc 2 = nRT,
= mc 2 =
.
3
2
2N
2N
(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
1
1
m H c H2 = mo c o2 , c H2  co2 . ( mH < mo)
2
2
(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 Real Gas
8.3.1
The non-applicable of the Kinetic Theory
8.3.1.1 At 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.)
8.3.1.2 At 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.)
P – V Characteristics
8.3.2
P
P
high T
high T
EABF Van der Waal
C
real gas B
F
E
low T
A
low T
V
Ideal Gas
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critical
temperature
V
Real Gas
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(a) For an ideal gas pV = RT and for a constant temperature T, p (pressure)  1/V (volume).
(b) For a real gas :
(i) the volume occupied by the molecules cannot be considered negligible and
(ii) the attractive forces between molecules may cause two or molecules to combine together
effectively reducing the effective number of molecules and the resulting pressure.
[
Van der Waal’s equation results : (p + a/V2)(V - b) = RT ] (optional)
Critical isothermal
P
Gas
Increasing
temperature
Liquid
C
R
P
T
critical
temperature
isothermal
Vapour
V
Liquid and saturated vapour
(iii) At high pressures, where molecules are near together departure 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
gas behaviour.
8.4 Thermodynamics
8.4.1
Heat, Work and Internal Energy
8.4.1.1 Definition of Heat
(a) Heat is a measure of energy transferred from a body at a higher temperature to one at a lower
temperature. This has the effect of increasing the kinetic energy of 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.)
8.4.1.2 Definition 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.
8.4.1.3 Definition of Internal Energy
(a) Internal energy includes potential energy, which depends upon the intermolecular forces.
(b) However there is a considerable contribution to the internal 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.)
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8.4.1.4 Internal Energy for a Gas and a Solid
(a) In a gas the intermolecular forces are small since 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 since atoms are close and these vibrate about their
equilibrium positions.
8.4.1.5 Energy 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.
8.4.2
First Law of Thermodynamics
8.4.2.1 Definition 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 the change/increase
in the internal energy of that system plus the work done by the system.
8.4.2.2 First 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.
8.4.2.3 Example
(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.
(b) Descriptions
(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.
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