1'9 The properties of solids and fluids

1
1.9 The properties of solids and fluids
0

• In this chapter we will consider some basic
  properties of solids and fluids.
• We will investigate the differences between
  solids, liquids and gasses.
• We will also consider issues such as the
  deformation of solids, pressure, buoyancy,
  viscosity and surface tension.
• The aim in this chapter is to gain a physical
  picture of why solids, liquids and gasses behave
  as they do.
• We will then move on to look at the thermodynamic
  properties of materials.

2
1.9.1 States of Matter
0

• One can think of four basic states of matter
• Solids
• Liquids
• Gasses
• Plasmas
• The differences between these different states
  can be understood in terms of the ways that the
  atoms are held within them, and the forces
  between the atoms.

3
Solids
0

• The atoms in a solid are mostly held together by
  electrical forces, forming bonds between the
  atoms.
• The atoms in this arrangement vibrate about an
  equilibrium position.
• If a solid is compressed, it has a tendency to
  return to its original shape. This we call its
  elasticity.

4
Liquids
0

• If we increase the temperature of a solid, the
  atoms vibrate with increased energy.
• At some points the bonds between the atoms break,
  and the atoms are more free to move. This is
  what happens when we form a liquid.
• In a liquid, the atoms or molecules undergo many
  collisions with other atoms/molecules as they
  move about.
• Note that for both solids and liquids, when you
  try to compress them, there is a strong repulsive
  force which resists the compression. Thus, it is
  difficult to compress solids and liquids.

5
Gasses
0

• If we continue to heat a liquid, the atoms move
  about much more energetically, and get further
  apart. The gas will expand to fill whatever
  container it is in.
• The average distance between the atoms is much
  larger than the size of the atoms or molecules.
• The atoms undergo very few collisions with each
  other, and spend most of their time flying about.

6
Plasmas
0

• If we continue to heat a gas, we will eventually
  start to remove electrons from the neutral atoms
  in the gas.
• These positive ions and negative electrons behave
  quite differently from a gas.
• Most of the universe is made up of plasmas
  (stars, nebulae, the intergalactic medium), we
  just happen to live on the 1 percent of the
  universe which isnt a plasma!

Solar plasma http//sohowww.nascom.nasa.gov/galler
y/Movies/filaments.html
Image of the JET tokamak in England. http//www.je
t.efda.org/
7
1.9.2 Deformation of Solids
0

• In our studies on mechanics, we assumed that when
  forces acted on an object, the object didnt
  undergo any change in shape or deformation. In
  reality this is often not the case.
• In order to quantify the deformation of solids,
  we will define two new terms
• The STRESS applied to an object is a measure of
  the force causing the deformation.
• The STRAIN on an object is a measure of the
  degree of deformation of the object.
• The deformation of a solid is quantified by the
  ELASTIC MODULUS, which is given by

8
Deformation Elasticity in length
0

• Consider trying to stretch a metal bar of cross
  section A and length L0. If a force F is applied
  to the end of the rod, causing a change in length
  of the rod ?L, then the elastic modulus is given
  by Youngs modulus

L0
?L
F
A
9
Elasticity of shape
0

• Consider an object where one side is fixed, and a
  force is applied to the other side, causing the
  object to change shape.
• The object undergoes a shear force. The top
  surface which is being sheared has area A, and
  moves a distance ?x.
• The volume doesnt change, only the shape.
• We quantify this elasticity via the shear
  modulus, given by

A
?x
F
h
-F
Side held fixed
10
Volume elasticity
0
F

• Consider an object which is being compressed by a
  force F on all sides (e.g. an object immersed in
  a fluid).
• The volume stress, we call the pressure, and is
  the force per unit area on the surface (?P ?F/A)
• The elasticity is given by the bulk modulus, and
  is defined by

11
1.9.3 Density and Pressure
0

• The density of an object is a measure of how much
  mass there is in a given volume. Thus, the
  density (?) of an object of mass M and volume V
  is
• The units of density are kg/m3
• The average pressure applied to an object is the
  force per unit area acting to the object.
• The units of pressure are N/m2 or Pascals Pa

12
Pressure
0

• Thus, the pressure caused by a force depends upon
  the area upon which it acts, as well as upon the
  size of the force.
• Consider a person standing in snow wearing normal
  shoes, compared to a person wearing snow shoes.
• They both exert the same force on the snow
• The person with the snow shoes spreads the force
  out over a bigger area, thus exerts a smaller
  pressure on the snow (and doesnt sink into the
  snow).

13
1.9.4 Variation of pressure with depth
0

• Consider a fluid at rest in a container. We can
  associate a pressure with the different depths in
  the fluid.
• All points at the same depth have the same
  pressure.
• If P0 is the pressure at the surface, and h is
  the depth below the surface, then it can be shown
  that pressure at depth h is given by
• We call P the absolute pressure, and P-P0 the
  gauge pressure.
• If the surface is at atmospheric pressure, then
  P01.013x105 Pa.

14
Pressure
0

• Note that from the previous equation, if we
  increase the pressure at the surface, we will
  instantly increase the pressure at each point in
  the fluid. This is called Pascals principle
• A change in pressure applied to an enclosed fluid
  is transmitted undiminished to every point of the
  fluid, and to the walls of the container.
• This is what allows hydraulics to work.
• The force applied to the top of the hydraulic
  tube is transmitted throughout the whole fluid in
  the tube.

15
1.9.5 Buoyant Forces and Archimedes Principle
0

• We use Archimedess principal to calculate the
  buoyancy force on an object.
• Any object completely or partially submerged in a
  fluid is buoyed up by a force whose magnitude is
  equal to the weight of the fluid displaced by the
  object.
• How do we work out the weight of the fluid
  displaced?
• We can use the density of the fluid and the
  volume of the object to work out the mass of the
  fluid displaced, and then Wmg to get the force.

16
1.9.6 Fluids in motion
0

• We will consider the flow of an ideal fluid.
  This is a fluid which
• Is incompressible, and has no turbulence in its
  flow.
• Is non-viscous, i.e. there is no internal
  friction inside the fluid.
• The fluid motion is steady, that is it does not
  change over time.

17
Fluid motion the continuity equation
0

• The rate at which water flows though a pipe must
  be the same everywhere in the pipe. Thus, we can
  use the following continuity equation relating
  the velocities of the fluid and the cross
  sectional areas of the pipe.

v1
v2
A1
A2
18
Bernoullis equation
0

• A Swiss scientist Daniel Bernoulli derived an
  expression for the conservation of energy of an
  ideal fluid.

Pressure
Kinetic energy per unit volume
Potential energy per unit volume
19
1.9.7 Surface tension
0

• In any fluid, there is a surface tension, which
  acts to make the total surface area of the fluid
  as small as possible.
• The surface tension (?) in a film of liquid is
  defined as the ratio of the magnitude of the
  surface tension force to the length along which
  the force acts.

• The upwards force depends upon the contact angle
  which the fluid makes with the object.
• If ? is the contact angle, then the upwards
  force is given by

F
F
Wmg
20
Viscosity and Stokes Law
0

• If an object is falling through air, its motion
  is impeded by air resistance. The force of air
  resistance depends upon the geometry of the
  object.
• The force on a small spherical object of radius
  r, falling with speed v is given by

Fr
v

• Here, ? (Greek letter eta) is called the
  viscosity of the fluid.
• Note that this can be used both for an object
  falling in air, and for an object falling through
  a fluid.

Wmg
21
THERMODYNAMICS
0

• In the next three sections we are going to look
  at some laws of thermodynamics. This will
  include things like thermal expansion, properties
  of gasses, heat and the laws of thermodynamics.

Movie taken from NASAs scientific visualization
studio http//svs.gsfc.nasa.gov/
22
1.10 Thermal physics
0

• Thus far we have been considering the mechanics
  of moving objects.
• We now start to consider what happens when
  objects are heated, cooled, compressed, expanded,
  put under pressure etc.
• We will start by considering the thermal
  properties on a macroscopic scale. That is, we
  will look at large scale properties, such as
  temperature, pressure and volume.
• Then we will consider what happens on the atomic
  level, and relate quantities like the velocity of
  the atoms to macroscopic quantities, such as
  pressure.

23
1.10.1 Temperature and the Zeroth Law of
thermodynamics
0

• We have an intuitive sense of what temperature
  means. As a first approximation we could use the
  fact that an object feels hot or cold to
  determine the temperature, but this could be
  misleading.
• Thus, we need a better way of measuring
  temperature. For this, we use a principal called
  the zeroth law of thermodynamics.
• We will need to understand two new concepts
• Thermal contact this means that two objects are
  able to exchange thermal energy with each other.
• Thermal equilibrium this occurs when two
  objects which are in thermal contact with each
  other cease to exchange energy.

24
1.10.1 The Zeroth Law
0
C

• Consider two objects, A and B, which are not in
  thermal contact with each other.
• A third object, C, is used as a thermometer.
• How can we tell if objects A and B would be in
  thermal equilibrium with each other?
• If objects A and B are separately in thermal
  equilibrium with a third object C, then A and B
  are in thermal equilibrium with each other.
• Thus, we can use the temperature of an object as
  a means of determining if two objects are in
  thermal equilibrium with each other.

T95
A
C
T95
B
A
B
25
1.10.2 Thermometers and temperature scales
0

• Temperature scales are defined by the
  temperatures of easily measured quantities.
• Thus the Celsius temperature scale is defined to
  have 0 oC at the freezing point of water, and 100
  oC at the boiling point of water.
• The Fahrenheit temperature scale is defined to
  be 32 oF at the freezing point of water, and 212
  oF at the boiling point of water.
• We convert from one scale to the other via

26
The Kelvin temperature scale
0

• If we were to measure the pressure and
  temperature of a gas for a constant volume, we
  would get something like the graph opposite. The
  greater the temperature of a gas, the greater the
  pressure.
• All gasses converge on zero pressure at the same
  temperature (-273.15 oC).
• Thus, we define a new scale with zero at this
  point. We call this point absolute zero and the
  new temperature scale we call the Kelvin scale.
  It has zero at absolute zero, and a change of 1 K
  1 oC.
• It is not possible to get to absolute zero, due
  to a quantum mechanical quantity called the zero
  point energy. But we can get very close.

P
0
-273.15
T (oC)
TCTK - 273.15
27
1.10.3 Thermal expansion of solids and liquids
0

• In general, if we increase the temperature of an
  object, we also increase its volume. This is
  known as thermal expansion.
• Let us first consider the change in length of an
  object.
• If we have an object with length L, and apply a
  temperature change of ?T to it, it will have a
  change in length given by
• Where ? is called the coefficient of linear
  expansion, with units (oC)-1.

28
1.10.3 Area of expansion due to a change in
temperature
0

• So we know that, upon heating, the linear
  dimensions of a solid or liquid will expand, and
  that this expansion will depended upon ?, the
  coefficient of linear expansion.
• This means that the surface area of the solid or
  liquid must also expand. This happens according
  to the relationship
• Where ? is called the coefficient of area
  expansion, and

29
1.10.3 Volume of expansion due to a change in
temperature
0

• Clearly, if the surface area of a solid or liquid
  expands, then the volume will also change.
• The change in volume is given by
• Where ? is called the coefficient of volume
  expansion, and

30
The unusual behavior of water
0

• Normally liquids expand when heated. However,
  water actually contracts when heated in the range
  of 0 4 oC.
• This means that it gets more dense. The peak
  density of water occurs at 4 oC. This is why ice
  forms on the surface of water, and not at the
  bottom (i.e. once ice forms, it is less dense
  that water at 4 oC, and so it floats to the top).
• If it were not for this fact, then most sea life
  would not survive through the winter.

31
1.10.4 Macroscopic description of an ideal gas
0

• We will now consider a container filled with an
  ideal gas. When a gas is introduced to a
  container, it expands to fill the whole volume of
  the container. We want to relate quantities
  such as the temperature (T), pressure (P) and
  volume (V) of the gas.
• In general the equation relating these quantities
  is quite complex. However, for the case of an
  ideal gas, it is actually quite simple.
• An ideal gas is a
• collection of atoms of molecules that move
  randomly, exert no long-range forces on one
  another, and occupy a negligible fraction of the
  volume of their container.
• This is true for relatively low temperature, and
  low density gasses. Note that most room
  temperature gasses behave like ideal gasses.

32
1.10.4 Moles and Molar Mass
0

• In order to determine the amount of gas in a
  given volume, we define a quantity called the
  number of moles (n) of the gas. This is related
  to the mass of the gas (m) via
• where the molar mass is the total atomic weight
  of the atom or molecule, expressed in grams. The
  units of molar mass is g/mol.
• One mole of any gas contains the same number of
  particles. This number is called Avogadros
  number, and it given by

33
1.10.4 Avogadros Number and the Ideal Gas Law
0

• Thus, the mass per atom is given by
• We can now describe the ideal gas law
• Where R is called the Universal gas constant, and
  is given by R8.31 J/(mol K)

34
1.10.4 The ideal gas law
0

• Let us consider the idea gas law in more detail.
• This means, if the number of moles (n) of a gas
  remain constant, we can relate P, V and T via

35
1.10.4 Avogadros number and the ideal gas law
0

• Avogadros number, and the properties of an ideal
  gas mean that
• at standard temperature and pressure, one-mole
  quantities of all gases contain the same number
  of molecules. This number is Avogadros number
• Thus, the number of atoms, N, in a gas is related
  to the number of moles, n, in the gas via

36
1.10.4 Avogadros number and the ideal gas law
0

• Thus, we can have an alternative expression for
  the ideal gas law,
• We define a new constant kBR/NA,, called
  Boltzmanns constant (1.38x10-23 J/K). Thus,

37
1.10.5 The kinetic theory of gases
0

• In this section we will be relating macroscopic
  quantities of gases, such as pressure,
  temperature and volume, to microscopic quantities
  such as the velocity of individual atoms.
• The theoretical model we will be looking at is
  called the kinetic theory of gases which assumes
  that
• The number of molecules in the gas is large, and
  the average separation between molecules is large
  compared with their dimensions.
• The molecules obey Newtons laws of motion, but
  as a whole move randomly.
• The molecules interact only by short-range forces
  during elastic collisions. The molecules make
  elastic collisions with the walls.
• The gas is a pure substance, containing identical
  atoms or molecules.

38
1.10.5 The kinetic theory of gases - Pressure
0

• It can be shown that the pressure exerted on a
  wall of a container by atoms (or molecules)
  moving with an average squared speed of is
  given by
• Thus, the pressure is proportional to the number
  of molecules per unit volume, and to the average
  translational kinetic energy of the atoms.

39
1.10.5 The kinetic theory of gases - Temperature
0

• It can be shown that the temperature of a gas is
  directly related to the average molecular kinetic
  energy.
• For monatomic gases, this is the only type of
  internal energy the gas can have, thus the
  internal energy (U) of the gas is given by

40
The kinetic theory of gases Root mean square
speeds
0

• The square root of is called the
  root-mean-squared speed, or rms speed of the
  molecules.
• Where M is the molar mass in kg/mol.

41
1.11 Energy in Thermal processes
0

• In this section we will be looking at the energy
  involved in changing either the temperature, or
  the state, of an object.
• By change of state, we mean the object goes from
  solid to liquid, liquid to gas, or in the other
  direction (gas to liquid or liquid to solid).
• We will also be considering all of the ways that
  energy can be lost by a hot object, namely
  conduction, convection or radiation.

42
1.11.1 Internal energy and heat
0

• We extend our definitions of the energy that an
  object can have to include internal energy.
• This internal energy includes, amongst other
  things, the temperature of an object. The formal
  definition is
• The internal energy (U) is the energy associated
  with the microscopic components of a system (i.e.
  the atoms and molecules).
• It includes kinetic and potential energy
  associated with the random translational,
  rotational, and vibrational motion of the atoms
  or molecules that make up the system as well as
  intermolecular potential energy.
• The units of internal energy are the Joule (J).

43
1.11.1 Heat
0

• We are going to use the phrases internal energy
  and heat quite precisely.
• We will define heat as
• The mechanism by which energy is transferred
  between a system and its environment because of a
  temperature difference between them.
• The symbol Q will be used to describe the amount
  of energy transferred by heat between two
  objects. The unit of heat will be the Joule (J).
• Note that there is an older unit, sometimes used,
  called the calorie. This is defined as the
  energy necessary to raise the temperature of 1g
  of water from 14.5 oC to 15.5 oC. We convert cal
  to Joules via
• 1 cal 4.186 J
• This is called the mechanical equivalent of
  heat.
• On food labels, the Calories that are quoted are
  actually kilocalories (1Calorie 1000 calories)

44
1.11.2 Specific heat
0

• So what is the energy required to raise the
  temperature of any object by a certain
  temperature? This clearly will depend upon what
  the object is that is being heated.
• The energy Q required to raise the temperature of
  an object of mass m by a temperature ?T is
• Here c is a constant which depends upon the
  object. It is called the specific heat of the
  material.

45
1.11.3 Calorimetry
0

• We can work out the specific heat of an object by
  heating it up to a known temperature, then
  placing it in water, and noting the change in
  temperature of the water after the system reaches
  equilibrium.
• The energy lost by the object is equal to the
  energy gained by the water. mw is the mass of
  the water, mx is the mass of the object, Tw is
  the initial temerature of the water, and Tx is
  the initial temperature of the object.

Tx
T
Tw
T
46
1.11.4 Latent heat and phase change
0

• In some circumstances, transferring energy via
  heat to an object does not results in a change of
  temperature or the object, but changes the phase
  of the object.
• This means that the object goes from solid to
  liquid, or liquid to gas. The energy required to
  change the phase of an object is given by
• Where m is the mass of the object, and L is the
  latent heat of the object.
• The or in the equation is determined from the
  direction of the energy flow (e.g. ve for going
  from solid to liquid, -ve for going from liquid
  to solid).

47
1.11.4 Latent heat
0

• The value for the latent heat depends upon the
  object, and upon the phase change occurring.
• To go from a solid to liquid, we use the latent
  heat of fusion, Lf.
• To go from a liquid to a gas, we use the latent
  heat of vaporization, Lv.
• The reason that there is no change in temperature
  during a phase change is that all the energy is
  going in to rearranging the molecules (e.g.
  breaking the bonds between the molecules).

T
Steam
Water steam
100
0
-20
Energy (J)
Ice
Ice water
Water
48
1.11.5 Energy transfer by thermal conduction
0

• If an object has a temperature difference with
  its surroundings, there are various ways it can
  transfer energy with those surroundings.
• We will first consider the mechanisms of
  conduction.
• Consider an object which is connected to a
  heating source at one side, and a cold source at
  the other. Energy will flow through the object
  from the hot side to the cold side.
• This is called conduction, or thermal conduction.
  It occurs because the molecules or atoms next to
  the hot side move more rapidly, and collide with
  their neighboring molecules. This continues
  along the length of the object, until energy
  flows across the whole object.

49
1.11.5 Energy transfer by thermal conduction
0
Th
Tc

• Consider a rod of length L, which is in contact
  with a hot (Th) and cold (Tc) reservoir.
• How well energy is transferred through the object
  depends upon a quantity of the material called
  the thermal conductivity, k (units J
  s-1 m-1 oC-1).
• It also depends upon the length of the object,
  the cross sectional area of the object, A, and
  the temperature difference between the two sides.
• The rate of energy transfer, or the power, is
  given by

L
50
1.11.5 Thermal conduction with compound materials
0

• If a material is made up of more that one
  material, all of which have different k values,
  and different lengths, we need to modify the
  previous equation for the rate of energy flow.
• We define a new quantity, called the R value, for
  each component of the object, where RiLi/ki. We
  can calculate an R-value for each part of the
  object. The rate of energy transfer through the
  object is given by

51
1.11.6 Energy transfer by convection
0

• If you hold your hand above a flame, then you can
  feel the heat of the flame. This is because of
  convection.
• Convection happens because the substance moves,
  bringing energy with it. In the example above,
  the hot air above the fire rises, carrying energy
  with it.
• The substance moves because of changes in the
  density. In the above example, the hot air above
  the flame expands. This decreases its density,
  the less dense air then rises (Archimedes
  principle), with colder air taking it place.
• Convection occurs in many places
• Convection currents in the air
• Water in a kettle
• The area known as the convection zone in the sun,
  transfers heat from the hot interior, to the less
  hot surface.

52
The solar surface looks like this
0
There is a region below the surface of the sun
called the convection zone
Here you can see the convection cells in motion
53
1.11.7 Energy transfer by radiation
0

• Consider again the flame from the convection
  section. If you are a short distance in front of
  the flame, you can still feel its heat. The
  reason you can feel the heat of the flame is
  because of radiation.
• All objects radiate energy in the form of
  electromagnetic radiation (e.g. infra-red,
  visible, X-rays depending upon the temperature
  of the object).
• This release of radiation represents a flow of
  energy away from the object.
• Note that a net flow of energy, due to radiation,
  only occurs if the object is at a different
  temperature from its surrounding. Otherwise, the
  flow into and out of the object are equal.

54
1.11.7 Energy transfer by radiation
0

• The rate of energy loss, due to radiation is
  given by
• Where P is the power in Watts
• A is the surface area of the object
• e is called the emissivity and depends upon the
  surface properties of the material (e.g. for a
  perfect black body e1)
• ? is a constant 5.669x10-8 Wm-2K-4

55
1.11.7 Energy transfer by radiation
0

• The previous equation just gives the energy
  radiated by an object. The object will also
  absorb radiation from the surroundings. Thus,
  the net power flow from an object at temperature
  T, which is surrounded by a material of
  temperature T0 is
• (note that T should be in Kelvin)

56
1.12 The Laws of Thermodynamics
0

• In this chapter we will look at the laws
  governing systems which have energy added or
  removed from them.
• Before we saw that PVnRT, but didnt look at
  what was causing the volume, pressure or
  temperature to change.
• In this section we will work out exactly what
  energy (Q) or work done (W) is required to make
  each of these properties change.

57
1.12.1 Work in thermodynamic processes
0

• Consider a piston that is being compressed by a
  force F. The compression is slow enough that the
  system is always in thermodynamic equilibrium.
• If the pressure does not change during the
  compression, the process is called isobaric.
• The work done by the force is

F
?y
P
58
1.12.1 PV diagrams in thermodynamics
0

• The work done on a gas that takes it from some
  initial state to some final state is the negative
  of the area under the curve on a PV diagram.
• This is true whether or nor the pressure remains
  constant.
• Thus, the work done on a system depends upon the
  process by which it goes from initial to final
  state.

P
i
f
- Area work done
V
P
i
f
- Area work done
V
59
1.12.2 The first law of thermodynamics
0

• We want to be able to relate the change in
  internal energy of a system (?U) to the energy
  transferred by heat (Q) and the work done on the
  system (W).
• The first law of thermodynamics states that
• The change in internal energy of a system is
  equal to the sum of the energy transferred across
  the system boundary by heat, and the energy
  transferred by work.

60
1.12.2 Sign convention for the 1st law.
0

• Q is
• Positive if there is a transfer of energy via
  heat into the system.
• Negative if there is a transfer of energy via
  heat out of the system.
• W is
• Positive if there is work done on the system
• Negative if the system does work on the
  surroundings.
• ?U is
• Positive if there is an increase in temperature
  of the system
• Negative if there is a decrease in the
  temperature of the system

61
1.12.2 Consequences of the 1st law
0

• If a system is in isolation (Q0, W0), the
  internal energy of the system must be constant.
• If either the pressure, volume or temperature are
  constant, then we can work out the energy
  transfer by heat (Q), and work done on the system
  (W) required to change the remaining P, V or T
  variables.
• In a cyclic process, where a system returns to
  its initial state, ?U0, and thus Q-W.

62
1.12.2 Isothermal process
0

• If the temperature is constant in the system.
  This is called an isothermal process.
• Since PnRT/V, if we increase the volume of the
  system, the pressure must drop.
• Since ?U(3/2)nR ?T, ?U0
• Thus
• This Q is the energy input required to maintain
  the temperature of the system.

P
1
2
V
P
1
2
T
63
1.12.2 Isovolumetric process
0

• If the volume of the system remains constant, it
  is known as isovolumetric.
• Since PVnRT, as the temperature increases there
  must be an increase in pressure.
• If there is no change in volume, then there is no
  work done (W-P?V0). Thus,
• That is, the increase in temperature is caused by
  an input of energy via heat to the system.

P
2
1
V
P
2
1
T
64
1.12.2 Isobaric process
0

• If the pressure doesnt change in the system, it
  is called isobaric.
• If the temperature is increased, then the volume
  must increase because
• In an isobaric process both the work done and the
  energy transferred by heat are non-zero, and we
  get the change in internal energy from

P
1
2
V
P
1
2
T
65
1.12.2 Adiabatic process
0

• If there is no energy transferred by heat to a
  system, it is called an adiabatic process (Q0).
• We can use
• To get the change in internal energy of an ideal
  monotonic gas, and hence the work done on the
  system.

P
1
2
V
P
1
2
T
66
Review of thermodynamic equations
0

• In solving thermodynamic, here are the main
  equations which are used.
• The ideal gas equation
• Work done
• 1st law of thermodynamics
• Note that the following phrases are often used.
• Isothermal process temperature doesnt change
• Isovolumetric process volume doesnt change
• Isobaric process pressure doesnt change
• Adiabatic process no heat energy transferred to
  system (?Q0)

67
1.12.3 Heat engines and the 2nd Law of
Thermodynamics
0

• A heat engine converts internal energy (U) of a
  system into other useful forms (e.g. mechanical,
  electrical).
• For a heat engine to keep going, the loss in
  internal energy must be replaced, usually from
  some source of heat.
• A heat engine has the following stages
• Energy (Qh) is transferred to the engine from a
  hot reservoir (e.g. a coal fire in a power
  station).
• Work (Weng) is done by the engine (in a turbine).
• Energy (Qc) is expelled (lost) to a cold
  reservoir (e.g. the surroundings).

Hot reservoir at Th
Qh
Weng
Engine
Qc
Cold reservoir at Tc
68
1.12.3 Heat engines
0

• Note that a heat engine is cyclic, the engine
  returns to its initial conditions after one cycle
  of the process (?U0).
• So the 1st law gives
• with
• Thus,
• Note that this is equal to the area enclosed in a
  PV diagram.

WengArea
P
V
69
1.12.3 Heat engine efficiency
0

• The thermal efficiency of a heat engine is the
  ratio of the work done by the engine to the
  energy absorbed from the hot reservoir.
• Thus, a heat engine is 100 efficient only if
  there is no energy lost to the cold reservoir.

70
1.12.3 The 2nd law of thermodynamics
0

• This leads us to the 2nd law of thermodynamics
• It is impossible to construct a heat engine that,
  operating in a cycle, produces no other effect
  than the absorption of energy from a reservoir
  and the performance of an equal amount of work.
• This is the same as saying as it is impossible to
  have a heat engine which is 100 efficient.

71
1.12.3 Carnot engine
0

• The most efficient heat engine possible is called
  a Carnot engine. This is a theoretical engine,
  in practice no real engine can be as efficient.
• The efficiency of a Carnot engine is

P
A
Qh
B
Th
D
Tc
C
Qc
V
72
1.12.4 Entropy
0

• We will define another state variable which can
  be used to describe the thermodynamic properties
  of a system.
• This new quantity we will call entropy (S).
• The change in entropy ?S between two equilibrium
  states is given by the energy Qr, transferred
  along the reversible path divided by the absolute
  constant temperature T of the system in this
  interval.
• You can think of entropy as a measure of the
  disorder in a system.
• The entropy of the universe increases in all
  natural processes.

73
1.12.5 Entropy and disorder some implications

• An isolated system tends towards greater
  disorder, and entropy is a measure of that
  disorder.
• A disorderly arrangement is much more probable
  than an orderly one if the laws of nature are
  allowed to act without interference
• One can have a decrease in the entropy in part of
  an isolated system, but only if there is an
  increase in the entropy of another part of the
  same system.
• Entropy makes perpetual motion machines
  impossible.
• Entropy also gives us a way to indicate the
  forward motion of time.