Topic 3: Thermal Physics
3.1 Thermal concepts
❑ Temperature, Heat and Internal energy
➢ Temperature
• Temperature tells us how hot or cold a body is with respect to some standard.
• Temperature is also the property that determines the direction of heat (thermal energy) transfer between two
objects.
• Temperature is a measure of the average kinetic energy of the molecules in a substance.
 The following points must be noted:
 The higher the temperature, the more do the atoms or molecules move.
 If two substances have the same temperature, then their molecules have the same average kinetic energy.
 TEMPERATURE SCALE Most of the time, there are only two sensible temperature scales to choose
between the Kelvin scale and the Celsius scale.
• Temperature is measured in
Kelvin (SI unit) or Celsius.
• To convert from oC to K, simply add 273 (0 oC = 273K)

T (K) = T (0C) + 273
 In the Kelvin scale the size of a "degree" is the same as in Celsius scale.
 The difference between the upper (the boiling point of pure water) and the lower point (melting point of
pure ice), in both scales, divided into 100 degree steps.
 The following points must be noted:
 A thermometer is a common instrument used to measure temperature.
 All temperature scales are based on some physical property that changes with changing temperature
(the property must have a different value at each temperature to be measured).
❑ Heat (otherwise known as thermal energy), heat transfer and work
Heat and work are terms used to describe energy in the process of transfer:
• Heat (Thermal energy) naturally flows from hot to cold.
• Heat is a form of energy that is transferred from one object to another due to a temperature difference
between the two objects. And it (naturally) flows from hot to cold.
• Heat (Thermal energy) is the transfer of energy between a system and its surroundings.
 Heat refers to non-mechanical energy transfer from one system to another (from microscopic point of view).
 The following points must be noted:
 Thermal contact: when objects are in contact such that heat is able to flow from one object to another,
the objects are said to be in thermal contact.
 Thermal equilibrium: When two objects are in thermal equilibrium, the net heat transfer between them
is zero (i.e. they are thermal equilibrium when the rate of energy absorption is equal to the rate of
energy emission/or when they temperature stay the same.
• Work is energy that is transferred by a force moving its point of application over a distance. Work is the
energy transmitted from one system to another.
 Work refers to the mechanical energy transfer from one system to another (from macroscopic point of view).
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 The following points must be noted:
When analysing something physical, we have a choice.
 The macroscopic: studying the system as a whole and sees how it interacts with its surroundings.
 The microscopic: studying from inside the system to see how its component parts interact with each other.
❑ Kinetic energy and potential energy of the molecules
 If the temperature of an object changes then it must have gained or lost energy. From the microscopic
point of view, the molecules must have gained or lost this energy.
 The two possible forms of energy are kinetic energy & potential energy.
 The molecules have random kinetic energy because they are moving. To be absolutely precise, the kinetic
energy is mainly due to translational motion (the whole molecule is moving in a certain direction),
rotational and vibrational motion (the molecule is rotating and vibrating about one or more axes).
 The molecules have intermolecular potential energy because of the intermolecular forces of attraction
between particles and the energy stored in bonds (bond energy).
❑ Internal energy
• Internal energy: is the total intermolecular potential energy plus total random kinetic energy of the
molecules.
 The following points must be noted:
 The internal energy of a system can be changed by heating and/or doing work on or by the system.
 When the molecules move faster (increases Ek) and move apart (increasing Ep), therefore the internal
energy increases.
❑ Thermal properties of matter: Heat capacity and Specific heat capacity
 Different substances have different capacities of storing internal energy.
• Heat capacity: is the heat required to raise the temperature of a substance by 10C (or by 1K).
Q
Heat capacity, C =  T

Q=CT
(Q: heat given in or taken out)
❖ The SI unit of heat capacity can be expressed as J 0C – 1 or JK– 1
• Specific heat capacity: is the heat required to raise the temperature of unit mass of a substance by 10C (or
by 1K).
Q
specific heat capacity, c = m  T
 Q=mcT
❖ The SI unit of specific heat capacity can be expressed as Jkg–1 0C –1 or Jkg– 1 K – 1
 Rearranging, we get: heat capacity = m c
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❑ Investigate: Determining the Specific heat capacity
(Paper 3)
➢ The specific heat capacity of a metal – Electrical methods
 The specific heat capacity of a metal such as aluminium can be determined using an electrical method as
shown in the diagram.
Procedur
e:
T1
T2
 Source of experimental error
 The loss of thermal energy from the apparatus.
 Container for the substance and heater will also
warmed up.
 It will take some time for the energy to be shared
uniformly through the substance.
Heat gained by aluminum block = m c (T2 – T1)
m c (T2 – T1) = V I t
Hence
T2 – T1
➢ The specific heat capacity of a liquid – Electrical methods
 The specific heat capacity of a liquid can be determined using an electrical method as shown in the
diagram.
With the set-up as shown:
 A calorimeter, usually made of copper or aluminium, is
used to contain the liquid. The value of the specific heat
capacity of the calorimeter must be known.
 Procedure:
 Measure the mass of the calorimeter when empty M
 Measure the mass of the liquid m
 Record the initial temperature T1
 Turn on the heater and start the stop clock at the same moment
 Record the voltage (V volts) and current ( I amps)
 Turn the heater off after 5 minutes
 Record the highest temperature T2 – may have to have a short time for heat to conduct through the sample.
Heat supplied by heater = I V t
Heat gained by liquid and calorimeter = m cliquid (T2 – T1) + mc calorimeter (T2 – T1)
Hence,
heat gained by liquid and calorimeter = heat supplied by heater
m c liquid (T2 – T1) + mc calorimeter (T2 – T1) = I V t
c liquid =
V I t – M c calorimeter
m
m T
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➢ The specific heat capacity of a liquid – mixture methods
 The known specific heat capacity of one substance can be used to find the specific heat capacity of another
substance.
 Set-up the apparatus as shown
Temperature TA (hot)
Temperature TB (cold)
Before
Mix together
Mass mA
Mass mB
After
Temperature Tmix
 Procedure:
 The main source of experimental error
 The loss of thermal energy from the
apparatus – particularly while the liquids
are being transferred.
 The changes of temperature of the
container also need to be taken into
consideration for a more accurate results.
 Measure the masses of the liquids mA and mB
 Measure the two starting temperatures TA and TB
 Mix the two liquids together.
 Record the maximum temperature of the mixture Tmix.
If no energy is lost from the system then,
Heat lost by substance A = Heat gained by substance B
mA cA (TA – Tmix) = mB cB (Tmix – TB)
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 KINETIC THEORY
• The kinetic theory of matter states that
 Matter is made up of tiny (a very small) particles (atoms, molecules) that are in constant motion.
 As well as being in continuous motion, molecules also exert strong electric force on one another when they
are close together. The forces are both attractive and repulsive.
➢ We can explain a number of observations in terms of the kinetic theory, such as:
 the three states of mater [solid, liquid and gas (or vapour)] and changes between the states
 evaporation
 the pressure exerted by a gas
 Phases (States) of matter
 Solids, liquids and gases are three familiar 'states of matter'
Water is an example of a substance that can exist in any of the three states.
 The differences between the three states of matter are given in the table below.
Solid
A solid has a fixed volume and
shape. Its atoms are close together,
and cannot move around - their
motion consists of continuous
vibrations
Liquid
A liquid has a fixed volume, but no
fixed shape - it takes on the shape of
any container it is placed in. Its atoms
are also close together, but they can
move around inside the liquid,
'slipping' over each other
Gas
A gas has no fixed volume and no fixed
shape - it fills all the space available to
it. Its atoms are far apart and move
around freely - they collide with each
other and with the walls of the container
 Phase changes and latent heat
→ An 'ideal' graph of temperature against time (not drawn to scale) would look like:
 Changes of state (or 'phase') occur at fixed temperatures.
 We know that water melts at 00C and boils at 1000C.
 On the graph that we get flat sections during the changes
of phase – as the temperatures are fixed.
• During a change of phase, all the heat supplied is used to
bring about the change, and none of it is used to raise the
temperature.
• The energy given to the molecules does not increase their
kinetic energy so it must increase their potential energy.
• Intermolecular bonds are being broken and this takes
energy.
 When the substance freezes bonds are created and this process releases energy.
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Mr. Khalid Zarour
Note: since the average KE, and therefore the average speed, of molecules in a substance depends on the
temperature of the substance, if the temperature is constant, then so is the average KE of the molecules.
Hence, when water boils, the average KE (and speed) of the water molecules stays constant, because the
temperature of the water is constant (at 1000C). All the heat absorbed is used to change the water to
steam, and none is used to raise the temperature of the water.
Question:
• Suggest why, in terms of the molecular model, the energy associated with melting is less than that
associated with boiling.
Answer:
• in boiling, energy is required to break bonds (in vaporization) and to separate molecules; in melting,
(more) energy available to overcome bond energies of molecules without large separation;
➢ Explain in terms of molecular behavior why temperature does not change during a phase change.
During phase change, energy is continuously provided, but temperature does not increase because energy is
used to break intermolecular forces between particles, the heat added transfers to increase in potential
energy, so the average kinetic energy stays the same, and so the temperature stays the same because
temperature is a measure of the average kinetic energy.
(milting)
Solid → liquid
(freezing/solidifying) Liquid → solid
(vaporization)
Liquid → gas
(condensation)
Gas → liquid
➢ Explain the process of phase changes in terms of molecular behavior.
Melting point
Boiling point
• When the solid is heated the particles of the solid
• Temperature between milting point and boiling
vibrate at an increasing rate as the temperature is
point → increases
increased.
• At boiling point, particles gain energy to
• The vibrational Ek of the particles increases.
overcome intermolecular forces
• At milting point, the Ep of the system increases as
• Ep increases
the particles move a part.
• Heating continuous until every particle changes
phase to gas
◼ Specific latent heat,
The specific latent heat of fusion, of a substance, Lf: is the heat required to change unit mass of the
substance from solid to liquid without change of temperature.
The specific latent heat of vaporisation of a substance, Lv: is the heat required to change unit mass of the
substance from liquid to vapour without change of temperature.
Q
Lf (specific latent heat of fusion) = m
→
Q = m Lf
Q
Lv (specific latent heat of vaporization) = m
→
Q = m Lv
(Q: heat given in or taken out)
 The SI unit of specific latent heat is Jkg .
–1
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Mr. Khalid Zarour
❑ Investigate: Determining the Specific latent heat
(Paper 3)
➢ The specific latent heat of vaporization – Electrical methods
The experiment would be set up as below:
V
d.c. supply
A
Water
Heater
Top-pan balance
g
 Procedure:
 Switch the current on and maintained constant using the variable resistor.
 Take the readings of the voltmeter and the ammeter were.
 Take the reading of the top-pan balance when the water was boiling steadily, and, simultaneously, start
stopwatch.
 Take the reading of the top-pan balance again after t seconds.
Itv
 The specific latent heat, L = (m1 – m2)
Sources of experimental error
 Loss of thermal energy from the apparatus.
 Some water vapour will be lost before and after timing.
➢ The specific latent heat of fusion – mixture methods
 Providing we know the specific heat capacity of water, we can calculate the specific latent het of fusion for
water.
 In the example below ice (at 00 C) is added to warm water and the temperature of resulting mix is measured.
 If no energy is lost from the system then,
ice
mass : mice
Temperature: 00 C
water
Mass : mwater
Temperature: T 0C
Mix together
Energy lost by water = energy gained by ice
mwater cwater (Twater – Tmix) = mice Lfusion + mice cwater Tmix
mix
mass : mice + mwater
Temperature: Tmix0 C
Sources of experimental error
 Loss (or gain) of thermal energy from the apparatus.
 if the ice had not started at exactly zero, then there would be an additional term in the equation in order to account
energy needed to warm the ice up to 0 0 C.
 Water clinging to the ice before the transfer.
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◼ Using a 'cooling curve' to determine melting point
 Stearic-acid is a white solid at room temperature, and has a fairly low melting point, which makes it suitable
for this experiment:
 The water is boiled till the acid melts and reaches about 900C.
 The tube is then taken out of the water and placed in an empty beaker.
The temperature of the acid is recorded every minute until it is
completely solid.
 If we plot temperature against time, we get a graph like:
 The graph becomes flat when the acid starts to turn solid, and this temperature is its freezing or melting point.
◼ Cooling Curves and Heating Curves
• Graphs with temperature (y) against time (x)
 In a cooling curve: you are taking energy away at a constant rate (making bonds)
 In a heating curve: you are giving energy in at a constant rate (breaking bonds)
Power (rate of adding heat) = mc  gradient
• They should actually be curved because there is heat loss due to surrounding.
◼ Boiling and evaporation
Boiling: causes liquids to change to gases. Happens
Evaporation: causes liquids to change to gases.
through and always at the same temperature.
Happens at the surface of the liquid and can happen at
all temperatures (without reaching its boiling point).
 The rate of evaporation increases if:
 The surface area of the liquid increases
 The temperature of the liquid increases
 The pressure above the liquid decreases
 The humidity of the air above the liquid decreases
 There is a breeze.
 Cooling by evaporation:
• In evaporation the faster moving molecules (and therefore those with the highest KE) leave the surface
causing the average KE of the liquid to fall; a fall in average K.E. is the same as a fall in temperature.
 The diagram shows the differences between
boiling and evaporation.
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3.2 Modelling a gas
❑ Assumptions of the kinetic model of an ideal gas
 The molecules obey Newton’s laws of mechanics.
 There are no intermolecular forces. (so, it has no potential energy and its internal energy is only the total KE.)
 The molecules are treated as points (the volume of the molecules is negligible compared with the volume of
the gas itself).
 The molecules are in random motion.
 The collisions between molecules are elastic (no energy is lost).
 The duration of collisions is very small compared with the time between collisions.
❑ Pressure
 Pressure is the force acting normally on the unit area of the surface. And it is calculated from:
Pressure, p =
Force, F
Area, A
N
m2
It’s in the data booklet
Nm–2 = pascal
 Pascal: the pressure exerts when a force of 1 N acts normally on an area of 1 m2.
❑ Pressure in gases
 Pressure in gas is the collisions of gas molecules with surfaces which produce the pressure exerted by a gas.
 Why a Gas Exerts a Pressure?
 Consider the molecules of a gas moving at random in
a container, as shown in the diagram.
 The molecules are continually colliding with each other and with the walls of the container. It is assumed that
all collisions are elastic. When a molecule collides with the wall, a change of momentum occurs. The change
in momentum is caused by the force exerted by the wall on the molecule. By Newton’s third law, the molecule
exerts an equal but opposite force on the wall. The total force due to all the colliding molecules divided by the
area over which the force acts gives the pressure of the gas.
The macroscopic behaviour of an ideal gas in terms of a molecular model
 Pressure law states that:
 Charles’s law states that:
Boyle’s law states that:
 For a fixed mass of gas:
 For a fixed mass of gas:
 For a fixed mass of gas:
at a constant volume, the pressure is
at a constant pressure, the
at a constant temperature, the
directly proportional to its absolute
temperature is directly proportional
pressure
is
inversely
temperature.
to the volume.
proportional to the volume.
 Microscopically explanation:
 Microscopically explanation:
 Microscopically explanation:
If the temperature of the gas
If the temperature of the gas is
If the volume of the gas is
increased,
the
average
kinetic
energy
increased, the average kinetic energy
increased, the rate with which
of its molecules increases. Therefore, the molecules hit the wall –
and speed of the molecules increases
the molecules hit the wall "harder"
(the higher speed, the larger the
average total force decreases.
and also more frequently. The total
change in momentum of the
Therefore the pressure
force
due
to
the
collisions
is
greater.
molecules). Thus, they will make more
decreases.
Therefore the pressure increases. But
collisions per second and harder
if the volume of the gas increases,
collisions, with the surfaces of the
container and also more frequently – then the rate at which these
collisions take place on a unit area of
for both these reasons, the total force
the wall must goes down. Then, the
due to the collisions is greater.
average force on a unit area of the
Therefore the pressure increases.
wall can thus be the same. Therefore
the pressure remains the same.
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Mr. Khalid Zarour
❑ Answered Questions
(1) Why the Temperature of a Gas Increases when it is compressed rapidly?
 The diagram below represents a quantity of gas in a cylinder with a moveable piston.
 Microscopically explanation, if a molecule experiences an elastic collision with a stationary wall it will
rebound at the same speed. However, a molecule colliding with the surface of the piston as it is moving so as
to compress the gas into a smaller volume will rebound moving faster than before the collision. Thus the
average speed of the molecules will increase. This means the temperature will increase.
(2) Why the Temperature of a Gas will stay the same when it is compressed slowly?
 Microscopically explanation, if a gas is compressed slowly, the speed with which the molecule rebound off
the piston is the same as that before the collision with the piston. Hence, the average kinetic energy of the
molecules stays the same. Since the average kinetic energy is proportional to the absolute temperature of the
gas, the temperature will stay the same.
 The macroscopic experimental laws of an ideal gas
 Mathematically we can write the  Mathematically we can write the
pressure law as:
Charles’s law as:
p/T = constant
p1/T1 = p2/T2
V/T = constant
V1/T1 = V2/T2
 Mathematically we can write the
Boyle’s law as:
p V = constant
p1 V1 = p2 V2
Where:
p: is the pressure (Pa≡ Nm-2)
T: is the temperature (K)
Where:
V: is the volume (m3)
T: is the temperature (K)
Where:
p: is the pressure (Pa≡ Nm-2)
V: is the volume (m3)
 This gives a straight line in a p-T
graph.
 This gives a straight line in a V-T
graph.
 This gives a hyperbola in a p-V
graph
 Since there can be no
 Since there can be no
negative pressure, the point
negative volume, the point
where the p-T graph hits the
where the V-T graph hits the
T-axis is the lowest possible
T-axis is the lowest possible
temperature: 0 K = –273 0C.
temperature: 0 K = –273 0C.
This temperature is known as
This temperature is known as
absolute zero.
absolute zero.
⚫ Absolute Zero of Temperature:
 It is the temperature at which a gas would exert no pressure.
Or
 It is the temperature at which a gas would have no volume.
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❑ The equation of state of an ideal gas
 The three preceding experimental laws can be combined together to obtain one mathematical relationship.
pV
T
= constant
[Mass must be the same (i.e. no particles escape)]
 The value of this constant depends on the mass and type of gas.
 The value of this constant is proportional to the number of moles n of the gas in the sample.
 So, the value of this constant = n R, where R: is the universal constant and it is called the molar gas
constant.
R = 8.314 J mol–1 K –1
 Thus, finally, the equation of sate is
PV=nRT
(T must always be in kilven.)
It’s in the data booklet
 Mole, molar mass and the Avogadro constant
 Avogadro constant: One mole of substance contains the same number of molecules as in 12 grams of
carbon-12.
 Its numerical value is NA = 6.02 x 10 23 molecules mol –1
Mole: An amount of substance containing the same
number of molecules as in 12 grams of carbon-12.
 The number of moles of a substance can be found
It’s in the data booklet
n=
N
NA
where: n: the number of moles of a substance (mol)
N: the total number of molecules
 Molar mass: the mass of one mole of a substance and is expressed in g mol–1.
 A simple rule applies:
If an element has a certain mass number, A, then the molar mass will be A g mol–1.
 The mass m, in gram, of a substance can be expressed in terms of the number of moles n, as
m
n = Mr
where: Mr is the molar mass of the substance (g)
 Ideal Gases and Real Gases
 Ideal Gas: An (imaginary) gas which follows the
ideal gas equation of state (PV = nRT) perfectly for
all values of P, V, and T. And it cannot be liquefied.
 In order for a gas to be considered ideal
 An ideal gas is made up of particles that are single
points with no volume.
 An ideal gas is made up of particles that do not
attract or repel one another.
 Real Gas: A gas that does not follow the ideal gas
equation of state (PV = nRT) perfectly for all values
of P, V, and T. the
 In order for a gas to be considered real
 A real gas is made up of atoms or molecules that
actually take up some space, no matter how small.
 A real gas is made up of atoms or molecules that
may attract one another strongly
Or they may attract one another hardly at all.
 This means that the total volume of its molecules
must be negligible compared with the volume
 This means that the real gas molecules attract each
occupied by the gas and there must be negligible
other and do not occupy negligible volume when the
forces of attraction between its molecules.
gas is at high pressure.
• Real gases, however, can approximate to an ideal gas behaviour providing that the intermolecular forces are
small enough to be ignored. For this to apply, the pressure/density of the gas must be low and the temperature
must be moderate.
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 Link between the macroscopic and microscopic
• The equation of state for an ideal gas, pV = nRT, links the three macroscopic properties of a gas (p, V and T).
• Kinetic theory describes a gas as being composed of molecules in random motion and for this theory to be
valid, each of these macroscopic properties must be linked to the microscopic behaviour of molecules.
• A detailed analysis of how a large number of randomly moving molecules interact beautifully predicts another
formula that allows the links between the macroscopic and the microscopic to be identified.
• The derivation of the formula only uses Newton’s laws and a handful of assumptions. These assumptions
describe from the microscopic perspective what we mean by an ideal gas.
(the detailed of this derivation is not required by the IB syllabus )
• The result of this derivation is that the pressure and volume of the idealized gas are related to just two
quantities:
2
pV = 3 N Ek
N: the number of molecules present
Ek: the average kinetic energy per molecule
Equating the right-hand side of this formula with the right-hand side of the macroscopic equation of state for
an ideal gas shows that:
2
nRT = 3 N Ek
𝑁
𝑁𝐴
but n =
𝑁
𝑁𝐴
2
RT = 3 N Ek
3 𝑅
Ek = 2
𝑁𝐴
T
→
Ek  T
It’s in the data booklet
the ratio
𝑅
𝑁𝐴
𝑅
is called the Boltzmann’s constant kB. kB =𝑁
𝐴
3
Ek = 2 kB T
It’s in the data booklet
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Mr. Khalid Zarour
 Experimental investigations
1. Pressure law
Independent
Temperature, t
V.
Dependent V.
Pressure, P
Controlled V
Volume, V
2. Charles’s law
Independent
Temperature, t
V.
Dependent V.
Volume, V
Controlled V
Pressure, P
3. Boyle’s law
Independent
V.
Dependent V.
Controlled V
Pressure, P
Volume, V
Temperature, t
• Fixed volume of gas is
trapped in the flask.
Pressure is measured by a
pressure gauge.
• Temperature of gas altered
by temperature of bath –time
is needed to ensure bath and
gas at the same temperature.
• Volume of gas is trapped in
capillary tube by bead of
concentrated sulphuric acid.
• Concentrated sulphuric acid
is used to ensure gas remain
dry.
• Heating gas causes it to
expand moving bead.
• Pressure remains equal to
atmospheric.
• Temperature of gas altered
by temperature of bath –time
is needed to ensure bath and
gas at the same temperature.
• Volume of gas measured
against calibrated scale.
• Increase of pressure forces
oil column to compress gas.
• Temperature of gas will be
altered when volume is
changed; time is needed to
ensure gas is always at room
temperature.
Good Luck
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