Particle model theory applied to energy transfer in state changes,
what is internal
energy and latent heat?
and particle motion in gases and gas pressure
Doc Brown's Physics Revision
Suitable for GCSE/IGCSE Physics/Science courses or
to using kinetic
particle theory to explain the properties of the three different states of matter
The particle model has been developed to explain the
properties of the three states of matter, namely gas, liquid and solid.
The particle model also provides a way of describing the
changes of state between a gas, liquid and the solid state of a material.
To change the state of a material requires either the
input of heat or the removal of heat from the material and this is called the
latent heat. and consider
the concept of internal energy.
The 'model' particle pictures below give you an idea of how the
states of matter (gas, liquid and solid) are viewed when applying the theoretical ideas
to explain how the three states of matter behave, especially when subjected to a
change in temperature.
You should be able to recognise
simple diagrams to model the difference between solids, liquids and gases
- the three states of matter.
Gases: There are almost
no forces of attraction between gas particles, they have the most kinetic
energy of the three states, the particles are completely free to move around
at random and they move at high speeds in all directions - so they have a
higher kinetic energy store than liquids. The free moving
particles have kinetic energy of movement and there is much empty space
between the particles.
Liquids: There are weak
forces of attraction between liquid particles (if there wasn't, you couldn't
have a liquid!), the particles are relatively close together but free to
move around at random but with lower speeds than in the gas. The free moving
particles still have kinetic energy of movement - not quite as high a
kinetic energy store as gases.
Solids: In solids there
are stronger forces of attraction between the particles which prevents the
particles moving around and passing each other. The particles are held in
fixed positions in a regular arrangement. Their even lower kinetic energy is
due to the particles (atoms or molecules) vibrating around their mean or
average positions in the crystal structure. So solids don't have as big a
movement kinetic energy store as gases or liquids.
The density of materials and the particle model of matter
More detailed descriptions of states
2. Internal energy
(KE shorthand for kinetic energy)
The particles of solids,
liquids and gases have different amounts of kinetic energy (KE).
In solids the particles vibrate with
kinetic energy but can't move around to another position, but in gases and
liquids the particles freely move from place to place with kinetic energy.
Particles have energy in their potential
energy stores due to their positions.
The energy stored in a system is stored
by the particles (atoms, ions, molecules) and the internal energy is the
total energy that the particles have in their kinetic and potential energy
When you heat a system energy is
transferred to the particles eg they move faster in gases and liquids
(increase in KE of movement from one place to another) or the particles
vibrate more strongly in a solid (increase in vibrational KE), so the
internal energy is increased when you heat a material.
Here, due to increase n temperature, the
increase in the thermal energy store is effectively the increase in
kinetic energy store of the particles because of the increased intensity
of vibration in a solid or the increase in speed of movement of the
particles moving about freely in a gas or liquid.
This absorption of heat, ie increase in
internal energy can cause an increase in temperature OR a change of state
e.g. melting or boiling if the particles are given sufficient thermal
Removing heat decreases the internal
energy, so the material cools to a lower temperature OR undergoes a change
of state e.g. condensing or freezing.
The size of the change depends on the
energy input, the mass of substance involved and the specific
heat capacity (which depends on the nature of the material).
Energy transfer in state changes and conservation of mass
BOILING or EVAPORATING
SUMMARY of the CHANGES of STATE between a gas, liquid and solid
All mass conserved in these
These are NOT
chemical changes !
As well as the transfer of heat energy by
conduction, convection and radiation, state changes like evaporation and condensation
also involves heat energy transfers and the particle model can be used to
When you heat a solid, the
vibrational kinetic energy of the particles is increased until they have enough KE to
weaken the interparticle bonds to allow melting and the particles are free
to move around in the liquid state.
With further heating above
the melting point, the inter-particle bonds are further weakened so that the particles at the surface with the highest KE can
escape the surface (evaporate) or vapourise to the gaseous state in the bulk liquid
(bubbles!) at the
If you cool the substance, the reverse
happens e.g. cool a gas so the interparticle bonds bring the particles
together to condense and form a liquid.
Further cooling reduces the KE of the
liquid particles so that when the temperature is reduced to the freezing
point, the interparticle forces are sufficient to 'club' the particles
together to form a solid.
All these physical state changes are
reversible by adding or removing heat energy, no new substances are formed
(NOT a chemical change) and all mass is conserved. What you start with is
what you finish with and all the original properties are retained.
The only difference between the states
of a substance is how the particles are arranged (as described in
section 1. above).
Note that in a closed system mass is
conserved in a system undergoing a change in state.
If you melt 100 g of ice, you get 100 g
However, even with mass conservation, you
can get a volume change, except for water, for the same mass, liquids occupy
a slightly larger volume and gases occupy a massively greater volume than
the liquid or solid form.
Ice is unusual that the solid ice
crystals are less dense than water - which is why ice floats!
State changes and LATENT HEAT
A historical curiosity - latent heat
('hidden' heat), which was unexplained until the particle theory of matter
Changes of state require either ...
(a) the addition of energy, increasing
the internal energy of the system, or ...
(b) the removal of energy, decreasing the
internal energy of the system
When a solid is heated from the solid
state to the gaseous state and the temperature of the system measured
continuously, there are two horizontal sections on the graph where the
temperature does not rise, despite the constant input of heat energy
(continuous heating). Typical results are shown in the heating curve
It is called the HEATING CURVE
As you heat the substance you are increasing the internal energy. BUT the temperature stays constant during the state changes of melting
at temperature Tm and boiling at temperature Tb (see diagram above).
This is because all the extra ('hidden') energy absorbed in
heating at these two temperatures
(called the latent heat of state change),
goes into weakening the inter–particle
forces (intermolecular bonds) to induce the state change without temperature rise,
to cause melting and then boiling to take place.
The heat gain at this point equals the heat energy
absorbed needed to
reduce the interparticle forces in melting or boiling - the latent heat.
During the state change the temperature stays
constant until all the latent heat is absorbed and the state change
completed, so no temperature rise can occur.
In between the 'horizontal' state change
sections of the graph, you can see the energy input increases the
kinetic energy of the particles and raising the temperature of the
substance as you expect as the internal energy increases.
For these state changes you have the addition of the
latent heat of melting at temperature Tm and the addition of the
latent heat of boiling at temperature Tb.
experiment to illustrate a 'heating curve'
You start with a beaker of crushed
ice into which you place a thermometer (-10 to 100oC
Place on a tripod and gauze and
record the temperature at the start.
To speed things up, heat the beaker
of ice steadily with a bunsen flame.
Continue to record the temperature
every minute until all the ice has melted and eventually the water will
Finish taking temperature readings
after 5 minutes of boiling.
Plot a graph of temperature versus
It should look like the graph above,
apart from the initial rise of temperature of solid ice.
You should get two horizontal
sections on the graph where the latent heat of fusion (melting at 0oC)
or the latent heat of boiling (vapourising at 100oC) are
being absorbed to weaken the intermolecular forces between the water
molecules, without rise in temperature.
As you cool a substance you are decreasing the internal energy. BUT the temperature stays constant during the state changes of
at temperature Tc and freezing at temperature Tf (see diagram below).
Similarly when a gas is cooled from
the gaseous state to the solid state and the temperature of the system
measured continuously, there are two horizontal sections on the graph
where the temperature does not fall, despite the constant removal of
heat energy (continuous cooling). Typical results are shown in the
cooling curve graph below.
It is called the COOLING CURVE
As you cool the substance you are decreasing the internal energy. BUT the temperature stays constant during the state changes of condensing
at temperature Tc, and freezing/solidifying at temperature Tf.
This is because all the extra
('hidden') heat energy removed on cooling at these temperatures (the
latent heat of state change), reduces the particle KE and allows the
strengthening of the inter–particle forces without temperature fall to
allow condensation and then freezing to take place.
The heat loss is compensated by the increased intermolecular force
attraction which releases heat energy.
During the state change the temperature stays
constant until all the latent heat is removed and the state change
completed, so no temperature fall can occur.
In between the 'horizontal' state change sections of the
graph, you can see the energy 'removal' reduces the kinetic energy of
the particles, lowering the temperature of the substance.
For these state changes you have the removal of the
latent heat of condensation at temperature Tc and the removal of
the latent heat of freezing at temperature Tf.
experiment to illustrate a 'cooling curve'
Its not so easy to do a cooling curve
by reversing the experiment described above for a 'heating curve'.
However, you can do a 'partial'
cooling curve experiment using a low melting solid like stearic acid.
You start with boiling tube with a
few cm depth of stearic acid in it plus a 0 to 100oC
Place the boiling tube in hot water
until all the 'waxy' stearic acid melts.
Keep on heating it until the
temperature reads at least 80oC.
Remove the boiling tube and record
the temperature of the melted acid.
Allow the tube of melted acid to cool
on its own and record the temperature every minute until all of the acid
has gone solid AND keep on recording for at least another 5 minutes.
Plot a graph of temperature versus
time and it should look like the right-hand sections of the graph above.
In the middle of the graph should be
a horizontal section corresponding to the transfer of the latent heat of
fusion to the surroundings at the freezing point - to enable the kinetic
energy of the molecules to fall sufficiently for the intermolecular
forces to increase and cause solidification (crystallisation of the
stearic acid molecules).
Note for (a) and (b) ...
You can use
Specific latent heat
The specific latent heat of a
substance is the quantity of energy need to change 1 kg of the material
from one state to another without change in temperature.
(a) In heating a material to effect a
state change e.g. melting or boiling, the specific latent heat must be
(b) In cooling a material to effect a
state change e.g. condensing or freezing, the specific latent heat must
be removed (released) from the system.
Specific latent heat values differ
from substance to substance because of different values of
inter-particle forces (intermolecular bonding) and also the state change
itself for a specific substance (solid <=> liquid OR liquid<=> gas).
Generally speaking latent heats of
boiling/condensing are numerical much greater than latent heats of
The latent heat for the state changes
solid <=> liquid is called the specific latent heat of fusion
(for melting or freezing).
The latent heat for the state changes
liquid <=> gas is called the specific latent heat of
vaporisation (for condensing, evaporation or boiling)
Specific latent heat
To work out the energy needed or
released to change the state of mass m of a substance the following
thermal energy (E in J) = mass (m in kg) x
specific latent heat (L in J/kg)
Some examples of calculations
(i) The latent heat of fusion of
water is 334 000 J/kg (334 kJ/kg).
How much energy is needed to melt 5.5
kg of ice?
E = mL
E = 5.5 x 334 000 =
1 837 000 J
(1837 kJ, 1.837 x 106 J)
(ii) The specific latent heat of
vaporisation of water is 2 265 000 J/kg (2265 kJ/kg).
How much energy is needed to boil 250
g of water at 100oC?
250g = 250/1000 = 0.25 kg
E = mL = 0.25 x 2 265 000 =
250 J (~566 kJ, 5.66 x 105 J)
(iii) For aluminium the latent heat
of fusion is 397 000 J/kg and the latent heat of vaporisation is 11 400
How much energy is needed to
completely vapourise 1.5 kg of aluminium
For melting: E = mL = 1.5 x 397 000 =
595 500 J
For vaporisation:: E = mL = 1.5 x 11
400 000 = 17 100 000 J
Total energy needed = 5955 + 1 710
000 = 17 695 500 J (17 696 kJ, ~1.77 x 107
(iv) What mass of ice can be melted
by 1 million J of heat energy?
Latent heat of fusion of water is 334
E = mL, rearranging gives m = E /
m = 1 000 000 / 334 000 =
(v) In an experiment 5 g of solid
gold required 322 J of heat energy to melt it at 1063oC.
Calculate the latent heat of fusion of gold.
5 g = 5 / 1000 = 0.005 kg
E = mL, rearranging gives L = E / m
L = 322 / 0.005 =
64 400 J/kg
The particle model of a gas - motion and gas pressure
particles have mass and their movement gives them kinetic energy and
The particles in a gas are in constant
random motion - random direction, variety of velocities and kinetic
Although the collisions occur at random
in any direction, there is a resultant force acting at right angles to
There will always be a gas pressure,
unless a container is under vacuum, no particles - no collisions - no
When the fast moving gas particles
collide with a surface, their millions of impacts create a force that we
measure as gas pressure - the total force of impacts per unit area.
The particles collide with the container
surface completely at random and impact at every angle, BUT, the effect is
to create a net force at right angles to the surface - gas pressure!
The more forceful the collisions on a
surface or the greater the number of collisions per unit area of surface,
the greater the pressure, assuming the gas volume keeps constant.
If the temperature is kept constant and
the volume increased, the impacts are more spread out and less frequent per
unit area, so the gas pressure decreases.
Conversely, if a gas is
compressed into a smaller volume at constant temperature, the number
of impacts per unit area increases, so the pressure increases.
If the sides of a gas container
are 'flexible' (e.g. balloon), the volume will only be constant when
the internal and external pressures are equal.
From measurements of volumes and
pressure of gases at constant pressure, a numerical inverse law can
pressure x volume = a constant
(at constant temperature)
pV = constant
p = pressure in pascals (Pa =
V = volume (m3)
You can connect two pressure and
two volumes by the simple equation
p1 x V1
= p2 x V2
where 1 represent the original
conditions, and 2 the final situation if an enforced change of p1
or V1 is made.
Examples of simple gas
For more gas calculation see
P-V-T pressure-volume-temperature gas
laws and calculations
What is the lowest temperature possible?
We know the temperatures of the cores of
stars can be millions of degrees, so there doesn't seem to be any upper
limit to temperature!
BUT, is there limit at the lower end of
the temperature scale? The answer is YES!
As you cool a material, the particles
have less and less kinetic energy of movement around (gases or liquids) or
vibration in fixed positions (solid).
The kinetic energy of particles is a
function of temperature.
You can also say, that what we
measure as temperature, is a measure of the average kinetic energy
BUT, eventually all movement ceases
at a temperature of -273oC
Therefore that's it as regards
particle KE, and the temperature as we know it, cannot fall any further!
So, the lowest possible temperature
that is possible is -273oC. (-273 on the Celsius scale, unit
Theoretically, at this temperature, the
particles have no kinetic energy of movement or vibration, the coldest they
can be - nothing left in the kinetic energy store of the particles.
In fact by then, every substance will
have solidified, but at -273oC there is zero vibration of the
In 1848 a Scottish-Irish scientist called
William Thompson (later became Lord Kelvin) proposed a new temperature scale
starting at zero (called absolute zero), which became known as the
'Kelvin' scale of temperature - unit K.
Therefore the difference between the
Celsius and Kelvin scales is 273.
To convert from one to the other, the
following simple formulae apply.
K = 273 + oC
or oC = K - 273
(absolute zero 0 K is the same temperature as - 273oC)
Examples of temperature Celsius and
Kelvin scale conversions:
Freezing point of water = 0oC,
therefore 0 + 273 = 273 K.
Boiling point of water = 100oC,
therefore 100 + 273 = 373 K.
Melting point of pure iron = 1811
K, therefore 1811 - 273 = 1538 oC
Note: Do NOT degrees Kelvin, do
NOT write oK !!!,
and don't write just C for
Celsius, you need the degree symbol o too!!
5b. Considering the
internal and external pressures of a container of gas
Pressure in fluids
Fluids are materials that can flow
because the attractive forces between the particles are weak in liquids
and almost non-existent in gases.
Since the particles are free to move,
they collide with any surface they make contact with.
This produces a net resultant force
at 90o to the surface.
The basic formula for pressure is:
Pressure = Force normal to the
surface ÷ area of of contact surface
P (Pa) = F (N)
÷ A (m2)
The effects of changing volume and
temperature of a container
The particles in a gas are in constant
motion - flying around in all directions with frequent collisions (e.g.
in air the collision rate is 109/s !!!).
As already described, increasing the
temperature of a gas, increases the kinetic energy store of the gas
In fact, the average kinetic energy of
the gas particles is directly related to the temperature.
The higher the gas temperature, the
greater the average kinetic energy of the particles,
and the cooler the gas the lower the
average kinetic energy of the particles.
As you increase temperature, the
average speed of the particles increases and so will the average kinetic
energy - remember the kinetic energy formula:
KE = ½mv2
(m = mass of particle, v = velocity of particle)
We can now discuss particular 'pressure'
situations and the starting point is the fact that ...
... gas pressure is caused by the
collision of particles with any surface ...
... because when particles collide
with a surface, the exert a force on that surface.
Pressure is related to the number or
force of particle impacts per unit area of the surface.
The more impacts or more forceful
impacts on the surface, the greater the pressure created.
Increasing temperature of a gas
actually increases both.
(i) Consider a steel cylinder of gas -
a rigid containing wall
When a gas is contained a rigid vessel
you can pump lots of gas in to a pressure much higher than the surrounding
Steel cylinders are used in industry to
store gaseous chemicals and in the home we used cylinders of hydrocarbon
gases for heating and cooking.
The more gas you force in, the greater
the internal pressure because of the increase in the number of particle impacts per
For a given cylinder, the gas volume is
constant and the pressure is proportional to the amount of gas pumped in at
Pressure and volume are inversely
proportional to each other.
P x V = constant, P =
pressure in Pa (pascals), V = volume in m3.
At constant temperature, increasing the
volume decreases pressure because the collisions are more spread out over
the same area - less particle collisions per unit area.
At constant temperature, decreasing the
volume increases pressure because the collisions are more concentrated over
the same area - more particle collisions per unit area.
P-V-T pressure-volume-temperature gas
laws and calculations
The internal and external pressures are
not balanced, but that's no problem with a strong steel walled cylinder!
If the cylinder is heated it will expand
a little, but this will not compensate for the increase in gas pressure as
the gas tries to expand.
If the cylinder and its contents increase
in temperature, then the thermal energy store is increased as the gas
particles gain kinetic energy.
This increase in the particle kinetic
energy store increases the rate of particle collision AND the force of the
particle impacts on the container surface - thus raising the pressure with
increase in temperature.
This is quite a dangerous situation that
fire-fighters face when tackling a fire at a factory where gas cylinders are
used - the high temperatures and high pressures created in the gas cylinders
will cause them to explode violently.
(ii) Consider a balloon of gas - a
flexible containing wall
If the sides of a gas
container are 'flexible' (e.g. like a balloon), the volume will only
be constant when the internal and external pressures are equal.
If the external pressure is greater than
the internal pressure the balloon will decrease in volume (size).
If the internal pressure is greater than
the external pressure the balloon will increase in volume (inflate).
To blow up the balloon you blow in
with a force greater than atmospheric pressure to create the volume of
The size of the balloon is then determined by how much air
you have blown in and the ambient atmospheric pressure.
The pressure of a gas in a balloon produces a net outward force at right angles to the
container surface due to the internal gas particle impacts.
BUT, as you observe with a blown-up
balloon, it doesn't seem to be expanding or contracting.
The reason being that the external air
particle impacts on the outside surface of the balloon create an opposing
and equal balancing pressure.
By blowing in air you increase the
internal pressure and force the balloon to expand, pushing the rubber skin
outwards, until the internal and external pressures are equal when expansion
When you blow in you are increasing the
number of particle impacts per unit area of the internal surface to create
the greater outward acting force.
Remember, increasing the volume of a gas
at constant temperature decreases the pressure (pV = constant).
The pressure you create initially when
blowing up the balloon, must decrease as it expands - less particle impacts
per unit area.
If you let air out of the balloon, or it
leaks out, there are less particle impacts per unit area of surface and the
pressure is reduced, so the greater external pressure causes the balloon to
contract until the volume is reduced creating a pressure equal to the
external atmospheric pressure.
If a balloon inflated with air is
heated, the gas particles inside will increase in kinetic energy
producing more collisions and more forceful collisions - increase in net
force acting on the surface.
Therefore the pressure increases and the
BUT, the expansion spreads out the
collisions (which decreases pressure - less force per unit area), so the
balloon only expands until the internal pressure equals the external
pressure of the cooler air.
When the balloon cools down it will
decrease in size, less forceful particle collisions, balloon shrinks until,
again, the internal and external pressures are equal.
When helium weather balloons are
released, they rapidly rise up through the atmosphere and greatly expand
because atmospheric pressure significantly decreases with increase in
height above the earth's surface.
As the external pressure decreases
(less particle impacts per unit area) the internal pressure is greater (more
impacts) and so the greater number of internal impacts per unit area force the volume of
the gas in the balloon to increase.
The helium balloon will continue to
expand as long as the external pressure is less than the internal pressure.
It will stop expanding when the internal
balloon pressure drops to the same as the external pressure.
However, since it is filled will less
dense helium, it will continue to rise and rise!
(iii) The same arguments apply to blowing
up a bicycle tyre or motor car tyre or anything else!
Any increases in the external
pressure from a pump system will allow expansion of the tyre if it
exceeds the internal pressure inside the tyre - otherwise no further
When you seal the end of a gas
syringe (like you see in chemistry), with your hand and press the
You can compress the air to create a greater gas pressure
than the external atmospheric pressure. BUT, although the pressures are
not initially balanced, as in the case of blowing up balloon, its your extra
muscle force that helps create the balancing force.
internal pressure in syringe =
atmospheric pressure + pressure from muscle force
5c. Increasing the energy store of gas
Increasing the energy store of gas
by compressing it
When you pump air into a bicycle tyre
as energetically as you can, you can detect a rise in temperature,
particularly near the pump connection point. So, why the increase in
temperature of the gas?
When you compress a gas by applying a
mechanical force you do work of compression on the gas.
This work in compressing the gas
increases the internal energy and increases the temperature - increasing
the thermal energy store.
You have to do work on the gas
because as you compress the air in the pump, the pressure rises as the
force of the particle impacts acts against you, so you
have to do work against this increased force/unit area (pressure) to get the air into
By doing work on a gas in this way
the increase in the internal energy store of the gas ends up as
increased kinetic energy of the particles, which causes the temperature
rise of the
air, tyre and pump.
Increasing the energy store of gas
by heating it
Increasing the temperature of a gas
increases its kinetic energy store.
Increasing the temperature increases the
average speed of particles and their kinetic energy.
In fact, the temperature of a gas is
proportional to the average kinetic energy of the particles.
This means on heating a gas in a sealed
container there are more particle impacts and more forceful impacts on the
surface per unit area.
Therefore heating a gas at constant
volume increases the gas pressure.
Conversely if you cool and sealed
cylinder of gas, the pressure decreases.
gases and more on
6. The factors that affect
the rate of evaporation and condensation
Condensation occurs when
a gas/vapour is cooled sufficiently to a low enough temperature to allow the
attractive forces to be strong enough to attract the particles together as a
liquid. This can only happen if the kinetic energy of the particles is low
enough (the lower the temperature the smaller the kinetic energy).
Water vapour in the air
condenses out on cold surfaces in the winter eg window condensation,
invisible steam from a boiling kettle condenses out into clouds of tiny
droplets of water, which technically isn't steam! and rain drops form in the
higher cooler regions of the atmosphere.
Factors affecting the rate of
The cooler the gas, the faster
it condenses - more lower KE particles can be attracted together.
The lower the temperature of the
surface the gas is in contact with.
The lower the airflow over the
surface, this keeps the concentration of the condensing gas as high as
Evaporation is when the
highest kinetic energy particles of a liquid escape from the surface ie can
overcome the attractive forces of the bulk of particles. The greater the KE
of a liquid surface particle, the greater the chance to escape and become a
gas particle. Evaporation can take place at any temperature between a
substance's melting point and boiling point. As the highest KE particles
escape, leaving the slower lower KE particles, the bulk of the liquid will
cool, so a cooling effect accompanies the evaporation of a liquid. The
cooling effect of sweating is due to evaporation of water from your skin.
Factors affecting the rate of
The higher the liquid
temperature, the faster the rate of evaporation - more particles with enough
kinetic energy to escape from the surface.
The greater the surface area,
the faster the evaporation - more area, more chance of evaporation.
The greater the airflow over the
surface of the faster the evaporation rate - the air can become saturated
with the vapour of the liquid, so it is more readily replaced if the already
evaporated liquid is swept away by air flowing over the surface.
notes particle model latent heat of state changes KS4 physics Science notes on
particle model latent heat of state changes GCSE physics guide
notes on particle model latent heat of state changes for schools colleges academies science course tutors images
pictures diagrams for particle model latent heat of state changes science revision notes on
particle model latent heat of state changes for revising physics modules physics topics notes to help on understanding of
particle model latent heat of state changes university courses in technical science
careers in physics jobs in the industry
technical laboratory assistant
apprenticeships technical internships in engineering physics USA US grade 8 grade 9 grade10 AQA
physics science GCSE
notes on particle model latent heat of state changes Edexcel physics science notes on
particle model latent heat of state changes for OCR 21st century
physics science OCR GCSE Gateway physics science
notes WJEC gcse science CCEA/CEA gcse science