Particle model theory applied to energy transfer in state changes, internal
energy, latent heat and particle motion in gases
Doc Brown's Physics Revision
Suitable for GCSE/IGCSE Physics/Science courses or
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.
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.
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).
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.
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.
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.
Note for (a) and (b) ...
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.
(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).
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
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 = 566
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 = 3.0 g
(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
The particles in a gas are in constant
random motion - random direction, variety of velocities and kinetic
Increasing the temperature of a gas
increases its kinetic energy store.
In fact, the temperature of a gas is
proportional to the average kinetic energy of the particles.
Increasing the temperature increases the
average speed of particles and their kinetic energy.
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 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.
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
The pressure of a gas in a container
(e.g. a balloon) produces a net outward force at right angles to the
BUT, as you observe with a blown-up
balloon, it doesn't seem to be expanding. The reason being that the air
particle impact on the outside surface of the balloon itself creates an
opposing and balancing pressure.
To blow up the balloon you blow in
with a force greater than atmospheric pressure to create the volume of
trapped gas. The size of the balloon is then determined by how much air
you have blown in and the ambient atmospheric pressure.
The same argument applies to blowing
up a bicycle or motor car tyre.
Any changes in the external pressure
(p) will allow expansion if p reduced or contraction if p increased.
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.
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.
You have to do work on the gas
because as you compress the air in the pump, the pressure rises, and you
have to do work against this increase in pressure to get the air into
By doing work on a gas in this way
you increase the internal energy store of the gas and this ends up as
kinetic energy of the particles causing a rise in temperature of the
air, tyre and pump.
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.
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