1
Thermal Physics
Occurs from higher to lower temperature regions
Topic 3.1 Thermal Concepts
Topic 3.2 Thermal Properties of Matter
♦ Temperature – Macroscopic
♦ Heat Capacity/Thermal Capacity, C
At a macroscopic level, temperature is the degree of
hotness or coldness of a body as measured by a
thermometer
Temperature is a property that determines the direction of
thermal energy transfer between two bodies in contact
Temp is measured in degrees Celsius (oC) or Kelvin (K)
T(K) = T(oC) + 273
Temperature in K is known as the absolute temperature
♦ Thermal Equilibrium
When 2 bodies are placed in contact
Thermal energy will flow from the body with lower temp
to the body with higher
Until the two objects reach the same temperature
They will then be in Thermal Equilibrium
This is how a thermometer works
♦ Thermometers
A temperature scale is constructed by taking two fixed,
reproducible temperatures
The upper fixed point is the boiling point of pure water at
atmospheric pressure
The lower fixed point is the melting point of pure ice at
atmospheric pressure
These were then given the values of 100oC and
0oC respectively, and the scale between them was
divided by 100 to give individual degrees
♦ Temperature - Microscopic
At a microscopic level, temperature is regarded as a
measure of the average kinetic energy per molecule
in a substance
♦ Internal Energy
The Internal energy of a body is the total energy associated
with the thermal motions of the particles
Is the total of the kinetic energy due to the motion of
molecules of a substance and the total potential energy
associated with the vibrational and electric energy of
atoms within molecules or crystals. It includes the energy
in all the chemical bonds, and the energy of the free,
conduction electrons in metals.
It can comprise of both kinetic and potential energies
associated with particle motion
Kinetic energy arises from the translational and rotational
motions
Potential energy arises from the intermolecular forces
between the molecules
♦ Heat
The term heat represents energy transfer due to a
temperature difference
When substances undergo the same temperature change
they can store or release different amounts of energy
They have different heat capacities
Defined as the amount of energy needed to change the
temperature of a body by unit temperature (1K)
C = Q / T
(JK-1)
o Q = thermal energy in joules
o T = the change in temperature in Kelvin
Applies to a specific BODY
A body with a high heat capacity will take in thermal
energy at a slower rate than a substance with a low heat
capacity because it needs more time to absorb a greater
quantity of
o thermal energy
They also cool more slowly because they give out thermal
energy at a slower rate
♦ Specific Heat Capacity, c
Defined as the amount of thermal energy required to
change temperature of 1 kg of material by unit
temperature (1K).
c = Q / (mT)
(J kg-1 K-1)
•
Q = thermal energy in joules
•
T = the change in temperature in Kelvin
•
m = the mass of the material
For an object made of one specific material:
o Heat Capacity = m x Specific Heat Capacity
Unit masses of different substances contain
• different numbers of molecules
• of different types
• of different masses
If the same amount of internal energy is added to each
unit mass
• it is distributed amongst the molecules
The average energy change of each molecule will be
different for each substance
Therefore the temperature changes will be different
So the specific heat capacities will be different
♦ Methods of finding the S.H.C
Two methods

Direct
 Indirect
2
♦ Direct Method – SHC of Liquids
Using a calorimeter of known heat capacity
(or specific heat capacity of the material and the mass of
the calorimeter)
Because: heat capacity = mass x specific heat capacity
♦ Calculations - Liquids
Electrical energy = V I t
Energy gained by liquid = ml cl Tl
♦ Indirect Method
Sometimes called the method of mixtures
In the case of solid, a known mass of solid is heated to a
known temperature (usually by immersing in boiling water
for a period of time – to be in thermal equilibrium with
water)
Then it is transferred to a known mass of liquid in a
calorimeter of known mass
The change in temperature is recorded and from this the
specific heat capacity of the solid can be found
Energy lost by block = Energy gained by liquid and
calorimeter
mb cb Tb = mw cw Tw + mc cc Tc
the SHC of water and the calorimeter are needed
Energy gained by calorimeter = mc cc Tc
Using conservation of energy
Electrical energy input = thermal energy gained by liquid +
thermal energy gained by calorimeter
V I t = ml cl Tl + mc cc Tc
The only unknown is the specific heat capacity of the liquid
♦ Direct Method – SHC of Solids
Using a specially prepared block of the material
The block is cylindrical and has 2 holes drilled in it
• one for the thermometer and one for the heater
• Heater hole in the centre, so the heat spreads evenly through
the block
• Thermometer hole, ½ way between the heater and the outside
of the block, so that it gets the average temperature of the
block
In the case of a liquid
A hot solid of known specific heat capacity is transferred to
a liquid of unknown specific heat capacity
A similar calculation then occurs
♦ Phases (States) of Matter
Matter is defined as anything that has mass and occupies
space
There are 4 states of matter
Solids, Liquids, Gases and Plasmas
Most of the matter on the Earth in the form of the first 3
Most of the matter in the Universe is in the plasma state
♦ Macroscopic properties
♦ Calculations - Solids
Again using the conservation of energy
Electrical Energy input is equal to the thermal energy
gained by the solid
Electrical energy = V I t
Energy gained by solid = m c T
s s s
V I t = m c T
s s s
The only unknown is the specific heat capacity of the solid
Macroscopic properties are all the observable behaviours
of that material such as shape, volume, compressibility
The many macroscopic or physical properties of a
substance can provide evidence for the nature of that
substance
♦ Macroscopic Characteristics
Characteristics
Shape
Volume
Compressibility
Diffusion
Comparative
Density
Solid
Definite
Definite
Almost
Incompressible
Small
Liquid
Variable
Definite
Very Slightly
Compressible
Slow
Gas
Variable
Variable
Highly
Compressible
Fast
High
High
Low
3
♦ Microscopic Characteristics
• At the boiling point a temperature is reached at which the
particles gain sufficient energy to overcome the inter-particle
forces and escape into the gaseous state. PE increases.
• Continued heating at the boiling point provides the energy for
all the particles to change
♦ Heating Curve
♦ Fluids
Liquids
Gases
are both fluids
because they FLOW
♦ Arrangement of Particles
Solids
•
•
•
•
Closely packed
Strongly bonded to neighbours
held rigidly in a fixed position
the force of attraction between particles gives them PE
♦ Changes of State
Liquids
Still closely packed
Bonding is still quite strong
• Not held rigidly in a fixed position
and bonds can break and reform
• PE of the particles is higher than a solid because the
distance between the particles is higher
•
•
Gases
• Widely spaced
• Only interact significantly on closest
approach or collision
• Have a much higher PE than liquids
because the particles are furthest
♦ Latent Heat
apart
♦ Changes of States
A substance can undergo changes of state or phase changes at
different temperatures
Pure substances have definite melting and boiling points which
are characteristic of the substance
• When the solid is heated the particles of the solid vibrate at an
increasing rate as the temperature is increased
• The vibrational KE of the particles increases
• At the melting point a temperature is reached at which the
particles vibrate with sufficient thermal energy to break from
their fixed positions and begin to slip over each other
• As the solid continues to melt more and more particles gain
sufficient energy to overcome the forces between the particles
and over time all the solid particles are changed to a liquid
• The PE of the system increases as the particles move apart
• As the heating continues the temperature of the liquid rises
due to an increase in the vibrational, rotational and
translational energy of the particles
The thermal energy which a particle absorbs in melting,
vaporising or sublimation or gives out in freezing,
condensing or sublimating is called Latent (“hidden”) Heat
because it does not produce a change in temperature
When thermal energy is absorbed/released by a body, the
temperature may rise/fall, or it may remain constant
• If the temperature remains constant then a phase change will
occur as the thermal energy must either increase the PE of the
particles as they move further apart
• or decrease the PE of the particles as they move closer
together
♦ Definition
The quantity of heat energy required to
change one kilogram of a substance
from one phase to another, without a
change in temperature is called the
Specific Latent Heat of Transformation

Specific Latent Heat = Q / m
(J kg-1)
♦ Types of Latent Heat
Fusion
Vaporisation
Sublimation
4
The latent heat of fusion of a substance is less than the
latent heat of vaporisation or the latent heat of
sublimation
♦ Questions
The process of evaporation is a change from
the liquid state to the gaseous state which
occurs at a temperature below the boiling point
♦ Explanation
When dealing with questions think about



♦ Evaporation
where the heat is being given out
where the heat is being absorbed
try not to miss out any part
♦ Methods of finding Latent Heat
Using similar methods as for specific heat capacity
The latent heat of fusion of ice can be found by adding ice
to water in a calorimeter
The change in temperature is recorded and from this the
latent heat of fusion of the ice can be found
Energy gained by block melting = Energy lost by liquid and
calorimeter
mb Lb = mw cw Tw + mc cc Tc
the SHC of water and the calorimeter are needed
The latent heat of vaporisation of a liquid could be found
by an electrical method
A substance at a particular temperature has a range of
particle energies
So in a liquid at any instant, a small fraction of the particles
will have KE considerably greater than the average value
If these particles are near the surface of the liquid, they
will have enough KE to overcome the attractive forces of
the neighbouring particles and escape from the liquid as a
gas
♦ Cooling
Now that the more energetic
particles have escaped
The average KE of the remaining
particles in the liquid will be lowered
Since temperature is related to the
average KE of the particles
A lower KE infers a lower temperature
This is why the temperature of the liquid falls as an
evaporative cooling takes place
A substance that cools rapidly is said to be a volatile liquid
When overheating occurs in a human on hot days, the
body starts to perspire
Evaporation of the perspiration cools the body
♦ Factors Affecting The Rate
Evaporation can be increased by
♦ Latent Heat of Vaporisation
•
Increasing temperature
•
(more particles have a higher KE)
•
Increasing surface area
•
(more particles closer to the surface)
•
Increasing air flow above the surface
•
(gives the particles somewhere to go to)
Ideal Gases
♦ The Mole
The initial mass of the liquid is recorded
The change in temperature is recorded for heating the
liquid to boiling
The liquid is kept boiling
The new mass is recorded
Energy supplied by heater = energy to raise temperature of
liquid + energy use to vaporise some of the liquid
(The calorimeter also needs to be taken in to account.)
V I t = ml clTl+ me Le + mc ccTc
The mole is the amount of substance which contains the
same number of elementary entities as there are in 12
grams of carbon-12
23
Experiments show that this is 6.02 x 10 particles
A value denoted by NA called the Avogadro constant
(units mol-1 )
5
♦ Molar Mass
♦ The Kinetic Molecular Theory Postulates
Molar mass is the mass of one mole of the substance
-1
SI units are kg mol
Gas consists of large numbers of molecules (or atoms, in
the case of the noble gases) that behave like hard,
spherical objects in a state of constant, random motion.
♦ Example
-3
-1
Molar mass of Oxygen gas is 32x10 kg mol
If I have 20g of Oxygen, how many moles do I have and
how many molecules?
-3
-3
-1
20 x 10 kg / 32 x10 kg mol
 0.625 mol
23
 0.625 mol x 6.02 x 10 molecules
23
 3.7625 x 10 molecules
The size of the particles is much smaller than the distance
between them, so they are treated as points
Collisions of a short duration occur between particles and
the walls of the container
No intermolecular forces act between the particles except
when they collide, so between collisions the particles move
in straight lines
Collisions are perfectly elastic (none of the energy of a gas
particle is lost in collisions)
♦ Thermal Properties of Gases
Energy can be transferred between molecules
during collisions.
An ideal gas can be characterized by three state variables
•
•
•
Pressure
Volume
Temperature
1 Pa (Pascal) = 1 N/1m2
m3
1 liter = 10-3 m3
K
Experiments use these macroscopic properties of a gas to
formulate a number of gas laws. That is historical
approach. There is another way:
The relationship between them may be deduced from
kinetic theory of gasses and is called the ideal gas law:
They all obey Newton’s Laws of motion
♦ Macroscopic behaviour
The large number of particles ensures that the number of
particles moving in all directions is constant at any time
With these basic assumptions we can relate the pressure
of a gas (macroscopic behaviour) to the behavior of the
molecules themselves (microscopic behaviour).
PV = nRT = NkT
•
•
•
•
n = number of moles: n = N/NA
R = universal gas constant = 8.3145 J/mol K
N = number of molecules
k = Boltzmann constant = 1.38066 x 10-23 J/K
♦ Pressure
Pressure exerted by the gas on the walls is due to
collisions of the molecules with the walls of the container.
Focus on one molecule moving toward the wall and
examine what happens when on molecule strikes this wall.
♦ The Kinetic – Molecular Theory of Gasses
"the theory of moving molecules";
Rudolf Clausius, 1857
The ideal gas equation is the result of experimental
observations about the behavior of gases. It describes how
gases behave.
Elastic collision – no loss of
kinetic energy, so speed remains
the same, only direction
changes.
you can imagine 3-D picture you
can “see” that only the
component of the molecule’s
momentum perpendicular to
If
• A gas expands when heated at constant pressure
• The pressure increases when a gas is compressed at
constant temperature
But, why do gases behave this way?
What happens to gas particles when conditions such as
pressure and temperature change?
That can be explained with a simple theoretical model
known as the kinetic molecular theory.
The kinetic theory relates the macroscopic behaviour of an
ideal gas to the microscopic behaviour of its molecules or
atoms
This theory is based on the following postulates, or
assumptions.
the wall changes.
Change in momentum implies that there must be a force
exerted by the wall on the particle.
That means that there is a force exerted on the wall by
that molecule.
The average pressure on the wall is the average of all
microscopic forces per unit area:
P=
F
A
It can be shown that the pressure on the wall can be
expressed as:
N
P= 31   m(v 2 )avg .
V
6
Now, finally we have the pressure in a gas expressed in
terms of molecular properties.
This is a surprisingly simple result! The macroscopic
pressure of a gas relates directly to the average kinetic
energy per molecule.
We got key connection between microscopic behaviour
and macroscopic observables.
If we compare the ideal-gas equation of state: PV= NkT
with the result from kinetic theory: PV = ⅓ N m(v2)avg ,
we find
KEavg =
3
2
kT
The average translational kinetic energy of molecules in a
gas is directly proportional to the absolute temperature.
The higher the temperature, according to kinetic theory,
the faster the molecules are moving on the average.
At absolute zero they have zero kinetic energy. Can not go
lower.
This relation is one of the triumphs of the kinetic energy.
♦ Absolute Temperature
The absolute temperature is a measure of the average
kinetic energy of its molecules
If two different gases are at the same temperature, their
molecules have the same average kinetic energy, but more
massive molecules will have lower average speed.
If the temperature of a gas is doubled, the average kinetic
energy of its molecules is doubled
♦ Molecular Speed
Although the molecules in a sample of gas have an average
kinetic energy (and therefore an average speed) the
individual molecules move at various speeds
Some are moving fast, others relatively slowly
At higher temperatures at greater fraction of the molecules
are moving at higher speeds
For O2 molecules at 300 K, the most probable speed is 390
m/s. When temperature increases to 1100 K the most
probable speed increases to roughly 750 m/s. Other speed
occur as well, from speeds near zero to those that are very
large, but these have much lower probabilities.
example: a closed jar, or aerosol can, thrown into a fire
will explode due to increase in gas pressure inside.
Microscopically:
As T increases, KE of molecules increase
That implies greater change in momentum when they hit
the wall of the container
Thus microscopic force from each molecule on the wall will
be greater
As the molecules are moving faster on average they will hit
the wall more often
The total force will increase, therefore the pressure will
increase
♦ The Charles’s law
Effect of a volume increase at a constant pressure
Macroscopically: at constant pressure, volume of a gas
is proportional to its temperature:
PV = NkT → V = (const) T
Microscopically:
An increase in temperature means an increase in the
average kinetic energy of the gas molecules, thus an
increase in speed
There will be more collisions per unit time, furthermore,
the momentum of each collision increases (molecules
strike the wall harder)
Therefore, there would be an increase in pressure
If we allow the volume to change to maintain constant
pressure, the volume will increase with increasing
temperature
♦ Boyle-Marriott’s Law
Effect of a pressure decrease at a constant temperature
Macroscopically: at constant temperature the pressure
of a gas is inversely proportional to its volume:
PV = NkT → P = (const)/V
Microscopically:
Application of the "Kinetic Molecular Theory" to
the Gas Laws
Microscopic justification of the laws
♦ Pressure Law (Gay-Lussac’s Law)
Effect of a pressure increase at a constant volume
Macroscopically: at constant volume the pressure of a
gas is proportional to its temperature:
PV = NkT → P = (const) T
Constant T means that the average KE of the gas molecules
remains constant
This means that the average speed of the molecules, v,
remains unchanged
If the average speed remains unchanged, but the volume
increases, this means that there will be fewer collisions
with the container walls over a given time
Therefore, the pressure will decrease