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CHAPTER3
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CORE
was knighted by King George III o England, and made a
Count in 1791 by Teodor in his brie reign as elector o
the Holy Roman Empire.
In 1793, Tompson lef England ultimately to take up a post
with the beore mentioned Teodor, elector o Bavaria. He
was appointed a major general in the Bavarian army. Hedesigned ortications and worked as an administrator
in munitions. It was here that he observed that a large
amount o heat was generated in the boring o cannons.
He read the ollowing extracts beore the Royal Society o
London in 1798.
Being engaged, lately, in superintending the boring
o cannon, in the workshops o the military arsenal at
Munich, I was struck with the very considerable degree o
Heat which a brass gun acquires, in a short time, in being
bored; and with the still more intense Heat (much greater
than that o boiling water as I ound by experiment) o the
metallic chips separated rom it by the borer.
From whence comes the Heat actually produced in the
mechanical operation above mentioned? Is it urnished by
the metallic chips which are separated by the borer rom
the solid mass o metal? I this were the case, then,
according to the modern doctrines o latent heat, and o
caloric, the capacity or Heat o the parts o the metal, so
reduced to chips, ought not only to be changed, but the
change undergone by them should be sufficiently great to
account or all the Heat produced.
Count Rumord was saying that the metal chips should
have undergone some alteration in their properties afer
the production o so much thermal energy. He noted that
some cannon shavings were hot enough to glow, but he
continued:
But no such change had taken place; or I ound, upon
taking equal quantities, by weight, o these chips, and o
thin slips o the same block o metal separated by means
o a ne saw, and putting them, at the same temperature
(that o boiling water), into equal quantities o cold water,
the portion o water into which the chips were put was
not, to all appearance, heated either less or more than the
other portion, into which the slips o metal were put. Fromwhence it is evident that the Heat produced [by boring the
cannon] could not possibly be urnished at the expense o
the latent Heat o the metallic chips.
Rumord urther went on to explain that he had immersed
cannons in water while they were being bored and noted
the rate at which the temperature rose. His results showed
that the cannon would have melted had it not been cooled.
Rumord concluded that heat was not a caloric uid in
which caloric is conserved but rather a concept o motion.
He argued that heat is generated when work is done, and
that the heat will continue to be generated as long as work
is done. He estimated a heat to work ratio within the order
o magnitude accepted today.
However, many scientists o the time were not convincedbecause Rumord could not give a clear explanation o
exactly what heat was in terms o the accepted model or
matter at that time. It would take another hal century
beore Joule supplied the accepted answers.
JAMES PRESCOTT JOULE
James Prescott Joule (1818-1889) conducted a series o
brilliant experiments between 1842 and 1870 that proved
beyond doubt that heat was a type o energy internal
energy o the particles o matter. Te caloric theory lost
popularity very quickly.
Joulewas the son o a wealthy brewer in Manchester, UK.
Because o his wealth, he never worked or a living. His
experiments were perormed in a laboratory that he built
at his own expense while he was in his twenties. He became
interested in ways to develop more efficient engines that
were driving various components o the brewing process.
Encouraged by the work o Count Rumford and others,
he began to investigate whether mechanical work could
produce heat.
Jouleperormed a variety o experiments and he rened
and elaborated his apparatus and his techniques. In one
o his rst experiments, he used a alling weight to drive
a small electric generator. Te current produced heated a
wire that was immersed in a denite mass o water, and
the change in temperature was noted. He reasoned that
the work done as the weight decreases its gravitational
potential energy should be equivalent to the heat energy
gained by the water. In another experiment he mounted a
large container lled with air into a tub o water. When the
air was compressed, the temperature o the gas increased.
He measured the amount o work needed to compress the
gas and the amount o heat energy given to the water as a
result o compression.
Perhaps Joules most amous experiment consisted o a
paddlewheel mounted inside a cylinder o water that was
driven by alling weights as shown in Figure 301. He wanted
to see i one could raise the temperature o the water simply
by turning the paddles. He repeated this experiment many
times continually improving the apparatus and rening
his analysis o the data. For example, he took great care
to insulate the container so that no heat was lost to the
surroundings, and he developed his own thermometer so
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THERMALPHYSICS
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that he could measure the temperature with a precision o
a raction o a degree.
moving vanes
xed vanes
calorimeter
ywheel
handles
to pulley withweights attached
to pulley withweights
(containing water)
spindle
attached
Figure 301 Schematic diagram of
Joules paddlewheel experiment.
Joule arranged the vanes o the paddlewheel so that they
would not interere with the particles o water set in
motion. He didnt want to bruise or damage the water
particles so that they might bleed heat.
In 1849 he published his results in which he reported
the quantity o heat produced by riction o bodies,
whether solid or liquid, is always proportional to the
quantity o [energy] expended.
the quantity o heat capable o increasing the
temperature o a pound o water by 1 Fahrenheit requires
or its evolution the expenditure o a mechanical energy
represented by the all o 772 pound through the distance
o one oot.
Joule ound that about 4.2 joules o work would yield one
calorie o heat or that the quantity o heat required to
raise the temperature o one gram o water by 1 C is one
calorie.
A modern day value or the mechanical equivalent o heat
is 4.18605 joules = 1 calorie.
Te experiments proved beyond doubt that mechanical
work can produce heat and as such no caloric uid can
be created or destroyed. Furthermore, Joule reasoned that
the temperature increase must be related to the energy o
the microscopic motions o the particles.
Finally, a paradigm shif in our way o reasoning had again
proved that science is not the ultimate truth.
Example
Calculate the mechanical equivalent o heat or Joules
paddlewheel experiment i a mass o 2.0 kg alls through a
height o 100 m, and increases the temperature o 10 g owater by 46.8 C.
Solution
Work done by the alling mass is given by
W = Ep = mgh
= 2.0 kg 9.8 m s -2 100 m
= 1.96 10 3J
Heat energy produced is given by
Q= m c T
= 10 g 1 cal 46.8 C
= 4.68 102calories
Mechanical equivalent o heat is given by
W
Q-----
1.96 103
J
4.68 102 cal----------------------------------=
= 4.19 J cal-1
Te mechanical equivalent o heat or water is 4.2 J cal -1.
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3.1.1 State that temperature determines the
direction of thermal energy transfer
between two objects.
3.1.2 State the relation between the Kelvin and
Celsius scales of temperature.
3.1.3 State that the internal energy of a
substance is the total potential energy and
random kinetic energy of the molecules of
the substance.
3.1.4 Explain and distinguish between the
macroscopic concepts of temperature,
internal energy and thermal energy (heat).
3.1.5 Define the mole and molar mass.
3.1.6 Define theAvogadro constant. IBO 2007
3.1.1 TEMPERATUREANDTHERMAL
ENERGYTRANSFER
Everyone seems to have a feel for the concept of heat
because there is so much talk in everyday conversation
of how hot or how cold it is. We endure the seasons of
the year wanting either to cool our bodies or heat up our
surroundings. We are aware of how difficult it was for
our ancestors to keep warm, and our present dwellings
are designed and insulated to suit the climate. Our
consumption of electrical and chemical energy for heating
and other purposes is a continual concern. We have
become aware that increased global warming could spell
the end of the world, as we know it.
But what is the difference between heat and temperature
in physics? Tey are denitely not the same physical
quantity. If you ll a cup and a dish with hot water at the
same temperature, and then place ice cubes into each, thedish full of hot water can melt more ice cubes than the
cup of hot water even though the water in each was at the
same temperature. Te dish containing the larger amount
of hot water has a greater mass of water as well as a greater
amount of heat or thermal energy. A greater mass infers
a greater number of water molecules and more thermal
energy infers that these molecules would have a greater
overall amount of energy. We cannot see the interaction
of the water molecules at the microscopic level because
we cannot see atoms. However, we can observe and
monitor the temperature change by using a macroscopic
temperature-measuring device.
Termal energyis a measure of the kinetic and potential
energy of the component particles of an object and is
measured in joules. Heat is the thermal energy that is
absorbed, given up or transferred from one object to
another.
emperatureis a scalar quantity that gives an indication of
the degree of hotness or coldness of a body. Alternatively,
temperature is a macroscopic property that measures
the average kinetic energy of particles on a dened scale
such as the Celsius or Kelvin scales. Te chosen scale
determines the direction of thermal energy transferbetween two bodies in contact from the body at higher
temperature to that of lower temperature. Eventually,
the two bodies will be in thermal equilibrium when they
acquire the same temperature in an isolated system. It will
be deduced later in this text that thermal energy cannot
be transferred from a body at lower temperature to that of
higher temperature.
3.1.2 TEMPERATURESCALES
Tere is no instrument that directly measures the amount of
thermal energy a body gives off or absorbs. A property that
varies with temperature is called a thermometricproperty.
Tis property can be used to establish a temperature scale
and construct a thermometer. Termometers are made
using the thermometric properties of a substance such as the
expansion of a liquid, the electrical resistance of a wire.
A typical laboratory thermometer as shown in Figure 302
contains a liquid such as mercury or coloured alcohol. Te
expansion of alcohol is six times greater than mercury.
Alcohol thermometers are safer and can be used at lower
temperatures than mercury which turns to a solid below
-38.9 C. Its disadvantage is that it boils above 78.5 C. o
make the thermometer sensitive, it has a narrow bore tubeand a large bulb. Te bulb is made of thin glass so that
heat can be transferred quickly between the bulb liquid
and the material being observed. Tere is a vacuum above
the thermometer liquid and it can move easily along the
glass bore.
3.1 THERMAL CONCEPTS
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100C
0 C
mercury or alcoholthin glassbulb
glassstem
capil lary tube
vacuum
Figure 302 Typical laboratory thermometer
A clinical thermometer as shown in Figure 303 does not
need the temperature range o a laboratory thermometer.
It is designed so that the maximum temperature remains
constant afer the patients temperature is taken. It has a
small constriction to stop the mercury owing back into
the bulb. Te mercury is then shaken back into the bulb
afer the temperature has been taken.
35 36 37 38 39 40 41 42
Figure 303 A Clinical Thermometer
In order to calibrate these thermometers, two xed points
are used to dene the standard temperature interval. Te
ice point (the lower xed point) marked at 0 C is the
temperature o pure ice at standard atmospheric pressure
and is in thermal equilibrium with the liquid in the bulb.
Te steam point (the upper xed point) marked at 100 C
is the temperature o steam at standard atmospheric
pressure and is in thermal equilibrium with the liquid in
the bulb. Te scale between these values is marked with
even spaces. Te Celsius temperature scale named afer
the Swedish astronomer Anders Celsius (1701-1774) isconstructed in such a manner.
Although thermometers constructed using thermometric
properties are useul or everyday use, they are not
accurate enough or scientic work. Unortunately, two
thermometers constructed using different thermometric
properties do not necessarily agree with each other as they
do not vary linearly over large temperature ranges. (Tey
are o course in agreement at the lower and upper xed
points). For example, different thermometers will give
different values or the boiling point o zinc (907 C).
Te standard undamental temperature scale in the SI
system is denoted by the symbol T. and is measured in
Kelvin, K. It is the thermodynamic temperature scale used
in scientic measurement.
Te lower xed point is absolute zero and is assigned a
value o 0 K. Tis is the point where molecular vibrations
become a minimum the molecules have minimum
kinetic energy but molecular motion does not cease. Te
upper xed point is the triple point o water. Tis is the
temperature at which saturated water vapour, pure water
and melting ice are all in equilibrium. For historical
reasons, it is assigned a value o 273.16 K.
Tin K = T in C + 273.16
Exercise 3.1 (a)
1. At room temperature, an iron rod eels cooler
when held in the hand than wood held in the samewood held in the same
hand. Tis is because:
A. thermal energy tends to ow rom the
metal to the wood
B. wood has a higher specic heat capacity
than the iron rod
C. wood has a lower specic heat capacity than
the iron rod
D. the iron rod conducts thermal energy better
than the wood
2. Explain the difference between heat and
temperature.
3. I you were travelling to Antarctica, deduce
what would be the better thermometer to take
mercury or alcohol?
4. State one advantage and one disadvantage o a
i. mercury in glass thermometer
ii. constant volume thermometer.
5. Te triple point o water is 273.16 K. Express this
as a Celsius temperature.
6. Determine the ice point and the steam point o
pure water on the Kelvin scale?
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7. Dene absolute zero.
8. If normal body temperature is 37.0 C, what is it
on the thermodynamic temperature scale?
3.1.3 HEATANDINTERNALENERGY
Termal energy of a system is referred to as internal energy
- the sum total of the potential energy and the random
kinetic energy of the molecules of the substance making
up the system.
Te potential energy is due to
the energy stored in bonds called bond energy
intermolecular forces of attraction between particles.
Te bond energy is a form of chemical potential energy. It
becomes signicant in chemistry when a chemical reaction
occurs, and bonds are broken and formed.
Te intermolecular forces of attraction between particles
is due to the electromagnetic fundamental force since the
gravitational force is too small to be of any signicance.
Figure 304 indicates how the intermolecular electro-
magnetic forceFbetween particles varies with the distance
rbetween their centres.
At distances greater than r0 (less than 2.5 10-10 m)
attraction takes place, and at distances closer than r0the
particles repel. At r0
the particles are in equilibrium. Any
displacement from the equilibrium position results in a
simple harmonic oscillation of a particle or molecule.
r 0
repulsion
attraction
solid and liquid phase
10r0
gaseous phase
nuclear separation, r / m
Force, F / N
+
Figure 304 Force versus separation of particles
Figure 305 shows the relationship between the potential
energy and the separation rof two molecules. At 0 K, the
average separation of particles centres is r0and the overall
force is zero. Tis is the point of minimum potential
energy. Work will need to be done to move the particles
apart and there will be an increase in potential energy.
r0
equil ibrium separationgas
liquid
separation, r / m
Pote
ntialenergy,
U
/J
solid
+
minimum potentialenergy =
Figure 305 Potential energy
versus separation of particles
Work done = force distance = F r = change in
potential energy
F=E
p
____
r
In other words, the gradient of the potential energy curve
at any point on the curve gives the force that must be
applied to hold the molecules at that separation. We can
classify the phases according to the sizes of the energy .
When less than
__
10
, the vibrations occur about xed
positions and the particles are in the solid phase. When
approximately equal to
__
10
, the particles have sufficient
energy to partly overcome the attractive forces and melting
occurs.
When greater than __10
, a liquid can form. When greater
than , the particles have sufficient energy to leave the
liquid and form a gas.
Te kinetic energy is mainly due to the translational,
rotational and vibrational motion of the particles as
depicted in Figure 306.
Vibrationalki netic energy
Rotationalki netic energy
Translationalki netic energy
Figure 306 major particle motion and energy
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3.1.4 MACROSCOPICCONCEPTSOF
TEMPERATURE
Internal energy and thermal
energy (heat)
A macroscopic property is one that can be observed.
Physical properties such as melting point, boiling point,
density, thermal conductivity, thermal expansion and
electrical conductivity can be observed and measured.
TEMPERATURE
At the macroscopic level, temperature is the degree
of hotness or coldness of a body as measured by a
thermometer. Termometers are made using the
thermometric properties of a substance such as:
the expansion of a column of liquid in a capillary
tube (laboratory and clinical thermometers).
the electrical resistance of a wire (resistance and
thermister thermometers).
the difference in the rates of expansion of two
metals in contact (bimetallic strips).
the pressure of a gas at constant volume.
the volume of a gas at constant pressure (gases
expand by a greater amount and more evenly than
liquids).
the heating of two metal wires wound together
(thermocouple thermometers rely on the two
metals producing different currents).
the colour of a solid heated to high temperatures
(pyrometers).
emperature is measured in Kelvin, K.
INTERNAL ENERGY
As already mentioned, internal energyis the sum total of
the potential energy and the random kinetic energy of the
molecules of the substance making up a system. In order
to apply the Law of conservation to thermal systems, onehas to assume that a system has internal energy.
At the macroscopic level, it can be observed that molecules
are moving. When pollen (a ne powder produced by
owers) is sprinkled on the surface of water and the set-
up is viewed under magnication, it can be seen that the
pollen particles carry out zig-zag motion called Brownian
Motion.Teir motion is caused by the kinetic energy of
the water molecules. Walking past a coffee shop you smell
the aroma of the coffee due to diffusion caused by the
kinetic energy of the air molecules allowing the aroma
molecules to spread.
Te expansion of solids, liquids and gases is a macroscopic
property that allows us to understand that matter in a
system has potential energy. When you heat a liquid it canbe seen to expand as in a thermometer and this means
that the potential energy of the system is increasing as
the molecules move further apart. Te compressibility of
gases allow us to understand that the potential energy of
the molecules is decreasing.
Although the internal energy in the examples above can
never be absolutely determined, the change in internal
energy can be observed.
THERMAL ENERGY HEAT
Students should understand that the term thermalenergy refers to the non-mechanical transfer of energy
between a system and its surroundings. IBO 2007
Terefore, it is incorrect to refer to the thermal energy in a
body. At the macroscopic level, thermal energy (heat) can
be transferred from one body to another by conduction,
convection, radiation or by combinations of these three.
Termal conductionis the process by which a temperature
difference causes the transfer of thermal energy from the
hotter region of the body to the colder region by particle
collision without there being any net movement of the
substance itself.
Termal convectionis the process in which a temperature
difference causes the mass movement of uid particles
from areas of high thermal energy to areas of low thermal
energy (the colder region).
Termal radiationis energy produced by a source because
of its temperature that travels as electromagnetic waves. It
does not need the presence of matter for its transfer.
Conduction can occur in solids, liquids and gases. Ingases it occurs due to the collision between fast and slow
moving particles where kinetic energy is transferred
from the fast to the slow particle. Te transfer of energy
is very slow because the particles are far apart relative
to solids and liquids. In liquids, a particle at higher
temperature vibrates about its position with increased
vibrational energy. Because the majority of the particles
are coupled to other particles they also begin to vibrate
more energetically. Tese in turn cause further particles
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to vibrate and thermal conduction occurs. Tis process is
also slow because the particles have a large relative mass
and the increase in vibrations is rather small. In solids, the
transfer can occur in one of two ways. Most solids behave
similarly to liquids.
However, solids are held in their xed positions morerigidly than liquids and the transfer of vibrational energy
is more effective. However, again their large masses do not
allow for large energy transfer. If a substance in the solid
or molten form has mobile electrons, as is the case for
metals, these electrons gain energy due to the temperature
rise and their speeds increase much more than those held
in their xed positions in the lattice. Metals are said to be
good conductors of heat but most other solids are good
insulators. Saucepans for cooking are usually made of
copper or aluminium because these metals conduct heat
quickly when placed on a stove. Te handle is made from
a good solid insulator to reduce the conduction of heat.
Generally, liquids and gases are not good thermal
conductors. However, they can transfer heat readily by
convection. Ocean currents, wind and weather patterns
suggest that the mass movement of particles from one area
to another can cause movement of particles on the grand
scale.
Figure 307 shows a potassium permanganate crystal placed
in water inside a convection tube. Heat is applied for a
short period of time and the direction of the purple trail
is noted. Particles in a region of high thermal energy are
further apart and hence their density is lower. In a region
of low thermal energy the particles are closer together and
the region is more dense. As a result, the less dense region
rises as it is pushed out of the way by the more dense
region and a convection current is produced.
Heat
Potassium
permanganatecrystal
water
Convection tube
Figure 307 Convection current.
Another way in which a uid can move is by forced
convection. In this case, a pump or fan system maintains
the movement of a uid. Te cooling system in nuclear
reactors operates on this principle.
All thermal energy ultimately comes from the Sun in our
solar system. It travels through 150 million km of mostly
empty space. At the Earths atmosphere the radiant energy
is mainly reected back into space. However, some is
transmitted and absorbed causing a heating effect. Just as
the Sun emits thermal radiation so does any source that
produces heat such as a light bulb or an electric heater.Termal radiation is mainly electromagnetic waves in
the infra-red region of the electromagnetic spectrum at
temperatures below 1000 C. Above this temperature,
wavelengths of the visible and ultra-violet regions are
also detected. Dull black bodies are better absorbers and
radiators than transparent or shiny bodies.
3.1.5,6 THE MOLE,
MOLAR MASS AND
AVOGADROS NUMBERTe mass of an atom is exceedingly small. For example,the mass of a uorine atom is 3.16 10-23g and the mass of
the isotope carbon12 is 1.99 10-23 g. Because the masses
of atoms are so small, it is more convenient to describe
the mass of an atom by comparing its mass with those of
other atoms.
In 1961 the International Union of Pure and Applied
Chemistry (IUPAC) dened the masses of atoms relative to
carbon12 that was assigned a value of 12.0000. Terefore,
the relative atomic mass is dened as the mass of an atom
when compared with 1/12 the mass of carbon12 atom.
Just as the relative atomic mass is used to describe the
masses of atoms, the relative molecular mass is used to
describe the masses of molecules. Terefore, the relative
molecular mass is dened as the mass of a molecule when
compared with 1/12 of the mass of a carbon12 atom.
It is convenient to group things into quantities. For
example, a box of diskettes, a ream of photocopy paper
(500 sheets), a dozen eggs are common groupings. Te
SI fundamental unit for the amount of a substance is the
mole(mol).
Te mole is the amount of substance that contains asmany elementary particles as there are in 0.012 kg of
carbon12.
Amadeo Avogadro(1776 1856) found that equal volumes
of gases at the same temperature and pressure contained
the same number of particles. One mole of any gas contains
the Avogadro numberof particles NA. It is now known
that one mole of a gas occupies 22.4 dm3 at 0 C and
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101.3 kPa pressure (SP) and contains 6.02 1023
particles.
When using the mole, the atoms or molecules should be
clearly stipulated. For example, one mole of copper atoms
contains 6.02 1023copper atoms. One mole of nitrogen
molecules (N2) contains 6.02 1023
of nitrogen moleculesand 12.04 1023nitrogen atoms.
If we have one mole of NH4NO
3, this contains:
1 mol of NH4
+ions = 6.02 1023ammonium ions
1 mol of NO3
ions = 6.02 1023nitrate ions
2 mol of nitrogen atoms = 1.204 1024nitrogen atoms
4 mol of hydrogen atoms = 2.408 10 24hydrogen atoms
3 mol of oxygen atoms = 1.806 1024oxygen atoms
Te amount of substance (the moles) is related to the mass
and the molar mass according to the following equation:
n = m__M
where
n= amount of a substance in mol, m= the mass in g and
M= the molar mass in g mol -1. Te molar mass can be
obtained from the periodic table.
Example
1. Calculate the number of moles of oxygen
molecules contained in 64.0 g of oxygen gas, O2.
2. Calculate the number of oxygen molecules in part
1 of this example.
3. Determine the volume of oxygen gas that would
be present at SP.
4. Calculate the mass in 0.75 mol of carbon dioxide gas.
Solution
1. n = m__M
=64.0 g
_________________
(
16.0 + 16.0)g mol1= 2 mol
2. Te number of oxygen molecules
= 2NA
the number of molecules
= 6.02 1023 2
= 1.024 1024 molecules.
3. Volume
= 2 mol 22.4 dm3
= 44.8 dm3
4. m = n M
= 0.75 mol (12 +16 +16) g mol-1
= 33 g
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Exercise 3.1 (b)
1. Te internal energy of a substance is equal to:
A. the total potential energy stored in thebonds of a substance
B. the potential and kinetic energy of
molecules in a substance
C. the energy stored in bonds and
intermolecular forces of a substance
D. the translational, rotational and vibrational
motion of particles in the substance
2. Te number of moles of sodium chloride (NaCl)
in 100g of pure sodium chloride is (Mrof NaCl =
58.5 gmol-1)
A. 5850 molB. 0.585 mol
C. 1.71 mol
D. 41.5 mol
3. wo different objects with different temperatures
are in thermal contact with one another. When the
objects reach thermal equilibrium, the direction of
transfer of thermal energy will be
A. from the lower temperature object to the
higher temperature object
B. half way between the temperatures of the
two objects
C. from the higher temperature object to the
lower temperature object
D. in many different directions
4. A sealed ask contains 16 g of oxygen (mass
number 16) and also 8 g of hydrogen (mass
number 1). Te ratio of the number atoms of
hydrogen to the number of atoms of oxygen is
A. 16
B. 8
C. 4D. 2
5. Te number of molecules present in 0.5 mol SO3is
A. 3 1023
B. 6 1023
C. 12 1023
D. 24 1023
6. Te number of atoms present in 0.5 mol SO3is
A. 3 1023
B. 6 1023
C. 12 1023
D. 24 1023
7. Calculate the approximate molar masses of each of
the following molecules and compounds:
(a) Cl2
(b) HCl
(c) CuSO4
(d) Na2CO
3
(e) CH4
8. Calculate the mass of the given amounts of each of
the following substances:
(a) 2.0 mole of iron, Fe(b) 0.2 mole of zinc, Zn
(c) 2.5 mole of carbon dioxide, CO2
(d) 0.001 mole of sulfur dioxide, SO2
(e) 50 mole of benzene, C6H
6
9. Calculate the amount of subtance (number of
mole) in:
(a) 100 g of copper
(b) 5.0 g of oxygen molecules
(c) 100 g of calcium carbonate, CaCO3
(d) 4.4 g of carbon dioxide
(e) 13.88 g of lithium
10. A sample of aluminium sulfate Al2(SO
4)
3has a
mass of 34.2 g. Calculate:
(a) the number of alumimium ions Al3+in the
sample
(b) the number of sulfate ions SO4
2-in the
sample
11. Classify the following as a macroscopic or
microscopic property of a gas
(a) volume
(b) specic heat capacity
(c) kinetic energy of a particle
(d) pressure
(e) temperature
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3.2.1 Define specific heat capacityand thermal
capacity.
3.2.2 Solve problems involving specific heat
capacities and thermal capacities.
3.2.3 Explain the physical dierences between
the solid, liquid and gaseous phases in
terms of molecular structure and particle
motion.
3.2.4 Describe and explain the process of phase
changes in terms of molecular behaviour.
3.2.5 Explain in terms of molecular behaviour
why temperature does not change during aphase change.
3.2.6 Distinguish between evaporation and
boiling.
3.2.7 Define specific latent heat.
3.2.8 Solve problems involving specific latent
heats. IBO 2007
3.2.1 THERMALCAPACITY
When different substances undergo the same temperature
change they can store or release different amounts of
thermal energy. Tey have different thermal (heat)
capacities. If a substance has a high heat capacity it will
take in the 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 thermal energy. Tey also
cool more slowly because they give out thermal energy at
a slower rate.
We dene the thermal (heat) capacity as,
Termal Capacity =Q
___
T J K -1
Qis the change in thermal energy in joules J
Tis the change in temperature in kelvin degrees K.
Water is used in car cooling systems and heating systems
because of its high thermal capacity. A metal heat sink is
used on the back of refrigerators because of its low thermal
capacity.
Example
Te thermal capacity of a sphere of lead is 3.2 103 JK-1
Determine how much heat can be released if the
temperature changes from 61C to 25C.
Solution
Q T apacity= Thermal c
3.2 103JK
1 61 25( ) C=
3.2 103
JK1
36 C
115200J
1.2 105
J
Note that a change in Kelvin temperature is the
same as a change in Celsius temperature
3.2.2 SPECIFICHEATCAPACITY
Heat capacity does not take into account the fact that
different masses of the same substance can absorb or
release different amounts of thermal energy.
Consider three one kilogram blocks of aluminium, zinc
and lead with the same sized base that have been heated
to the same temperature of 80 C. Tey are quickly placed
on top of a large block of candle wax for a time period as
shown in Figure 308.
Figure 308 Front-on view of the
metal blocks after a period of time.
3.2 THERMAL PROPERTIES OF MATTER
C A N D L E WAX
Aluminium Zinc Lead
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Te aluminium block melts the most wax and the lead
melts the least. Tereore, the metals o the same mass
give out different amounts o thermal energy in a certain
time period. Tis can be explained rom a microscopic
viewpoint. Te kilogram unit masses have different
numbers o particles o different types and masses. Te
metal blocks were given the same amount o thermalenergy when they were heated to 80 C. When the thermal
energy gained by each metal is distributed amongst its
particles, the average energy change o each particle will
be different or each metal.
o obtain a characteristic value or the heat capacity
o materials, equal masses o the materials must be
considered. Te physical property that includes the mass
is called the specific heat capacity o a substance c.
Specic heat capacityor specific heat is the heat capacity
per unit mass. It is defined as the quantity o thermal
energy required to raise the temperature o a unit mass oa substance by one degree Kelvin.
c=Q
_____
m
Q= m c
Q= the change in thermal energy required to produce a
temperature change in Joules, J.
m= mass o the material in grams (g) kilograms (kg)
= the temperature change in Kelvin, K.
Note that is always positive because heat always
transers rom the higher temperature region to the lower
temperature region.
For gases, the molar heat capacity at constant volume Cv
and the molar heat capacity at constant pressure Cp are
more commonly used. Molar heat capacity is the quantity
o heat required to raise the temperature o one mole o the
gas by one degree Kelvin under the constant condition.
Figure 309 shows the specific heat capacity or some
common substances at room temperature (except ice)
Substance Specic heatJ kg -1K -1 Substance Specic heatJ kg -1K -1
Lead 1.3 102 Iron 4.7 102
Mercury 1.4 102 Aluminium 9.1 102
Zinc 3.8 102 Sodium 1.23 103
Brass 3.8 102 Ice 2.1 103
Copper 3.85 102 Water 4.18 103
Figure 309 Specific heat of some common substances
Example
Determine how much thermal energy is released when
650 g o aluminium is cooled rom 80 C to 20 C.
Solution
Using the fact that Q = m.c., we have,
Q = 0.650 kg 9.1 102J kg-1K-1 (80 20) K
= 3.549 104J
= 4 104J
Tat is, 4 104J of heat is released.
Example
An active solar heater is used to heat 50 kg o water initially
at a temperature o 12 C. I the average rate that thermal
energy is absorbed in a one hour period is 920 J min -1 ,
determine the equilibrium temperature afer one hour
Solution
Quantity of heat absorbed in one hour = 920 J min -1
60 min = 5.52 104J
Using the fact that Q = m c , we have
5.52 104J = 5.0 101kg 4.18 103J kg-1K-1 (f 12)K
5.52 104J = 2.09 105JK-1 (f 12) C
5.52 104J = 2.09 105f 2.51 106J
2.09 105f= 5.52 104J + 2.51 106J
f=
2.553 106J
______________
2.09 105(J K1)
f= 12.26 C
f= 12 C
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EXTENSION METHODS TO DETERMINE
SPECIFIC HEAT CAPACITY
A calorimeter is a useul piece o equipment or
investigations in Termal Physics because it allows masses
at different temperatures to be mixed with minimum
energy loss to the surroundings. It is used or direct andindirect methods in determining the specific heat capacity
o a substance. (Te name o the instrument is derived
rom the Imperial unit, the calorie.)
copper vessel
heating coil
liquid
thermometer
stirrer
lagging
joulemeter
Figure 310 Calorimeter being used to measure the
heating effect of a current
Figure 310 illustrates the use o a calorimeter to determine
the specific heat capacity o a liquid, in this case water.
Te heating coil is used to convert electrical energy to
thermal energy. Te electrical energy can be measured by
a joulemeter or by using a voltmeter/ammeter circuit. Te
duration o time o electrical input is noted.
Te thermal energy gained by the calorimeter cup and the
water is equal to the electrical energy lost to the calorimeter
cup and water.
Electrical energy lost =
V I t = [m c T]calorimeter cup
+ [m c T]water
where Vis the potential difference across the heating coil
in volts V and Iis the current in the amperes, A.
Te specific heat capacity, c, o the calorimeter cup isobtained rom published values. Te other quantities are
recorded and the specific heat capacity o the water is
calculated.
In calorimeter investigations, heat losses to the
surroundings need to be minimised. It is normal to polish
the calorimeter cup to reduce loss o heat due to radiation.
Te calorimeter is also insulated with lagging materials
such as wool or polystyrene to reduce heat loss due to
conduction and convection.
Afer the power supply is switched off, the temperature
should continue to rise or a period, and then level out or
an infinite time. However, heat is lost to the surroundings,
and the maximum temperature that could be achieved,in theory, is never reached. Instead appreciable cooling
occurs. One method used to estimate the theoretical
maximum temperature is to use a cooling correction
curveas shown in Figure 311.
{Note that cooling correction is not required in the syllabus
but is included or possible extended essays.}
t 2t 3t
A1
A2
2
A1
A2------ =
1
3 2 +=
3
, so that
2
1=( )
(= correction)
Temperatur
e,
C
Time, minutes
actual curve
theoreticalcurve
roomtemp
Figure 311 Graph of cooling correction.
A cooling correction is based on Newtons Law o Cooling.
It states that the rate o loss o heat o a body is proportional
to the difference in temperature between the body and its
surroundings (excess temperature). A ull explanation o
this Law will not be given. I the power supply is switched off
at time 2tminutes, then the temperature should continue
to be recorded or a urther t minutes. Te correction
to the temperature can be obtained rom the graph as
shown. Te final temperature, 3,is then given as the final
temperature o the thermometer plus the correction .
Another direct electrical method used to determine the
specific heat capacity o a metal is shown in Figure 312.
An immersion heater is placed into a metal block. Te
hole or the heater is lubricated with oil to allow evenheat transmission. Te electrical energy lost to the block
is recorded or a given period o time and the specific
heat o the metal is calculated. Cooling correction is more
important in this case because the temperatures under
which the investigation is carried out could be much
higher than was the case when using a calorimeter.
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metal block
thermometer
lagging
V
A
Low voltagesupply
immersionheater
Figure 312 Electrical method using
an immersion heater and a metal block
A common indirect method to determine the specific
heat capacity of a solid and liquids is called the method of
mixtures. In the case of a solid, a known mass of the solid
is heated to a certain temperature, and then transferred
to a known mass of liquid in a calorimeter whose specific
heat capacity is known. Te change in temperature is
recorded and the specific heat of the solid is calculatedfrom the results obtained. In the case of a liquid, a hot
solid of known specific heat is transferred to a liquid of
unknown specific heat capacity.
Example
A block of copper of mass 3.0 kg at a temperature of
90 C is transferred to a calorimeter containing 2.00 kg of
water at 20 C. Te mass of the copper calorimeter cup is
0.210 kg. Determine the final temperature of the water.
Solution
Te thermal energy gained by the water and the calorimeter
cup will be equal to the thermal energy lost by the copper.
Tat is, [mc]copper
= [mc]calorimeter cup
+ [mc]cup
We also have that,
Termal energy lost by the copper
= (3.0 kg) (3.85 102J kg -1K -1) (90.0 f) K
Termal energy gained by the water
= (2.0 kg) (4.18 103J kg -1K -1) (f 20.0) K
Termal energy gained by the cup
= (0.21 kg) (9.1 102J kg -1K -1) (f 20.0) K
1.04 105 1.155 103f
= (8.36 103f 1.67 105) +(1.91 102f 3.82 103)
Tat is,
9.71 103f = 2.75 105
Giving
f = 28.3 C
Te nal temperature of the water is 28 C
Exercise 3.2 (a)
1. Te amount of thermal energy required to raise
the temperature of 1.53 103g of water from 15 K
to 40 K is
A. 1.6 107J
B. 1.6 105J
C. 4.4 107J
D. 4.4 105J
2. Te specific heat capacity of a metal block of mass
mis determined by placing a heating coil in it, as
shown in the following diagram.
Te block is electrically heated for time t and the
maximum temperature change recorded is . Te
constant ammeter and voltmeter readings during
the heating are Iand V respectively. Te electrical
energy supplied is equal to VIt.
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metal block
thermometer
lagging
V
A
Low voltagesupply
immersionheater
Te specific heat capacity is best calculated using
which one of the following expressions?
A. c=VI
m
B. c=
m
VI
C. c=m
VIt
D. c=VIt
m
3. 5.4 106J of energy is required to heat a 28 kg
mass of steel from 22 C to 450 C. Determine the
specific heat capacity of the steel.
4. Liquid sodium is used as a coolant in some
nuclear reactors. Describe the reason why liquid
sodium is used in preference to water.
5. 6.00 102kg of pyrex glass loses 8.70 106J of
thermal energy. If the temperature of the glass was
initially 95.0 C before cooling, calculate is its final
temperature.
(ake the specific heat capacity of pyrex glass to be
8.40 10 2J kg -1 K-1)
6. A piece of wood placed in the Sun absorbs more
thermal energy than a piece of shiny metal of the
same mass. Explain why the wood feels cooler
than the metal when you touch them.
7. A hot water vessel contains 3.0 dm3 at 45 C.
Calculate the rate that the water is losing thermal
energy (in joules per second) if it cools to 38 C
over an 8.0 h period.
8. Determine how many joules of energy are released
when 870 g of aluminium is cooled from 155 C to
20 C.
9. If 2.93 106J is used to raise the temperature of
water from 288 K to 372 K, calculate the mass of
water present.
10. 1.7 mJ of energy is required to cool a 15 kg mass of
brass from 400 C to 25 C. Determine the specific
heat capacity of brass.
11. A piece of iron is dropped from an aeroplane at
a height of 1.2 km. If 75% of the kinetic energy
of the iron is converted to thermal energy on
impact with the ground, determine the rise in
temperature.
12. If 115 g of water at 75.5 C is mixed with 0.22 kg of
water at 21 C, determine the temperature of the
resulting mixture.
13. Describe an experiment that would allow you to
determine the specific heat capacity of a metal.
(i) Sketch the apparatus.
(ii) Describe what measurements need to be
made and how they are obtained.
(iii) State and explain the equation used to
calculate the specific heat capacity of the
metal.
(iv) Describe 2 main sources of error that are
likely to occur in the experiment.
(v) Is the experimental value likely to be higher
or lower than the theoretical value, if the
experiment was carried out in a school
laboratory? Explain your answer.
14. A heating uid releases 4.2 107 Jkg-1 of heat as it
undergoes combustion. If the uid is used to heat
250 dm3of water from 15 C to 71 C, and the
conversion is 65% efficient, determine the mass
of the heating uid that will be consumed in this
process.
15. A large boulder of 125 kg falls off a cliff of height
122 m into a pool of water containing 120 kg of
water. Determine the rise in temperature of the
water. Assume that no water is lost in the entry ofthe boulder, and that all the heat goes to the water.
16. A thermally insulated container of water is
dropped from a large height and collides
inelastically with the ground. Determine the
height from which it is dropped if the temperature
of the water increases by 1.5 C.
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17. A piece of copper is dropped from a height of
225 m. If 75% of its kinetic energy is converted to
heat energy on impact with the ground, calculate
the rise in temperature of the copper. (Use the
table of specific heat capacities to find the value for
copper).
18. 5kg of lead shot is poured into a cylindrical
cardboard tube 2.0 m long. Te ends of the tube
are sealed, and the tube is inverted 50 times. Te
temperature of the lead increases by 4.2 C. If
the specific heat of lead is 0.031 kcal kg-1C-1,
determine the number of work units in joules that
are equivalent to the heat unit of 1 kilocalorie.
3.2.3 PHASESTATES
An understanding of thermal energy is based upon a theory
called the moving particle theory or kinetic theory (forgases) that uses models (Figure 314) to explain the structure
and nature of matter. Te basic assumptions of this moving
particle theory relevant to thermal energy are:
all matter is composed of extremely small particles
all particles are in constant motion
if particles collide with neighbouring particles, they
conserve their kinetic energy
a mutual attractive force exists between particles
solid liquid gas
Figure 314 Arrangement of particles
in solids, liquids and gases
An atom is the smallest neutral particle that represents an
element as displayed in a periodic table of elements. Atoms
contain protons, neutrons and electrons and an array of
other sub-atomic particles. Atomic diameters are of the
order of magnitude 1010
m. Atoms can combine to formmolecules of substances. In chemistry, the choice of the
terms e.g. atoms, molecules, ions are specific to elements
and compounds. In physics, the word particle is used to
describe any of these specific chemistry terms at this stage
of the course.
As previously mentioned, evidence for the constant motion
of particles can be gained from observation of what is
known as Brownian Motion. If pollen grains from owers
are placed on water and observed under a microscope, the
pollen grains undergo constant random zig-zag motion.
Te motion becomes more vigorous as the thermal energy
is increased with heating. A Whitley Bay smoke cell uses
smoke in air to achieve the same brownian motion. In both
cases, the motion is due to the smaller particles striking
the larger particles and causing them to move.
Te large number of particles in a volume of a solid, liquid
or gas ensures that the number of particles moving in all
directions with a certain velocity is constant over time.
Tere would be no gaseous state if the particles were losing
kinetic energy.
A mutual attractive force must exist between particles
otherwise the particles of nature would not be combined
as we know them. Further explanation of this assumption
will be given later in this topic.
Matter is defined as anything that has mass and occupiesspace. Tere are four states of matter which are also called
the four phases of matter solids, liquids, gases and
plasma. Most matter on Earth is in the form of solids,
liquids and gases, but most matter in the Universe is in the
plasma state. Liquids, gases and plasma are uids.
A plasma is made by heating gaseous atoms and molecules
to a sufficient temperature to cause them to ionise. Te
resulting plasma consists then of some neutral particles but
mostly positive ions and electrons or other negative ions.
Te Sun and other stars are mainly composed of plasma.
Te remainder of this chapter will concentrate on the other
three states of matter, and their behaviour will be explained in
terms of their macroscopic and microscopic characteristics
of which some are given in Figures 315 and 316.
Characteristic Solid Liquid Gas
Shape Definite Variable Variable
Volume Definite Definite Variable
CompressibilityAlmost
Incompressible
Very slightly
Compressible
Highly
Compressible
Diffusion Small Slow Fast
Comparative
Density High High Low
Figure 315 Some macroscopic
characteristics of solids, liquids and gases
Macroscopic properties are all the observable behaviours of
that material such as shape, volume and compressibility.
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Te many macroscopic or physical properties of a substance
can provide evidence for the nature and structure of that
substance.
Characteristic Solid Liquid Gas
Kinetic energy Vibrational
Vibrational
Rotational
Some
translational
Mostly
translationalHigher
rotational
Higher
vibrational
Potential energy High Higher Highest
Mean molecular
Separation (r0)
r0
r0
10r0
Termal energy
of particles ()< /10 < > /10 >
Molecules per m3 1028 1028 1025
Figure 316 Some microscopiccharacteristics of solids, liquids and gases
Microscopic characteristics help to explain what is
happening at the atomic level, and this part of the model
will be interpreted further at a later stage.
Te modern technique of X-ray diffraction that will be
studied in detail in a later chapter has enabled scientists
to determine the arrangement of particles in solids. Te
particles are closely packed and each particle is strongly
bonded to its neighbour and is held fairly rigidly in a fixed
position to give it definite shape in a crystalline lattice.
Some patterns are disordered as is the case for ceramics,
rubber, plastics and glass. Tese substances are said to be
amorphous. Te particles have vibrational kinetic energy
in their fixed positions and the force of attraction between
the particles gives them potential energy.
In liquids the particles are still closely packed and the
bonding between particles is still quite strong. However,
they are not held as rigidly in position and the bonds can
break and reform. Tis infers that the particles can slowly
and randomly move relative to each other to produce
variable shape and slow diffusion. Particles in a liquid
have vibrational, rotational and some translational kineticenergy due to their higher mean speeds. Te potential
energy of the particles in a liquid is somewhat higher than
for a solid because the spacing between the particles is
large.
In gasesthe particles are widely spaced and the particles
only interact significantly on collision or very close
approach. Because of the rapid random zig-zag motion of
the particles, a gas will become dispersed throughout any
container into which it is placed. Diffusion (the spreading
out from the point of release) can occur readily. Gases
are compressible because the particles are widely spaced
at a distance much greater than the size of the particles.
Te much higher mean speeds are due to an increased
translational kinetic energy of the particles. Gases have
a much higher potential energy than liquids because theparticles are much further apart.
3.2.4 THEPROCESSOFPHASE
CHANGES
A substance can undergo changes of state or phase changes
at different temperatures. Pure substances (elements and
compounds) have definite melting and boiling points
which are characteristic of the particular pure substance
being examined. For example, oxygen has a melting point
of -218.8 C and a boiling point of -183 C at standard
atmospheric pressure.
Te heating curve for benzene is illustrated in Figure 317.
A sample of benzene at 0C is heated in a closed container
and the change in temperature is graphed as a function
of time. Te macroscopic behaviour of benzene can be
described using the graph and the microscopic behaviour
can be interpreted from the macroscopic behaviour.
SO L I D
L I QU ID
G AS
L iquid-gas phasechange
Solid-liquidphase change
Temperature /C
H eating time /min
meltingpoint
boilingpoint
5.5C
80C
Figure 317 Heating curve for benzene.
When the solid benzene is heated the temperature
begins to rise. When the temperature reaches 5.5 C the
benzene begins to melt. Although heating continues the
temperature of the solid liquid benzene mixture remains
constant until all the benzene has melted. Once all thebenzene has melted the temperature starts to rise until the
liquid benzene begins to boil at a temperature of 80 C.
With continued heating the temperature remains constant
until all the liquid benzene has been converted to the
gaseous state. Te temperature then continues to rise as
the gas is in a closed container.
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3.2.5 MOLECULARBEHAVIOURAND
PHASECHANGES
he moving particle theory can be used to explain the
microscopic behaviour o these phase changes. Whensolid benzene is heated the particles o the solid vibrate
at an increasing rate as the temperature is increased.
he vibrational kinetic energy o the particles increases.
At the melting point a temperature is reached at which
the particles vibrate with suicient thermal energy to
break rom their ixed positions and begin to slip over
each other. As the solid continues to melt, more and
more particles gain suicient energy to overcome the
orces between particles and over time all the solid
particles change to a liquid. he potential energy o
the system increases as the particles begin to move. As
heating continues the temperature o the liquid rises
due to an increase in the vibrational, rotational andpart translational kinetic energy o the particles. At
the boiling point a temperature is reached at which the
particles gain suicient energy to overcome the inter-
particle orces present in the liquid benzene and escape
into the gaseous state. Continued heating at the boiling
point provides the potential energy needed or all the
benzene molecules to be converted rom a liquid to a
gas. With urther heating the temperature increases
due to an increase in the kinetic energy o the gaseous
molecules due to the larger translational motion.
3.2.6 EVAPORATIONANDBOILING
When water is lef in a container outside, exposed to the
atmosphere, it will eventually evaporate. Mercury rom
broken thermometers has to be cleaned up immediately
due to its harmul effects. Water has a boiling point o
100 C and mercury has a boiling point o 357 C. Yet they
both evaporate at room temperature.
Te process o evaporation is a change rom the liquid
state to the gaseous state that occurs at a temperature
below the boiling point.
Te moving particle theory can be applied to understandthe evaporation process. A substance at a particular
temperature has a range o kinetic energies. So in a liquid
at any particular instant, a small raction o the molecules
will have kinetic energies considerably greater then the
average value. I these particles are near the surace o the
liquid, they may have enough kinetic energy to overcome
the attractive orces o neighbouring particles and escape
rom the liquid as a vapour. Now that the more energetic
particles have escaped, the average kinetic energy o the
remaining particles in the liquid has been lowered. Since
temperature is proportional to the average kinetic energy
o the particles, a lower kinetic energy implies a lower
temperature, and this is the reason why the temperature o
the liquid alls as evaporative coolingtakes place. Another
way o explaining the temperature drop is in terms o latent
heat. As a substance evaporates, it needs thermal energyinput to replace its lost latent heat o vaporisation and this
thermal energy can be obtained rom the remaining liquid
and its surroundings.
A substance that evaporates rapidly is said to be a volatile
liquid. A liquids volatility is controlled by a actor known
as its equilibrium vapour pressure. Tere are orces that
must be overcome beore a particle can leave the surace o
a liquid. Different liquids exert different vapour pressures
that depend on the relative strengths o the intermolecular
orces present in the liquids. Hydrouorocarbons and
CFCs used in rerigerators, and ether, chloroorm and
ethanol have relatively high vapour pressures.
Te values in Figure 318 compare the vapour pressure o
some liquids at 293 K.
Substance Vapour pressure / kPa
Ether 58.9
Chloroorm 19.3
Ethanol 5.8
Water 2.3
Mercury 0.0002
Figure 318 Some common vapour pressures
Although the vapour pressure o mercury is much lower
than the other substances listed at room temperature,
some evaporation does occur. Because o its extreme
toxicity any mercury spill is treated seriously. Ether has a
high vapour pressure. I a stream o air is blown through a
sample o ether in a beaker that is placed on a thin film o
water, the water will eventually turn to ice.
When overheating occurs in a human on hot days, the
body starts to perspire. Evaporation o the perspiration
results in a loss o thermal energy rom the body so thatbody temperature can be controlled. Local anaesthetics
with high vapour pressures are used to reduce pain on the
skin. Termal energy ows rom the surrounding esh
causing its temperature to drop and thereby anaesthetises
the area.
A liquid boils when the vapour pressure o the liquid
equals the atmospheric pressure o its surroundings.
As the boiling point is reached, tiny bubbles appear
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throughout the liquid. I the vapour pressure o the bubble
is less than the atmospheric pressure the bubbles are
crushed. However a point is reached when the pressures
are equal. Te bubble will then increase in size as it rises to
the surace o the liquid.
Exercise 3.2 (b)
1. When smoke is strongly illuminated and viewed
under a microscope it is possible to observe
A. all particles moving in straight lines
B. smoke particles moving randomly by air
molecules
C. smoke particles colliding with each other
D. air molecules in random motion
2. Te internal energy o a monatomic gas such asneon is mainly due to
A. the potential energy holding the atoms in
fixed positions
B. the vibrational energy o the atoms
C. the random translational energy o the
atoms
D. the rotational energy o the atoms
3. For a given mass o a certain liquid, the magnitude
o the thermal energy transer is the same or the
ollowing two processes
A. reezing and sublimation
B. melting and evaporation
C. evaporation and condensation
D. sublimation and condensation
4. Which o the ollowing is a unit o thermal
energy?
A. watt
B. the product o the newton and the metre
C. the quotient o the watt and the second
D. the product o the joule and the second
Base your answers to Questions 5 and 6 on the ollowing
graph. Te graph shows the temperature o an unknown
substance o mass 10.0 kg as heat is added at a constant
rate o 6300 Jmin-1. Te substance is a solid at 0 0C.
Time / min
0 5 10 15 20
Temperature/oC
150
100
50
5. Te internal potential energy o the unknown
substance increases without any change in internal
kinetic energy rom the beginning o the:
A. first minute to the end o the ourth minute
B. seventh minute to the end o the
seventeenth minuteC. seventeenth minute to the end o the twenty
first minute
D. nineteenth to the end o the twenty fifh
minute
6. Te specific heat capacity o the substance when it
is solid is:
A. 63 Jkg-1K-1
B. 105 Jkg-1K-1
C. 126 Jkg-1K-1
D. 504 Jkg-1K-1
7. Give five macroscopic and five microscopic
characteristics o the liquid/gas in a butane lighter.
8. Describe the components o internal energy in
each o the ollowing situations
(a) air at room temperature
(b) a jar o honey
(c) a melting ice cream.
9. Explain the difference between heat, thermal
energy and temperature.
10. Does a block o ice contain any heat? Explain your
answer ully.
11. Draw a ully labelled cooling curve or the
situation when steam at 110 C is converted to ice
at 25 C.
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12. (a) Convert 63 C to Kelvin
(b) Convert 52 K to degrees Celsius
13. Te temperatures o the same volume o air and
water are raised by a small amount. Explain why
a different amount o heat is required or each
process.
14. I you increase the heat under a pot o water in
which you are boiling potatoes, will the potatoes
be cooked aster?
15. I you wanted to cool a bottle o sof drink at the
beach, would you be better to wrap a wet towel
around it or to put it into the seawater? Explain
your answer.
16. Why is it important not to stand in a draught afer
vigorous exercise?
17. Describe and explain the process o evaporative
cooling in terms o its microscopic properties.
18. A kettle made o stainless steel containing water
is heated to a temperature o 95 C. Describe
the processes o thermal energy transer that are
occurring in the stainless steel kettle and the water.
3.2.7 LATENTHEAT
Te thermal energy which a particle absorbs in melting,
evaporating or sublimating or gives out in reezing,
condensing or sublimating is called latent heat because it
does not produce a change in temperature. See Figure 320.
T H E R M A L E N E R G Y A D DE D
melting evaporation
SO L ID L IQUID G A S
freezing condensation
sublimation
T H E R M A L E N E R G Y GIV E N OU T
Figure 320 Macroscopic
transformations between states of matter.
Sublimation is a change o phase directly rom a solid to
a gas or directly rom a gas to a solid. Iodine and solid
carbon dioxide are examples o substances that sublime.
When thermal energy is absorbed/released by a body,
the temperature may rise/all, or it can remain constant.
I the temperature remains constant then a phase change
will occur as the thermal energy must either increase the
potential energy o the particles as they move urther
apart or decrease the potential energy o the particles as
they move closer together. I the temperature changes,then the energy must increase the average kinetic energy
o the particles.
Te quantity o heat required to change one kilogram o
a substance rom one phase to another is called thelatent
heat of transformation.
Q = mL
Qis the quantity o heat absorbed or released during the
phase change in J,
mis the mass o the substance in kg and
Lis the latent heat o the substance in J kg -1
Lcould be the latent heat o usion L, the latent heat o
vaporisation Lvor the latent heat o sublimation L
s. Te
latent heat o usion o a substance is less than the latent
heat o vaporisation or the latent heat o sublimation. More
work has to be done to reorganise the particles as they
increase their volume in vaporisation and sublimation
than the work required to allow particles to move rom
their fixed position and slide over each other in usion.
Figure 321 lists the latent heat o some substances.
Substance Melting
point
K
Latent heat
of fusion
105 J kg-1
Boiling
point
K
Latent heat of
Vaporisation
105J kg-1
Oxygen 55 0.14 90 2.1
Ethanol 159 1.05 351 8.7
Lead 600 0.25 1893 7.3
Copper 1356 1.8 2573 73
Water 273 3.34 373 22.5
Figure 321 Some Latent Heat Values
Example
Calculate the heat energy required to evaporate 5.0 kg o
ethanol at its boiling point.
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Solution
Given that m = 5.0 kg and Lv= 8.7 105J kg -1.
We then have,
= 4.35 106J = 4.4 106J
Te heat energy required for the vaporisation is 4.4 106J.
Example
Determine the heat energy released when 1.5 kg of
gaseous water at 100 C is placed in a freezer and
converted to ice at -7 0C. Te specific heat capacity of ice
is 2.1 103J kg1 K1..
Solution
Te energy changes in this process can be represented as
shown in Figure 322.
Using
Q = mLV+ mc
WAER+ mL
f+ mc
ICE
= m [LV+ c
WAER+ L
f+ c
ICE]
= 1.5 [22.5 105+ (4180 100) + 3.34 105+ (2100 7)]
= 4.52 106J
Tat is, the energy released is 4.5 106J or 4.5 MJ.
T H E R M A L E N E R G Y R E L E A SE D
I C E at L IQUID water at GASE OUS water at
7C 0 C 0 C 100 C 100 C
L atent heat of fusion L atent heat of evaporation
Specic heatI ce Specic heat water
Figure 322 Energy released in steam-ice change.
Te latent heat of vaporisation can be found using a self-
jacketing vaporiser as shown in Figure 323. Te liquid
to be vaporised is heated electrically so that it boils at a
steady rate. Te vapour that is produced passes to the
condenser through holes labelled H in the neck of the
inner ask. Condensation occurs in the outer ask and
the condenser.
A
C old water
C ondenser
Water outow
Liquid underinvestigation
Heating coil
Vapour acting asa jack et
C ollecting vessel
C ondensed vapour
V
H H
Figure 323 Latent heat of vaporisation apparatus.
Eventually, the temperature of all the parts of the apparatus
becomes steady. When this steady state is reached, a
container of known mass is placed under the condenser
outlet for a measured time t, and the measured mass of the
condensed vapour mis determined. Te heater current I
is measured with the ammeter A and potential difference
V is measured with a voltmeter V. Tey are closely
monitored and kept constant with a rheostat.
Te electrical energy supplied is used to vaporise the liquid
and some thermal energy His lost to the surroundings.
Terefore:
V1I
1t= m
1L
V+ H
In order to eliminate Hfrom the relationship, the process
is repeated using a different heater potential difference
and current. Te vapour is collected for the same time t
Te rate of vaporisation will be different but the heat lost
to the surroundings will be the same as each part of the
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apparatus will be at the same temperature as it was with
the initial rate vaporisation.
Terefore:
V2I
2t= m
2L
V+ H
By subtracting the two equations:
(V1I
1 V
2I
2)t= (m
1 m
2)L
V
From this equation, the value of the latent heat
of vaporisation of the unknown substance can be
determined.
Exercise 3.2 (c)
1. Te specific latent heat of fusion of ice is the heatrequired to
A. raise the temperature of ice from 0 C to 10 C
B. change 1 dm3of ice at 0 C to water at 0 C
C. change 1kg of ice at 0 C to water at 0 C
D. change the temperature of 1 kg by 10 C
2. A substance changes from liquid to gas at its
normal boiling temperature. What change, if
any, occurs in the average kinetic energy and the
average potential energy of its molecules?
Average kinetic Average potential
energy energy
A. constant increases
B. increases constant
C. increases decreases
D. constant constant
3. Termal energy is transferred to a mass of water
in four steps. Which one of the four steps requires
the most thermal energy?
A. 5 C to 20 CB. 15 C to 35 C
C. 75 C to 90 C
D. 95 C to 101 C
4. Determine the amount of thermal energy that is
required to melt 35 kg of ice at its melting point.
5. A 5.0 102g aluminium block is heated to 350 C.
Determine the number of kilograms of ice at 0 C
that the aluminium block will melt as it cools.
6. Steam coming from a kettle will give you a nastier
burn than boiling water. Explain why.
7. An immersion heater can supply heat at a rate of
5.2 102J s -1. Calculate the time that it will take
to completely evaporate 1.25 10-1kg of water
initially at a temperature of 21 C?
8. A 3.45 kg sample of iron is heated to a temperature
of 295 C and is then transferred to a 2.0 kg copper
vessel containing 10.0 kg of a liquid at an initial
temperature of 21.0 C. If the final temperature of
the mixture is 31.5 C, determine the specific heatcapacity of the liquid?
9. A mass of dry steam at 1.0 102C is blown over
a 1.5 kg of ice at 0.0 C in an isolated container.
Calculate the mass of steam needed to convert the
ice to water at 21.5 C.
10. A freezer in a refrigerator takes 2.00 hours to
convert 2.15 kg of water initially at 21.5 C to just
frozen ice. Calculate the rate at which the freezer
absorbs heat.
11. Describe an experiment to determine the specific
heat capacity of an unknown metal. Sketch the
apparatus used and describe what measurements
are made. State the main sources of error and
explain how they can be minimised.
12. Calculate how much thermal energy is released
when 1.2 kg of steam at 100 C is condensed to
water at the same temperature.
(Lv= 2.25 106Jkg-1)
13. Determine how much energy is released when
1.5 kg of gaseous water at 100 C is placed in afreezer and converted to ice at 7 C . (the specific
heat capacity of ice is 2.1 103J kg-1 K-1).
14. Describe an experiment that can be used to
determine the latent heat of vaporisation of a
liquid.
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KINETIC MODEL OF AN IDEAL GAS
3.2.9 Define pressure.
3.2.10 State the assumptions of the kinetic model
Of an ideal gas.
3.2.11 State that temperature is a measure of
the average random kinetic energy of the
molecules of an ideal gas.
3.2.12 Explain the macroscopic behaviour of an
ideal gas in terms of a molecular model. IBO 2007
3.2.9 PRESSURE
Investigations into the behaviour of gases involve
measurement of pressure, volume, temperature and mass.Experiments use these macroscopic properties of a gas to
formulate a number of gas laws.
In 1643 orricelli found that the atmosphere could
support a vertical column of mercury about 76 cm high
and the first mercury barometer became the standard
instrument for measuring pressure. Te pressure unit
760 mm Hg (760 millimetres of mercury) represented
standard atmospheric pressure. In 1646, Pascal found that
the atmosphere could support a vertical column of water
about 10.4 m high.
For our purposes in this section, pressurecan be defined
as the force exerted over an area.
Pressure = Force / Area
P = F /A
Te SI unit of pressure is the pascal Pa.
1 atm = 1.01 105Nm-2= 101.3 kPa = 760 mmHg
3.2.10 THEKINETICMODELOFAN
IDEALGAS
An ideal gas is a theoretical gas that obeys the ideal gas
equation exactly. Real gases conform to the gas laws under
certain limited conditions but they can condense to liquids,
then solidify if the temperature is lowered. Furthermore,
there are relatively small forces of attraction between
particles of a real gas, and even this is not allowable for
an ideal gas.
Most gases, at temperatures well above their boiling pointsand pressures that are not too high, behave like an ideal gas.
In other words, real gases vary from ideal gas behaviour at
high pressures and low temperatures.
When the moving particle theory is applied to gases it is
generally called the kinetic theory of gases. Te kinetic
theory relates the macroscopic behaviour of an ideal gas to
the behaviour of its molecules.
Te assumptions or postulates of the moving particle
theory are extended for an ideal gas to include
Gases consist of tiny particles called atoms(monatomic gases such as neon andargon) or
molecules.
Te total number of molecules in any sample of a
gas is extremely large.
Te molecules are in constant random motion.
Te range of the intermolecular forces is small
compared to the averageseparation of the
molecules.
Te size of the particles is relatively small compared
with the distance between them.
Collisions of short duration occur between
molecules and the walls of the container and the
collisions are perfectly elastic.
No forces act between particles except when they
collide, and hence particlesmove in straight lines.
Between collisions the molecules obey Newtons
Laws of motion.
Based on these postulates the view of an ideal gas is one
of molecules moving in random straight line paths at
constant speeds until they collide with the sides of the
container or with one another. Teir paths over time are
therefore zig-zags. Because the gas molecules can move
freely and are relatively far apart, they occupy the total
volume of a container.
Te large number of particles ensures that the number of
particles moving in all directions is constant at any time.
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3.2.11 TEMPERATUREANDAVERAGE
RANDOMKINETICENERGY
Temperature is a measure of the average random kinetic
energy of an ideal gas.
At the microscopic level, temperature is regarded
as the measure o the average kinetic energy per
molecule associated with its movements. For gases,
it can be shown that the average kinetic energy,
Ek1
2---mv2
3
2---kT= = where k= Boltzmann constant
v2 T
Te term average kinetic energy is used because, at a
particular temperature different particles have a wide
range o velocities, especially when they are converted to agas. Tis is to say that at any given temperature the average
speed is definite but the velocities o particular molecules
can change as a result o collision.
Figure 325 shows a series o graphs or the same gas
at three different temperatures. In 1859 James Clerk
Maxwell (1831-1879) and in 1861 Ludwig Boltzmann
(1844-1906) developed the mathematics o the kinetic
theory o gases. Te curve is called a Maxwell-Boltzmann
speed distribution and it is calculated using statistical
mechanics. It shows the relationship between the relative
number o particles N in a sample o gas and the speeds v
that the particles have when the temperature is changed.
(T3> T
2> T
1)
Te graphs do not show a normal distribution as the
graphs are not bell-shaped. Tey are slightly skewed to
the lef. Te minimum speed is zero at the lef end o
the graphs. At the right end they do not touch the x-axis
because a small number o particles have very high speeds.
Te peak o each curve is at the most probable speed vp
a large number o particles in a sample o gas have their
speeds in this region. When the mathematics o statistical
mechanics is applied it is ound that mean squared speed
vav
2 is higher than the most probable speed. Another
quantity more ofen used is called the root mean square
speed Vrmsand it is equal to the square root o the meansquared speed.
vrms v2
=
Te root mean square is higher than the mean squared
speed.
Other eatures o the graphs show that the higher the
temperature, the more symmetric the curves becomes.
Te average speed o the particles increases and the peak
is lowered and shifed to the right. Te areas under the
graphs only have significance when N is defined in a
different way rom above.
Figure 326 shows the distribution o the number o
particles with a particular energy N against the kinetic
energy o the particles Ekat a particular temperature. Te
shape o the kinetic energy distribution curve is similar to
the speed distribution curve and the total energy o the
gas is given by the area under the curve.
T1
T2
T2 T1>
N
Ek
Figure 326 Distribution of kinetic energies
for the same gas at different temperatures.
Te average kinetic energy o the particles o all gases is
the same. However, gases have different masses. Hydrogen
molecules have about one-sixteenth the mass o oxygenmolecules and thereore have higher speeds i the average
kinetic energy o the hydrogen and the oxygen are the same.
Because the collisions are perectly elastic there is no loss
in kinetic energy as a result o the collisions.
Figure 325 Maxwell-Boltzmann speed distribution for
the same gas at different temperatures.
vmpv vrms
T1
T2
T3
T3 T2 T1> >
N
vms 1
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3.2.12 MACROSCOPICBEHAVIOUROF
ANIDEALGAS
Robert Boyle (1627-1691) discussed that the pressure of a
gas at constant temperature is proportional to its density.He also investigated how the pressure is related to the
volume for a fixed mass of gas at constant temperature.
Boyles Law relates pressure and volume for a gas at fixed
temperature.
Boyles Law for gases states that the pressure of a fixed mass
of gas is inversely proportional to its volume at constant
temperature.
P 1__V
PV= constant
When the conditions are changed, with the temperature
still constant
P1V
1= P
2V
2
Te readings of Pand Vmust be taken slowly to maintain
constant temperature because when air is compressed, it
warms up slightly.
When a pressure versus volume graph is drawn for the
collected data a hyperbola shape is obtained, and when
pressure is plotted against the reciprocal of volume a
straight line (direct proportionality) is obtained. See
Figure 327.
pressure, Pmm H g pr ess ure, P mm Hg PV
volume, V cm3
1V
cm3 P
Figure 327 (a), (b) and)c) pressure-volume graphs.
Te pressure that the molecules exert is due to theircollisions with the sides of the container. When the
volume of the container is decreased, the frequency of the
particle collisions with the walls of the container increases.
Tis means that there is a greater force in a smaller area
leading to an increase in pressure. Te pressure increase
has nothing to do with the collisions of the particles with
each other.
In 1787 Jacques Charles (17461823) performed
experiments to investigate how the volume of a gas
changed with temperature. Gay-Lussac (17781850)
published more accurate investigations in 1802.
A very simple apparatus to investigate Charles Law is
shown in Figure 328. A sample of dry air is trapped in acapillary tube by a bead of concentrated sulfuric acid. Te
capillary tube is heated in a water bath and the water is
constantly stirred to ensure that the whole air column is at
the same temperature.
thermometer
water bath
bead of acid(e.g. sulfuric acid)
air column
capillary tube
H E A T
Figure 328 Apparatu