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THERMAL EXPANSION
 Generally, when heat is supplied to a body, the body increases is size and when it is cooled, it decreases in
size. This increase in size of the object when it is heated is called thermal expansion. On the other hand,
the decrease in size of the object when it is cooled is called thermal contraction.
 THERMAL EXPANSION OF SOLIDS
 Generally, when a solid is heated, it expands (increases in size) and when cooled, it contracts (reduces in
size). When a solid is heated, its expansion occurs in three dimensions. i.e.
(i) increase in its length called linear expansion
(ii) increase in its cross-sectional area called area or superficial expansion
(iii) increase in its volume called cubical expansion
NOTE:
 The increase in size of a solid when it is heated results from the increase in distance between its
particles due to the weakening of its forces of attraction by heat energy.
 The increase in size of a solid when it is heated also results from the increase in the extent of vibration
of its particles due to the increase in kinetic energy by heat energy
 Demonstration of linear, area and cubical expansion
1. Linear expansion:
The increase in length of a solid when it is heated can be demonstrated as follows:
Materials:
 metal gauge
 metal bar
 source of heat
Method:
(i) Before the metal bar is heated, try to pass it through the metal gauge and write your observation
(ii) Heat a metal bar for a few minutes and then try to pass it through the metal gauge again. Write
your observation
Observation:
 The metal bar passes through the metal gauge before it is heated, but, it fails to pass through it
after it is heated as illustrated in figures 1.0 (a) and (b);
Conclusion:
 The metal bar undergoes linear expansion after it is heated
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2. Area (superficial) expansion:
The increase in cross-sectional area of a solid when it is heated can be demonstrated as follows:
Materials:
 metal gauge with a hole at the edge
 metal bar
 source of heat
Method:
(i) Before the metal bar is heated, try to pass it through the hole of a metal gauge and write your
observation
(ii) Heat a metal bar for a few minutes and then try to pass it through the hole of the metal gauge again.
Write your observation
Observation:
 The metal bar passes through the metal gauge before it is heated, but, it fails to pass through it after
it is heated as illustrated in figures 2.0 (a) and (b);
Conclusion:
 The metal bar undergoes area (superficial) expansion after heated
3. Volume (cubical) expansion
The increase in volume of a solid when it is heated can be demonstrated as follows:
Materials:
 metal ball and ring apparatus
 source of heat
Method:
(i) Before the metal ball is heated, try to pass it through the ring and write your observation
(ii) Heat a metal ball for a few minutes and then try to pass it through the ring again. Write your
observation
Observation:
 The metal ball passes through the ring before it is heated, but, it fails to pass through it after it is
heated as illustrated in figures 3.0 (a) and (b);
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Conclusion:
 The metal ball undergoes volume (cubical) expansion after heated
 EFFECTS AND APPLICATION OF THERMAL EXPANSION IN SOLIDS
1. Gaps in railway lines:
 Railway tracks expand on hot days and if no gaps are left to allow for expansion, it is very dangerous.
The train can derail because of an expanded rail track and endanger passengers.
 Space is left between railway tracks as shown in figure 4.0 to allow for their expansion when
temperature increases, otherwise the rails may buckle.
Fig. 4.0; gaps between rails
2. Roller bearings on steel bridges:
 Similarly, long steel bridges are designed to include expansion joints to allow for their expansion
by fixing one end and resting on other end on rollers as shown in figure 5.0.
3. Loose overhead cables:
 Overhead electric cables and telephone lines expand during hot days and contract during (become
taut) during cold days. They are hung loosely on pylons and electric poles to allow for expansion and
contraction.
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4. Small gaps in concrete structures:
 Concrete structures such as roads, bridges and paths expand when heated and contract when cooled.
Small gaps are left every few metres in the concrete structures to allow for expansion and contraction,
otherwise, they could develop cracks become weak.
5. Looped pipes:
 Pipes carrying water or steam are looped at intervals to allow for expansion, or else, the pipes will
burst.
6. Thin and pylex glass:
 Glass tends to crack when heated or cooled rapidly.
 Consider the effect of very hot water poured into a bottle made of thick glass. The inside is heated
first and tends to expand while the outside of the glass is still cool and unexpanded. This causes the
glass to crack. Thin glass vessels such as laboratory beakers and flasks are less likely to crack
because they are made of thin glass which is more easily heated throughout so that all parts expand
together. Pylex glass expands little when heated and so does not easily crack. These are often
preferred to use for heating purposes.
7. Fitting axles to wheels:
 While making train wheels, a steel axle is fitted onto a steel wheel by making the axle slightly too
large to fit the hole in the wheel and then dipping it into liquid air at about -183 0C so that it contracts.
The contracted axle will fit into the wheel and as it regains its normal temperature it expands and fits
firmly into the hole.
8. A bimetallic strip:
 If strips of any two metals that expand unequally are fixed together, they form a bimetallic strip or
compound bar as shown in figure 6.0.
 If such a bar is heated, because one metal (A) expands more than the other (B), the bar bends with
the more expansible metal on the outside of the curve. Brass or copper expands and contracts more
than steel or iron.
 Supposing metal ‘A’, in figure 6.0 is brass or copper and metal ‘B’ is steel or iron, such a bimetallic
strip when heated will bend downwards and when cooled will bend upwards.
 Bimetallic strips can be used to compare the expansivity of different metals and also in many other
uses as described below;
 Thermostat
 A bimetallic strip is used in making a thermostat. A thermostat is a device used to control the source
of heat so that heated object is kept at a constant temperature. For example, supposing the temperature
in a brooder (a house for chicks) has to be kept at 30 0C. This can be done by an electric light bulb
placed in a brooder if we can cause it to be switched off whenever the temperature in the brooder
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reaches 30 0C and to be switched on again whenever the temperature drops below 30 0C. This
switching on and off is done by a thermostat like the one shown in figure 7.0;
9. Loosening a jammed stopper or metal part:
 Thermal expansion can be useful in loosening a stopper which has become tightly jammed in
the neck of the bottle.
 Warm the bottle neck; the expansion of the glass makes it possible to remove the stopper inside
it.
 A similar method may be used in garage, when one metal part has become solidly jammed
inside another.
10. Joining materials by riveting:
 Contraction or cooling is made use of in the process of riveting.
 A rivet is a metal pin used to fasten pieces of a metal together. The rivet is placed in a fire or
flame until it is red hot, and then quickly carried with a pair of tongs, pushed through the holes in
two metal plates to be joined together and hammered flat.
 As the rivet cools, it contracts, pulling the plates firmly together.
 Most steel ships and many other large structures made of steel are rivet structures. Figure 8.0
shows how riveting is done;
 EXPANSION OF LIQUIDS
 Generally, when liquids are heated they expand and when cooled they contract. The expansion of
liquids results from the increase in distance between the particles due to the weakening of the
forces of attraction by heat. It also results from the increase in translational movement of the
particles.
 Expansion of liquids can be demonstrated as follows;
Materials:
 Flat-bottomed flask
 Water
 Tripod stand
 Wire gauze
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 rubber bang
 glass tube
 source of heat
Method:
(i) Arrange the apparatus as shown in figure 9.0;
(ii)
Apply heat to the flask and write your observation on the changes of the water level in the
glass tube.
Note:
Since water is colourless, it has to be coloured so that it is more visible in the glass tube.
Observation:
 When heat is applied to the flask, after a few minutes, the water level in the tube drops
slightly before it starts to rise. Thereafter, the water level in the tube continues to rise as
long as heat is being is applied.
 When heat is removed from the flask, the level of water in the tube starts to drop gradually.
Conclusion:
 Liquids expand when heated and contracts when cooled.
 Comparing the expansion of liquids
 the comparison of the expansion of liquids is done as follows;
Materials:
 water bath
 source of heat
 different liquids
 flat-bottomed flasks
 glass tubes
 rubber bang
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Method:
(i)
set the apparatus as shown in figure 10.0;
Note:
 The liquids put in the flasks must be of the same volume and at the same initial levels in the
glass tube.
 The flasks containing the liquids must be put in the water bath so that they receive the same
amount of heat.
Observation:
 When heat is applied to the liquids through a water bath, the liquids start to expand which is
shown by the rise in their levels in the glass tube. Mercury shows the highest level followed
by ethanol and water shows the lowest level. This simply means that that mercury expands
the most followed by ethanol and water expands the least.
Conclusion:
 Mercury expands more than water and ethanol
Explanation:
 Mercury being a metal responds quickly to heat and therefore, expands the most. Ethanol
expands more than water because ethanol has weaker forces of attraction between its
particles than water.
 Anomalous (unusual) expansion of water
 When a cube of ice is heated, it expands till it starts melting. During melting, its temperature
remains 0 0C but its volume decreases. If water is continuously heated from 0 0C to 4 0C, it
contracts-its volume decreases and its density increase. When it is heated above 4 0C it
expands-its volume increases and its density reduces. Cooling water from 4 0C to 0 0C, water
expands-its volume increases and its density reduces. Therefore, water has a greatest density
at 4 0C. The value of this greatest density is 1.0 g/cm3 or 1000.0 kg/m3.
 Effects of anomalous expansion of water;
1. Preservation of aquatic life
 The anomalous expansion of water helps preserve aquatic life during cold weather. When
temperature falls, the top layer of water in a pond contracts, becomes denser and sinks to the
bottom. A circulation is thus set up until the entire water in the pond reaches its maximum
density at 4 0C. If the temperature falls further, the top layer expands and remains on the top till
it freezes. Thus, even though the upper layer is frozen, the water near the bottom is at 4 0C and
the fish and other aquatic life survive in it easily.
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2. Bursting of water pipes in very cold weather
 In a very cold climate, if the water in pipes freezes, it may split the pipe. To prevent this, pipes
and taps in exposed positions should be wrapped with a material which is poor conductor of heat
like strips of blanket material in order to prevent the water in the pipes from losing heat and
causing it to freeze.
3. The killing of plants due to frost in cold climate
 Some plants in very cold climates are killed because the watery fluids in the plant cells freeze and
expand causing the cell walls to burst.
4. Breaking or bursting of bottled or canned liquid food;
 Water is a main component in most bottled or canned liquid food. That is why companies that
bottle all kinds of liquid food leave some space when filling up their bottles or cans. If no
allowance is left for expansion, the bottles burst.
TEMPERATURE
 Temperature is defined as a measure of the hotness or coldness of an object. In short, temperature
is a measure of heat energy.
 The SI unit for temperature is the Kelvin, K, but, it is also measured in other units such as degrees
Celsius, 0C, and Fanren heit, 0F.
 THE KELVIN SCALE
 Another scale used in science for measuring temperature is the Kelvin scale, named after a scientist
called Lord Kelvin. He first suggested the use of the gas thermometer for accurate temperature
reading. On this scale, the absolute zero temperature is equal to -273.15 0C. The absolute zero
temperature is the coldest possible temperature. At absolute zero temperature, the particles which
make up substances have their lowest possible energy.
 When a sample of a gas at constant volume is heated, its pressure is proportional to its temperature
as shown in figure 11.0;
 Extrapolation of the graph suggest that the pressure of the gas would become zero at -273 0C. This is
called the absolute zero temperature (0 K) on the Kelvin scale.
 It is useful to be able to convert from degrees Celsius to Kelvin units and vice versa using the
following equation;
TK = T 0C + 273
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 THERMOMETER
 A thermometer is an instrument which is used to measure temperature.
 A thermometer uses a physical property of matter which varies (changes) uniformly with
temperature. The table below shows the types of thermometers and the physical properties of matter
used to measure to temperature;
Physical property of matter
Type of thermometer
Volume of a liquid such as mercury and ethanol
Liquid-in-glass thermometer
Resistance of a metal
Resistance thermometer
Volume of a solid
Bimetallic strip thermometer
Pressure of a fixed mass of a gas at constant
volume
Pressure at constant volume
thermometer
Electromotive force (e.m.f)
thermocouple
 LIQUID-IN-GLASS THERMOMETERS
 This is a type of a thermometer which uses the volume of the liquid to measure temperature.
Examples of such liquids which are used in liquid-in-glass thermometer include; mercury and
ethanol.
Advantages of using mercury in liquid-in-glass thermometer
(i) It is does not stick to the glass
(ii) It has high boiling point of about 357 0C and therefore, can be used to measure high
temperatures
(iii) It responds more quickly to heat as it is a metal and hence a good conductor of heat
(iv) It expands uniformly
(v) It is coloured or opaque and therefore, it is easy to see
Disadvantages of using mercury in liquid-in-glass thermometer
(i) It is expensive
(ii) It is poisonous
(iii) It has a high freezing point of about -39 0C and therefore, cannot be used to measure lower
temperatures.
Advantages of using ethanol in liquid-in-glass thermometer
(i) It is cheaper
(ii) It is safe
(iii) It has a low freezing point of about -114 0C and therefore, can be used to measure lower
temperatures.
Disadvantages of using mercury in liquid-in-glass thermometer
(i) It stick to the glass
(ii) It has low boiling point of about 78 0C and therefore, cannot be used to measure high
temperatures
(iii) It does not respond quickly to heat as it is a covalent compound and hence poor conductor of
heat
(iv) It has non-uniform expansion
(v) It is colourless therefore, it is not easy to see. It needs to be coloured
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 CALIBRATING / GRADUATING A LIQUID-IN-GLASS THERMOMETER
 In order to calibrate or graduate a liquid-in-glass thermometer, we use a lower and upper fixed
point.
 Lower fixed point is a temperature of pure melting ice, i.e. 0 0C.
 On the other hand, an upper fixed point is a temperature of steam from pure boiling water, i.e. 100
0
C.
 Determining the position of the lower fixed point on the ungraduated thermometer
(i) Put the bulb of the thermometer in a funnel containing pure melting ice as shown in figure
11.5;
The level of the liquid in the thermometer falls until it remains at the melting point of ice,
i.e. 0 0C.
(ii)
Mark the position of the liquid level in the thermometer and then remove it from the melting
ice.
(iii) Measure the distance from the bulb to the position of the lower fixed point and record it as
L0 oC, i.e. length of the liquid at 0 0C.
 Determining the position of the upper fixed point on the ungraduated thermometer
(i)
Put the bulb of the thermometer in a hypsometer which contains boiling water as shown in
figure 13.0;
 Make sure that the bulb of the thermometer does not touch the boiling water, but, suspended in
steam.
 The level of the liquid in the thermometer rises until at a particular point where it remains
constant corresponding to the temperature of steam from the boiling water which is 100 0C
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 The manometer measures the atmospheric pressure which should be equal to the steam pressure
when water boils.
(ii)
Mark the position of the upper fixed point on the thermometer and remove it from the
apparatus.
(iii) Measure the distance from the bulb of the thermometer to the position of the 100 0C. Record
it as L100 oC, i.e. length of the liquid at 100 0C. i.e.
Linterval = L100 oC - L0 oC
 Find the length interval by subtracting L0 oC from L100 oC
 Find the temperature interval by subtracting the lower fixed point (i.e. 0 0C) from the upper fixed
point (i.e. 100 0C). i.e.
Tinterval = 100 0C - 0 0C
= 100 0C
 In a space of the length interval (i.e. Linterval), make one hundred (100) equal divisions where a
division would correspond to a temperature of 1 0C as shown in figure 13.0;

Calculation of unknown temperature on the ungraduated thermometer
 You can calculate the value of the unknown temperature on the ungraduated using the following
formula;
Unknown temperature =
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒍𝒊𝒒𝒖𝒊𝒅 𝒍𝒆𝒗𝒆𝒍
𝒍𝒆𝒏𝒈𝒕𝒉 𝒊𝒏𝒕𝒆𝒓𝒗𝒂𝒍
x temperature interval
Where; unknown temperature = ⱷ
Change in liquid level = Lⱷ - L0 oC
Length interval = L100 oC - L0 oC
Temperature interval = 100 0C
Then;
𝑳 −𝑳
ⱷ = 𝑳 ⱷ −𝟎𝑳𝒐𝑪 x 100 0C
𝟏𝟎𝟎 𝒐𝑪
𝟎 𝒐𝑪
Solved problems
1. In an experiment to graduate a thermometer, the upper and lower fixed points are determined at 1cm
and 5 cm respectively. Calculate….
(a) The temperature on the thermometer when the liquid level is 9 cm from the bulb
(b) The liquid level when the temperature reading is 90 0C
Soln.
(a) Data
ⱷ =?
L100 oC = 15 cm; Lⱷ= 9 cm; L0 oC = 5 cm; Tinterval = 100 0C
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ⱷ=𝑳
𝑳ⱷ − 𝑳𝟎 𝒐𝑪
− 𝑳𝟎 𝒐𝑪
𝟏𝟎𝟎 𝒐𝑪
x 100 0C
9 cm − 5 cm
ⱷ = 15 cm − 5 cm x 100 0C
4 cm
ⱷ = 10 cm x 100 0C
ⱷ = 40 0C
(b) Data
ⱷ = 90 0C; Lⱷ=?
L0 oC = 5 cm; L100 oC = 15 cm; Tinterval = 100 0C
𝑳ⱷ − 𝑳𝟎 𝒐𝑪
ⱷ=𝑳
𝟏𝟎𝟎 𝒐𝑪
90 0C =
− 𝑳𝟎 𝒐𝑪
𝑳ⱷ − 5 cm
15 cm − 5 cm
𝑳ⱷ − 5 cm
90 0C =
10 cm
x 100 0C
x 100 0C
x 100 0C
900 cm 0C = 100 0C𝑳ⱷ -500 cm 0C
100 0C𝑳ⱷ = 900 cm 0C + 500 cm 0C
100 0C𝑳ⱷ = 1400 cm 0C
𝑳ⱷ = 14 cm
2. In an experiment to graduate a resistance of a metal thermometer, the upper and lower fixed points
where determined at 404 Ω and 400 Ω respectively. Calculate…..
(a) The temperature on the thermometer when the resistance of the metal is 403 Ω
(b) The resistance of the metal when the temperature reading is 25 0C
Soln.
(a) Data
ⱷ =?
R100 oC = 404 Ω; Rⱷ= 403 Ω; R0 oC = 400 Ω; Tinterval = 100 0C
ⱷ=𝑹
𝑹ⱷ − 𝑹𝟎 𝒐𝑪
𝟏𝟎𝟎 𝒐𝑪
ⱷ=
− 𝑹𝟎 𝒐𝑪
x 100 0C
403 Ω − 400 Ω
404 Ω − 400 Ω
ⱷ=
3Ω
4Ω
x 100 0C
x 100 0C
ⱷ = 75 0C
(b) Data
ⱷ = 25 0C; Lⱷ=?
L0 oC = 400 Ω; L100 oC = 404 Ω; Tinterval = 100 0C
ⱷ=𝑹
𝑹ⱷ − 𝑹𝟎 𝒐𝑪
𝟏𝟎𝟎 𝒐𝑪
25 0C =
− 𝑹𝟎 𝒐𝑪
𝑹ⱷ − 400 Ω
4Ω
x 100 0C
x 100 0C
100 Ω 0C = 100 0C𝑹ⱷ -40 000 Ω 0C
Prepared & compiled by Nyirenda D. @ mbass-2019
100 0C𝑹ⱷ = 100 Ω 0C + 40 000 Ω 0C
100 0C𝑹ⱷ = 40100 Ω 0C
𝑹ⱷ = 401 Ω
 TYPES OF LIQUID-IN-GLASS THERMOMETER
 There are two types of liquid-in-glass thermometers. These are;
1. Laboratory thermometer:
Figure 14.0 shows the structure of a laboratory thermometer;
 Every feature of the laboratory thermometer is designed in such a way that it increases the
sensitivity of the thermometer. The table below shows the design of each feature and how it
increases the sensitivity of the thermometer;
FEATURE
PURPOSE
thin glass bulb
so that heat is quickly transferred to the liquid
small glass bulb
to contain a small amount of a liquid which would
respond quickly to heat.
narrow bore
to ensure that there is a noticeable movement in the
liquid thread for a small change in temperature
thick glass stem
it acts as a magnifying glass for the liquid thread
Wide range scales (i.e. 120 0C)
to measure a wide range of temperatures of solutions
in the laboratory
the back of the scale is painted
So as to see the liquid thread as well as the readings
easily.
vacuum
To allow a complete expansion of liquids as there is no
built up of air pressure
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2. Clinical thermometer:
 Figure 15.0 shows the structure of a clinical thermometer;
 Every feature of the clinical thermometer is designed in such a way that it increases the sensitivity of
the thermometer. The table below shows the design of each and how it increases the sensitivity of the
thermometer in addition to those discussed under laboratory thermometer;
FEATURE
PURPOSE

constriction
to prevent a sudden backflow of the liquid
Short range scale
it is used to measure the temperature of human
being’s body whose normal temperature is
between 35 0C and 37 0C
Oval shaped glass stem
in to magnify the liquid thread
Differences between laboratory and clinical thermometers
Laboratory thermometer
Clinical thermometer
No constriction
It has a constriction
Wide range of temperature scale
Short range of temperature scale
 SENSITIVITY, RANGE, AND RESPONSIVENSEE OF LIQUID-IN-GLASS THERMOMETER
1. Sensitivity: the change in reading of the thermometer for a small change in temperature. If the
reading of the thermometer has a noticeable change in liquid thread for small change in
temperature, the sensitivity is high. The sensitivity of a liquid-in-glass thermometer can be
increased by;
(i)
narrowing the bore tube
(ii)
enlarging the bulb
2. Range: the span of temperature that the thermometer can measure. The range of a thermometer
is determined by subtracting the minimum temperature from the maximum temperature that the
thermometer can measure. For example;
(i)
Laboratory thermometer; range = 110 0C –(-10 0C) = 120 0C
(ii)
Clinical thermometer; rang = 42 0C – 35 0C = 7 0C
3. Responsiveness: the ability of the thermometer to give a reading in a short time. In order to get a
thermometer quick-acting, its bulb should be made of thin glass and its stem should be made of
thin glass so that heat can get through easily.
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THERMO COUPLE
 A thermometer is a thermometer which uses thermo-electric effect to measure to temperature. It
is made up of two different metals joined together at their ends. One junction is kept at constant
temperature of pure melting ice (i.e. 0 0C) and the temperature of the other junction is increased
by means of a Bunsen burner as shown in figure 16.0;
 When the junctions are kept at different temperatures, electric current flows through the metals.
The larger the difference in temperatures between the junctions, the larger is the electric current
produced.
 The milli-ampere (mA) meter reads the value of temperature directly. It is initially calibrated
using the melting point of pure ice (i.e. 0 0C) and the boiling of pure water (i.e. 100 0C)
 A series connection of thermo couples form a thermo pile.
 Advantages of thermo couple over liquid-in-glass thermometer
(i)
It is made of metals with higher melting points and therefore, can be used to measure very
high temperatures such as temperatures of a furnace or kiln.
(ii)
It is very sensitive to temperature changes and therefore, can be used to measure rapidly
changing temperatures.
(iii) It can measure a wide range of temperatures
EXERCISE
1. In an experiment to calibrate a liquid-in-glass thermometer, the lower and upper fixed points were
determined at 3 cm and 13 cm respectively. Calculate…
(a) the temperature reading when the liquid thread is at 7 cm
(b) length of the liquid thread when the temperature is 80 0C
2. In an experiment to calibrate a thermo couple thermometer, the electric current at lower and upper
fixed points were determined as 4.0 A and 4.4 A respectively. Calculate…
(c) the temperature reading when the electric current reading is 4.2 A
(d) the value of the electric current when the temperature is 75 0C
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