8. Figure below shows a bimetallic strip.  
Explain how a rise in temperature causes the pointer to move in the direction shown.  
Thermal Expansion of Liquids  
•
It is easier to observe expansion in liquids than in solids. This is because liquids expand  
much more than solids for equal change of temperature.  
Explain why when heating a liquid, its level initially decreases and then it Increases to  
become more larger than the original level?  
•
The liquid level drops due to the expansion of its container which initially absorbed all  
the heat. After a while, the heat reaches the liquid it compensates for the expansion of  
the container and rises much more than the original level.  
To compare the expansions of various liquids  
•
Different liquids have different thermal expansions. To demonstrate this, several fairly large  
glass bulbs with glass stems are filled to a short distance above the bulb with various  
liquids (see figure below).  
•
In order to make a fair comparison, the bulbs and stems must all be of the same size.  
The bulbs are immersed in a metal trough containing cold water and left until they have  
reached a steady temperature. A little extra liquid should now be added, where necessary,  
to make all levels the same.  
•
The bath is now heated and well stirred to ensure a uniform temperature. When the  
bulbs and their contents have acquired the new temperature of the bath it will be seen  
that the liquid levels have risen by different amounts.  
•
Thus, for a given rise in temperature, equal volumes of different liquids show different  
expansions in volume (ie,. some liquids expand more than others for a given rise in  
temperature).  
Apparent volume expansion of a Liquid  
•
Is the difference between the initial volume of a liquid and its final volume without  
consideration of the expansion of the container  
Absolute (Real) expansion of the liquid  
Is the difference between the final volume of a liquid and its intermediate volume  
•
The intermediate volume of a liquid  
Is the volume of a liquid attains due to the change that was caused by the expansion of the  
container  
•
Volume expansivity of a Liquid (coefficient of volume of expansion)  
•
•
Volume expansivity Is the fractional change in volume per unit temperature change.  
Its SI unit is K-1 or °C-1.  
풊풏풄풓풆풂풔풆 풊풏 풗풐풍풖풎풆 풐풇 풍풊풒풖풊풅  
•
Volume expansivity  
=
풐풓풊품풊풏풂풍 풗풐풍풖풎풆 × 풓풊풔풆 풊풏 풕풆풎풑풆풓풂풕풖풓풆  
푽 – 푽  
ퟐ
ퟏ
β =  
∴
푽 × 휟휽  
ퟏ
Whereby  
:
Original/initial volume of liquid = 푽ퟏ, Final volume =푽ퟐ  
Increase in volume of liquid, ∆푽 = 푽ퟐ − 푽ퟏ  
Initial temperature = 휽ퟏ , Final temperature = 휽ퟏ  
Rise in temperature = ∆휽 = 휽ퟐ − 휽ퟏ  
Volume expansivity =  
β
Worked Examples;  
1. The increase in volume of 10 cm3 of mercury when the temperature rises by 1000C is 0.182 cm3.  
What is the volume expansivity of mercury?  
∆푽  
ퟎ.ퟏퟖퟐ  
= ퟏ. ퟖퟐ × ퟏퟎ−ퟒ0C-1  
ANSW: 휸 =  
=
ퟏퟎ×ퟏퟎퟎ  
푽 ∆푻  
ퟏ
2. A 500 cm3 Pyrex beaker is 95% full of methanol at 150C. At what temperature will it be 100%  
with the methanol? (Volume expansion of methanol = 122 x 10-5K-1)  
ANS; 푽ퟏ = ퟗퟓ%, ∆푽 = 푽ퟐ − 푽ퟏ = ퟏퟎퟎ% − ퟗퟓ% = ퟓ%  
(OR; 푽ퟏ = ퟗퟓ% × ퟓퟎퟎ = ퟒퟕퟓcm3, ∆푽 = 푽ퟐ − 푽ퟏ = ퟏퟎퟎ% −ퟗퟓ% = ퟓ% × ퟓퟎퟎ = ퟐퟓcm3)  
∆푽  
∆푽  
ퟓ%  
= ퟒퟑ. ퟏퟒ0C  
→ ∆푻 =  
휸 =  
=
−ퟓ  
ퟗퟓ%×ퟏퟐퟐ×ퟏퟎ  
푽 ×휸  
ퟏ
푽 ×∆푻  
ퟏ
∴ 푻ퟐ = 푻ퟏ + ∆푻 = ퟏퟓ + ퟒퟑ. ퟏퟒ = ퟓퟖ. ퟏퟒ0C  
3. A hollow glass sphere has a density of 1.30g/cc at 200C. Glycerin has a density of  
1.26g/cc at 200C. At what temperature would the sphere begin to float in Glycerine? Given  
coefficient of volume expansion of glycerine is 53 × 10-5°C-1.  
ANSW:  
NB:  
•
Due to volume expansion of Glycerin which has been given from the question, it seems that  
glycerin was to be heated  
•
Therefore, in order for the glass sphere starts floating in Glycerin, the Glycerin must be  
heated so as its density must change from 1.26g/cc to 1.3g/cc (The glass sphere will  
float when it has the same density as glycerine  
When Glycerine is heated, it expands from volume  
풊풆, . 흆ퟏ = 흆ퟐ = ퟏ. ퟑg/cm3)  
to volume V₂:  
•
•
V₁  
The mass of Glycerine is the same before and after heating (m1=m2)  
0
Now; 흆ퟏ = ퟏ. ퟐퟔg/cm3, 흆ퟐ = ퟏ. ퟑg/cm3, 푻ퟐ =200C, 휸푮푳풀 = ퟓퟑ × ퟏퟎ−ퟓ 푪−1, 푻ퟐ =?  
∆푽  
푽 −푽  
ퟐ
ퟏ
From; 휸 =  
=
(
)
→ 푽ퟐ − 푽ퟏ = 휸 × 푽ퟏ × 푻ퟐ − 푻ퟏ  
푽 ×∆푻  
ퟏ
푽 ×(푻 −푻 )  
ퟏ
ퟐ
ퟏ
(
)
푽ퟐ = 푽ퟏ[ퟏ + 휸 × 푻ퟐ − 푻ퟏ ]--------(i)  
흆 푽  
ퟏ
=
ퟏ----------- (ii)  
But; m1 = m2 → 흆ퟏ 푽ퟏ = 흆ퟐ 푽ퟐ  
→ 푽ퟐ  
흆
ퟐ
Substitute equation (ii) into (i)  
흆
흆
ퟏ
흆 푽  
ퟏ
ퟏ
ퟏ )]  
(
→
= ퟏ + 휸 × 푻  
= 푽ퟏ  
[
(
)
ퟏ + 휸 × 푻ퟐ − 푻  
ퟐ − 푻ퟏ  
흆
ퟐ
ퟐ
−ퟎ.ퟎퟑퟎퟖ  
= 1 + 53 × 10−5 푇 − 20  
→
+ 20 =T2  
1.26  
1.3  
(
)
−ퟓ  
ퟓퟑ×ퟏퟎ  
T2 = -58 + 20 = - 380C  
∴
The glycerine must be cooled to −ퟑퟖ°C for the hollow glass sphere start floating.  
Alternatively;  
∆푉  
푚
푚
−
푉 −푉  
From; 훾 =  
, 푏푢푡; 푣 = 푚 , 푡ℎ푒푛, 훾 =  
휌
휌
1
2
1
2
=
=
푚
×(푇 −푇 )  
푉 ×∆푇  
1
푉 ×(푇 −푇 )  
휌
1
2
1
2
1
휌
1
ퟏ
ퟏ
(흆 흆 )  
ퟏ− ퟐ  
흆 흆  
(흆 흆 )  
ퟏ− ퟐ  
흆 흆  
−
(
흆
)
흆
흆
ퟏ
흆
흆
ퟏ− ퟐ  
ퟏ
ퟐ
ퟏ ퟐ  
ퟏ ퟐ  
휸 =  
− 푻  
(
)
→ 푻ퟐ  
=
=
ퟏ
ퟏ
ퟏ
ퟏ
×(푻 −푻 )  
×(푻 −푻 )  
휸흆 흆  
ퟐ
ퟏ
ퟐ
ퟏ
× 휸  
ퟏ
ퟐ
흆
흆
ퟏ
흆
ퟏ
ퟏ
(휌 휌 )  
1.26−1.3  
−0.04  
1−  
2
+ ퟐퟎ  
푇 =  
+ 푇 =  
+ 20 =  
2
1
−5  
−5  
훾휌  
53×10 ×1.3  
68.9×10  
2
∴ 푇2 = −ퟓퟖ + ퟐퟎ = −380C  
NB;  
•
•
If the glass sphere was to be heated, its density could change from 1.3g/cc to 1.26g/cc  
But here it not the case, since its volume expansion has not been given.  
Linear expansivities between (0 – 100)°C  
Liquid  
Volume expansivity  
Liquid  
Volume expansivity  
(K-1) x ퟏퟎ−  
(K-1) x ퟏퟎ−  
ퟓ
ퟓ
Benzene  
Gasoline  
Glycerin  
Kerosene  
124  
95  
53  
Mercury  
18  
122  
21  
Methanol  
Water at 20  
℃
99  
Water at 900  
70  
Anomalous expansion of Water  
•
•
When water is heated from 00C to 40C it contracts continuously instead of expanding.  
Conversely expands when cooled down from 40C to 00C. This unusual expansion of water  
from 40C to 00C is called anomalous expansion.  
When heated from 40C to 1000C its expansion is normal like the expansion of other liquids.  
Since water contracts when heated from 00C to 40C and expands from 40C to 1000C  
,
its volume is smallest and the density is maximum at 40C. Hence water is heaviest at  
40C.  
•
Therefore; the anomalous expansion of water is defined as the property of water that  
causes it to expand rather than contract when the temperature changes from 4°C to 0°C,  
causing it to become less dense. .  
OR  
•
•
Anomalous expansion of water Is the unusual behavior of water where its volume  
decreases when the temperature rises from 00 C to 40 C and increases when the  
temperatures falls from 40 C to 00 C  
The two graphs below represent the change in volume and density of 1 g of water, with the  
increase in temperature  
What happens below 4°C to 0°C  
At 4°C, just above the freezing point, water reaches its maximum density. As the water cool further  
toward its freezing point, the liquid water expands to become less dense.  
Effect of Anomalous Expansion of water on Marine life  
•
•
Due to anomalous expansion of water, fishes and various living creatures can survive under  
frozen lakes, rivers or seas. In cold countries, with the fall in atmospheric temperature, upper  
surfaces of lakes, seas and various ponds gradually cool. Water of the upper surface, then  
being denser and heavier, moves down. Water below it, being comparatively warmer and  
lighter, moves up.  
This convection process in water continues until the density of the water in the lower part  
becomes maximum i.e., the temperature of the lower water reaches 4°C. As the  
temperature of the upper surface decreases further below 4°C, density begins to decrease.  
So water cannot move down further. It then begins to cool further and at last turns into ice. As  
ice is lighter than water, a thick layer of ice, thus formed, floats over the surface of water.  
Both ice and water are bad conductors of heat. So, a negligible amount of heat can be  
conducted from the lower levels of water to the atmosphere outside.  
•
So, the entire volume of water (top to bottom) in a pond cannot freeze. The temperature just  
below the floating ice-slab remains at 0°C [Fig. above]. The temperature of water gradually  
increases with depth and the lowest layer remains at 4°C, where the living creatures can  
easily survive.  
Effects of Anomalous expansion of water  
•
A daily life example of the anomalous expansion of water is observed in deep freezers. Water  
containers (glass bottles) tend to bust in deep freezers at 0°C due to volume increase, as volume  
increases when cooling from 4°C to 0°C.  
•
It supports the life of aquatic organism. In cold countries during the winter season, the surface  
of the lakes will be at lower temperature than the bottom. Since the solid water (ice) has lower  
density than its liquid form, below 4°C, the frozen water will be on the top surface above the  
liquid water (ice floats). This is due to the anomalous expansion of water. As the water in lakes  
and ponds freeze only at the top the species living in the lakes will be safe at the bottom.  
In winter season the water supply pipes open to the atmosphere after burst when the  
temperature of the surrounding falls below 40C. This is due to the fact that water below 40C  
expands (anomalous expansion) and exerts pressure on the walls of the pipes and thus  
causes damage to it  
•
•
•
In rainy season a lot of water sweeps through numerous cracks and fissures in rocks. In water  
season when temperature falls below 40 going down to 00C or below, expansion of water take  
place, thus developing a high pressure. This results in the breaking of the rocks  
.
Icebergs, being less dense than water, float in oceans thus posing a danger to ships.  
Effects of Expansion of Liquids  
•
The expansion of liquids used in liquid thermometers. Liquid-in-glass thermometers are  
based on the principle of thermal expansion of substances. A liquid in a glass tube (called  
a capillary) expands when heated and contracts when cooled. A calibrated scale can then be  
used to read off the respective temperature that led to the corresponding thermal expansion.  
Weathering of rocks .This happen when water freezes in the cracks of a rock the volume of  
water increases .This causes the rock to break into small pieces  
Industrial bottling of liquids provides empty space to allow for expansion during freezing  
of the liquids. Liquids exhibit thermal expansion in volume, due to this expansion the bottle  
might break, as the bottles are sealed. In order to avoid breakage of bottles and to allow the  
space for liquid to expand, industrial bottles are always provided with some empty space.  
•
•
•
When boiling water is poured into a thick tumbler its inner surface expands. However, due to low  
thermal conductivity of glass, the expansion of outer surface of the tumbler is quite small. Due to  
uneven expansion of the outer and inner surfaces, the tumbler breaks.  
Class Activity – 6:4  
1. What is the anomalous expansion of water?  
2. An ice sheet 5m thick covers a lake that is 20m deep. What is the temperature of the water at the  
bottom of the lake? Explain your answer  
3. How do fishes and aquatic animals survive when the pond gets covered with thick ice?  
4. Deep pond of water has its top layer frozen during winter. State the expected temperature of water  
layer (i) just in contact with ice, (ii) at the bottom of pond. [ANS; 00C , 40C]  
5. (a) If a 500-mL glass beaker is filled to the brim with ethyl alcohol at a temperature of 5.00C,how  
much will overflow when its temperature reaches 22 0C, given that 휸 = ퟏퟏퟎ × ퟏퟎ−ퟓ푲-1  
[ANS; 9.35mL]  
(b) How much less water would overflow under the same conditions?, given that  
휸 = ퟐퟏ × ퟏퟎ−ퟓ푲-  
[ANS; V = V – V’ = 9.35 – 1.785 = 7.565mL]  
6. Explain why filled bottles of water when placed in a freezer may burst when water is frozen?  
7. Draw a labeled diagram for a set up of an experiment to show that alcohol expands more than  
an equal volume of water for the same rise in temperature  
8. As an expert in thermal expansion, you are consulted by a company to construct a thermometer.  
The company has provided you with mercury, alcohol and gasoline. With justification, explain  
which liquid you will use in constructing the thermometer.  
9. Explain why the surface of a lake freezes while the deepest water stays at 4 0C?  
ANS;  
When the weather gets cold, the temperature of water at the surface drops down and it  
becomes more dense than the water underneath. The dense water starts to sink and warmer  
water is pushed up. The water will keep circulating until the temperature of all water in lake  
become 4 0C. When the water temperature at the surface drops below 4 0C its volume starts to  
increase and its density starts to decrease. At this stage, the water is less dense than the water  
underneath and it stays on the surface. In time, ice forms on the surface and the water  
0
temperature at the bottom of the lake will remain at 4 C. Thus, fish can survive a severe winter  
by staying in the deep warm water.  
10. The density of mercury is 13.6 g cm−3 at 00C and its coefficient of cubical expansion  
is 1.82×10−4 0C−1. Calculate the density of mercury at 500C  
ANSW: Given; 휌1 = 13.6 g/cm3,  
훾
= 1.82×10−4 0C−1, ∆푇 = 50  
휌2 =?  
,
풎
흆ퟐ  
풎
흆ퟏ  
∆푽  
푽 − 푽  
−
ퟐ
ퟏ
풎
흆
=
, 풃풖풕; 풗 =  
, 풕풉풆풏, 휸 =  
휸 =  
풎
흆ퟏ  
(
× 푻  
푽ퟏ × ∆푻  
(
)
푽ퟏ × 푻ퟐ − 푻ퟏ  
)
ퟐ − 푻ퟏ