: Introduction

Temperature – it is the degree of coldness or hotness of a body on some chosen scale. It is measured using a thermometer. The SI unit of temperature is the Kelvin (K). Other units include degrees Celsius (⁰C), Fahrenheit, F. Temperature is a basic physical quantity as well as a scalar quanity.

6.2: Temperature scale

The scale of a thermometer is obtained by selecting two temperatures called fixed points; the lower fixed point and the upper fixed point. The lower fixed point is the temperature of pure melting ice. It is taken to be 0⁰C. The upper fixed point is the temperature of steam above pure boiling water at normal atmospheric pressure. It is taken to be 100⁰C. The temperature of steam is used since impurities do not affect its temperature but will raise the boiling point of water. The range between these two points is then divided into equal divisions.

On the Kelvin (absolute) scale, 0⁰C is at 273 K while 100⁰C is at 373 K. Hence to convert ⁰C to K, add 273 to the temperature in ⁰C.

Activity 6.1

1. Convert the following into Kelvin:

1. 35⁰C b) -111⁰C c) -273 ⁰C

1. Convert the following into ⁰C:

1. 123 K b) 323 K

6.3: Types of thermometers

A thermometer is designed according to the purpose for which it is required. The following are some of the commonly used thermometers:

6.3.1: Liquid-in-glass thermometer

Stem

Liquid thread

Bulb

In this thermometer the liquid expands up a capillary tube when the bulb is heated. The liquid used in this thermometer should posses the following qualities for the thermometer to be effective:

• Be easily visible
• Expand and contract uniformly
• Have a wide range of temperature i.e high boiling point and low freezing point
• Be sensitive to small temperature changes
• Should not wet the glass

The most commonly used liquid is mercury althoughcoloured alcohol can also be used. Water does not meet all the above desirable properties. The table below compares mercury and alcohol as a thermometric liquid:

Mercury	Alcohol
Has high b.p, 3570C	Has low b.p, 780C
Relatively high freezing point, -390C	Low freezing point, -1150C
Good thermal conductor	Poor thermal conductor
Has regular expansion	Has a slight irregular expansion
Does not wet the glass	Wets the glass
Easily visible	Ii coloured to make it easily visible

These thermometers are commonly used in normal laboratories.

6.3.2: A clinical thermometer

This is a special thermometer used to measure human body temperature. It has a short scale between 35—43⁰C. This is because the optimal body temperature is 37⁰C. It has a constriction to prevent back flow of the mercury into the bulb. This is to allow time to take the reading. After use the thermometer is shaken to return the mercury back to the bulb.

Methylated spirit can be used to sterilize the thermometer after use.

6.3.3: Six’s maximum and minimum thermometer

Saturated vapour

Oil

Maximum index

Bulb Minimum index

Mercury

It is used to record minimum and maximum temperatures of a given place. When the temperature of the surrounding rises, the oil in the bulb A expands pushing the mercury which in turn pushes up the oil in the other arm. This compresses the vapour above the oil and the maximum index is pushed up to the maximum position. This is the maximum temperature.

When the temperature falls, the oil contracts back into the bulb. Mercury flows back pushing the minimum index to the minimum position. This gives the minimum temperature.

After taking the readings, the indices are pulled down to the level of the mercury using a magnet.

6.3.4: A bimetallic thermometer

It is made up of a coiled bimetallic strip whose one end is fixed and the other end connected to a pointer. Commonly used metals are brass and invar. When the temperature rises brass expands more than invar. The strip thus curls forcing the pointer to move over a calibrated scale.

6.4: Expansion in solids

A solid can expand in three ways:

• Linear expansion; increase in length
• Superficial expansion; increase in surface area
• Cubic expansion; increase in volume

Solids expand when heated and contract when cooled. During expansion the volume increases, density decreases but mass remains the same. Expansion in solids can be demonstrated by the ball and ring experiment.

When both the ball and ring are at room temperature, the ball easily passes through the ring but when the ball is heated it does not go through the ring. When left in contact for some time the ball finally passes through the ring again.

On heating the ball expanded and so could not go through the ring. After sometime it went through because the ball lost some of its heat to the ring which then expanded while the ball slightly contracted.

Different solids like metals will expand at different rates when exposed to the same amount of heat for the same duration. This can be investigated by the bar and gauge experiment.

One end of the metal bar is fixed while the other end is kept in contact with the pointer. Any slight expansion of the bar is magnified by the long pointer and can be read from the scale. The experiment is then repeated using bars of other materials. The pointer readings are then used to compare their rates of expansion.

In the above experiment, the following parameters must be kept constant:

• Length of the rods
• Diameter / thickness of the rods
• Source of heat
• Duration of heating

The measure of the tendency of a material to expand is called its expansivity. The ability of a material to expand when heated is referred to as its linear expansivity.

Linear expansivity, α = expansion (change in length)/ {original length * temperature change}

The SI unit of linear expansivity is per Kelvin (K^-1).

Linear expansivity of a substance may also be defined as the fraction of its original length by which a rod of the same substance expands per Kelvin rise in temperature.

Example 6.1

1. Consider a brass rod of length 50.2 cm at 16.6⁰ if the rod is heated until a temperature of 99.5⁰C where its new length is 50.279 cm, determine the linear expansivity of brass.

Linear expansivity, α = e/l₀*ΔT = (50.279-50.20) cm/50.2 cm * (99.5-16.6) K

= 0.079/50.2-82.9

= 1.9 * 10^-5 K^-1

The table below shows some substances with their linear expansivities:

Material	Linear expansitivty ( * 10-5) K-1
Aluminum	2.6
Copper	1.68
Brass	1.9
Iron	1.2
Steel	1.1
Concrete	1.1
Platinum alloy	0.9
Glass	0.85
Invar	0.1
silica	0.042

The knowledge of linear expansivity is used in designing various materials to ensure that they are able to operate well under varying thermal conditions. For instance ordinary glass has a higher linear expansivity than a pyrex glass. When hot water is put in an ordinary glass, it breaks but when a pyrex glass is used it does not crack. The pyrex glass has lower linear expansivity and cannot suffer very large forces of expansion while the ordinary glass does as it undergoes temperature changes.

In building and construction, concrete is always reinforced using steel because both have the same linear expansivity.

6.5: Bimetallic strip

It is formed when two metals of different linear expansivitiesare riveted together e.g. brass and iron or brass and invar. When the temperature of the strip is raised, brass expands more than iron. Hence the strip curves with brass curving outwards and iron inwards. When the temperature falls, brass again contracts more than iron and the strip curves with brass now on the inner side and brass on the outer side.

6.6: Applications of expansion and contraction in solids

6.6.1: Railway lines

Railway lines are fixed with gaps to allow for expansion when temperature rises. The bolt holes are also oval in shape for the same reason. Another way of creating room for expansion in railway lines is by planing the ends of the rails so that they are able to overlap during expansion.

6.6.2: Telephone/electricity wires

Telephone and electricity wires are loosely fixed during installation to allow for contraction during cold weather.

6.6.3: Steam pipes

Pipes carrying steam from boilers are fitted with expansion loops to allow for expansion and contraction. Without the loop the pipe is likely to break due to the resultant force as a result of expansion and contraction. It is necessary that oil companies make this allowance when constructing fuel pipelines.

6.6.4: Steel bridges

In the construction of steel bridges, one end is fixed while the other end is placed on rollers. This is to allow for expansion and contraction.

6.6.5: Rivets

Rivets are fitted when hot and then hammered flat. On cooling, the rivet contract, pulling the two plates firmly together.

6.6.6: Thermostat

It is a device that can be used to control the temperature of a room. It uses a bimetallic strip. It is connected to a heater circuit. When the temperature of the room rises beyond the set value, the bimetallic strip expands and bends away breaking the contact. Hence the heater circuit is switched off.

The strip cools and contracts and the contact is remade switching on the heater circuit. The setting knob is used to adjust the temperature at which the thermostat is switched on and off.

Other uses of the thermostat include controlling the temperature of electric iron, cookers and fridge, fire alarms and car indicators.

6.7:Expansion and contraction in liquids

The rate expansion in liquids is more than in solids because the particles are slightly far apart. When temperature increases, the liquid molecules gain more energy increasing their rate of movement. The weak bonds between these molecules are further weakened. The molecules thus expand and occupy more space. Expansion in liquids can be demonstrated by the set up below:

Liquid

When heated, the level of the liquid in the glass tube first drops and then starts rising. This initial fall in the level is because the glass was heated first and expanded. Later the liquid received the heat energy and expanded hence the rise in the level.

Just like solids, liquids expand at different rates. In order to investigate this, a number of identical flasks are filled with different liquids ensuring that their initial levels are the same in the glass tubes. For a fair comparison, the tubes should be identical i.e. of same diameter. The flasks are then simultaneously immersed in a bath of hot water. The bath of water should be stirred continuously to ensure that temperature is uniform.

It will be observed that the level of the liquids in the tubes differ after some time. If water, alcohol and methylated spirit were used, it would be observed that methylated spirit expanded the most, followed by alcohol and water the least.

6.8: Expansion in gases

Gases have the highest rate of expansion because their particles are very far apart and are held by very weak forces. When heated, they gain more energy and move farther apart occupying more space. It can be shown by a round bottomed flask fitted with a glass tube in a tight-fitting cork. The flask is first inverted with the glass tube dipped in water. By use of the palms, the flask is warmed for some time.

Air

It will be observed that the level of water in the tube drops and if warmed for a longer time, bubbles are observed escaping from the end of the tube in water. This shows that air expanded on heating and needed more space, hence the drop in the level of water in the tube and the bubbles.

If the heat is withdrawn, the level of the water rises again in the tube. Expansion and contraction in gases is the basis of the formation of land and sea breezes.

6.9: The Unusual expansion (anomalous) expansion of water

It is normal experience that substances expand on heating and contract on cooling. But for water, this is never to be between the temperatures 0⁰C and 4⁰C. Water can exist as a solid (ice), liquid (liquid water) and as a gas (steam).

At temperatures below 0⁰C, water exists as a solid, occupying a bigger volume. When heated, it expands just like any other solid up to 0⁰C. At 0⁰C, ice melts at constant temperature. Melting is accompanied by a decrease in volume by about 8%. Beyond 0⁰C, water contracts further up to 4⁰C. Therefore water has minimum volume at 4⁰C and hence maximum density which is slightly higher than 1 g/cm³.

Above 4⁰C, water expands like any other liquid. This behavior of water is described as anomalous, unusual, or irregular.

The variation of volume with temperature and density with temperature when water is heated is illustrated by the graphs below:

6.9.1: Effects of anomalous expansion of water

1. Biological importance

During cold weather, the temperature of lakes and ponds drops and water contracts, becomes denser and sinks. A circulation of water is thus set up until all the water attain maximum density i.e. at 4⁰C. If further cooling occurs (below 4⁰C), then any water below 40C will stay at the top due to its lower density. At 0⁰C, ice forms on top and this acts as an insulator to the layers below. Hence the warmth underneath can sustain aquatic life and thus the aquatic animals and plants can survive there.

1. Icebergs

Ice has a slightly lower density, about 0.92 g/cm³, than that of water and hence it floats with a small portion above the water surface. The rest and a bigger portion of the ice rests under water. This is called an iceberg. Icebergs pose a great danger to ships as the submerged parts cannot be seen easily by navigators.

1. Weathering of rocks

Water sometimes finds its way into cracks within the rocks. When such water freezes during cold weather, it expands forcing the rock to break into smaller pieces. This is very important for agriculture as soil is formed.

1. Bursting of water pipes

At times the water flowing through a pipe may freeze when it passes through a cold region. The water thus contracts, expanding and this may lead to pipe bursts if expansion allowances were not catered for.