� INTRODUCTION

You have learnt that one of the seven SJ base quantities is temperature. Temperature is a measure of degree of hotness or coldness of an object or material. What causes the rise or decrease of temperature. In this topic, you will learn the difference between temperature and heat. You will also discover that a two objects are in contact with each other, heat will flow from the hotter object to the colder object until an equilibrium condition is reached. Thermal equilibrium is reached when the two object reaches a point where the temperature of both objects are the same.

TTooppiicc

55 � Heat

By the end of this topic, you should be able to:

1. Compare between temperature and heat;

2. Explain thermal equilibrium;

3. Describe thermometry and different types of thermometers;

4. Determine specific heat capacity of a solid or liquid;

5. Define specific latent heat of fusion and vaporisation; and

6. Explain three types of gas laws and their applications.

LEARNING OUTCOMES

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TEMPERATURE AND HEAT

If you taste some hot curry, the energy is transmitted to your tongue because the curry is warmer than your tongue. When you eat a scoop of ice cream, the energy flows from your tongue to the colder ice cream. This kind of energy is called hheat. Heat is persistently transferred from warmer objects to cooler objects. It is important to note that a substance itself does not contain heat. Hot curry does not contain heat. Ice cream does not contain heat. Even your tongue does not contain heat. Heat does not exist coincidently or purposely in any substance. Although there is energy in many substances, that energy is not heat. Only if the energy is transferred from a warmer substance to a colder substance then the energy ceases to be heat (refer to Figure 5.1).

Figure 5.1: Heat

If a substance does not contain heat, is there any other energy in it? And, what kind of energy is contained in a substance? Yes, there are kinetic energy and potential energy which form the overall internal energy in a substance. We have seen that the moving molecules of an object have internal energy. When an object is heated, its internal energy increases. Like all forms of energy, internal energy is measured in a unit called the joule (usually written as J). We always hear about calories in commercials, especially if it is about a weight loss programme or dieting. So, what is the relationship between calories and heat? CCalorie is a common unit of heat although heat is like other forms of energy that can be measured in jjoules (J). However, calorie is a heat unit that is popularly used as an indicator of energy released by burning food. One calorie is equal to 4.184 joules.

5.1

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Calorie means the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius (1 Kelvin).

Now try this simple activity. Take an eraser and rub it for a minute and then touch the surface of the eraser. What do you feel? Is it warm? How warm was it compared with before it was rubbed? Should we measure the warmth of the eraser before and after it was rubbed? Such questions underlie the concept of temperature. Temperature cannot be used interchangeably with heat although both concepts play important roles in heating and cooling processes.

Temperature has several standard scales such as Fahrenheit, Celsius and Kelvin. To understand more about its usefulness, let us analyse the following scenario:

On the other hand, instead of using qualitative ideas of hot and cold based on our sense of touch, we should consult more reliable sources to determine whether we have fever. Thus, it is suggested that you find a thermometer and record the temperature. What does this reading tell you? It indicates whether you have normal body temperature or a fever. The thermometer shows a quantitative measure of how hot or cold things are. It is also a basis for comparing your current body temperature with your normal one. By referring to the temperature, you can justify confidently that you have a fever. But you would have to go to a clinic to obtain the correct treatment for the symptom you have.

Calorie means the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius (1 Kelvin).

You have to attend a lecture today but you think you have a fever. To check whether you have fever, you put your palm on your forehead and try to feel whether it is hot. Then, you ask your friend to put his or her hand on your forehead to confirm that you have a fever. If your friend agrees, you have to go to a clinic and see a doctor for further examination.

Temperature is a measure of the degree of hotness or coldness of certain objects.

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We can say that almost all materials are affected by temperature change. Most materials contract when the temperature is low and expand when it is high. You have learnt about thermometers and how it can be used to measure temperature. Now that you have understood the concept of temperature, explain why it is different from heat. There are several points which show the differences between temperature and heat. Let us look at Table 5.1 to find out the answer.

Table 5.1: Differences between Temperature and Heat

Temperature Heat

� Measurement Scale: Fahrenheit and Celsius

� Measurement Scale: joules or calories

� Not a form of energy. � Not a form of energy.

� However, related with the kinetic energy of molecules of material.

� Temperature is a measure of hotness or coldness of a substance.

� The hotter the substance, the higher the kinetic energy of the substance.

� Temperature itself does not represent the amount of heat.

� Heat is not contained in a substance.

� Heat is energy which flows from an object of higher temperature to an object of lower temperature.

� The energy can be considered as heat only if it flows from a warmer to a colder object.

Based on the points shown in Table 5.1, we can conclude that temperature shows us which direction the heat will flow. We now understand clearly that if two objects have different temperatures, the energy will flow from an object of higher temperature to an object of lower temperature. This energy is called hheat. But can you predict the direction of the heat if those two objects are at the same temperature? Activity 5.1 will explain more on this situation.

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If you look carefully at the thermometer, you will notice that it is partially filled with some fluid. Usually, the fluid is mercury. The structure of the thermometer consists of a sealed glass tube. The diameter or the stem of the tube is uniformly small except at the bottom where it forms a bulb. The bulb is relatively larger because it acts like a reservoir for the mercury. To get our body temperature, the thermometer is usually placed under the tongue. It is assumed that the temperature of the tongue represents the body temperature. In order to get an accurate reading from the thermometer, you are supposed to wait for a few minutes until the temperature stabilises. We can conclude that the mercury moves due to its expansion and contraction. When the mercury in the bulb expands, there is a rise in the thermometer. When the mercury contracts, there is a fall in the reading.

Set up three beakers and fill half of each with water. Make sure the beakers are small (100ml) and have enough water to only completely cover a bolt and a nail. Measure the temperature of the water in each beaker. Put the nail and bolt into the water in the first beaker. Then, heat the water until boils. Make sure that the temperature and volume of water in the second and third beaker are same. By using tongs, transfer the bolt into the second beaker and the nail into the third. Record the temperature of the water in the second and third beakers over four-minute intervals; for every 20 seconds. With the readings, draw a graph to show the temperature change over time. Can you see that the temperature change between the nail and the bolt is different? Although initially the bolt and the nail had the same temperature when both were placed in boiling water (first beaker), but because the bolt is bigger than the nail, it raised the temperature of the water in the second beaker more than the nail in the third beaker. Do you find this activity can help you and your students to see thedifferences between heat and temperature?

ACTIVITY 5.1

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The mercury will rise when the temperature inside the mouth is higher than the initial temperature of the thermometer. Why is that so? Most materials expand as they get warmer, and mercury and many other liquids expand at a greater rate than glass. The reason behind this is that when it gets warmer, the heat will flow from the surrounding area to the mercury inside the thermometer. In this case, the heat flows from the tongue, which is relatively warm, to the thermometer which is relatively colder. As the mercury in the tube expands, the mercury in the bulb must go somewhere. So it rises in the narrow tube. On the other hand, if the temperature in the mouth is lower than that of the thermometer, the mercury contracts and the reading drops. When the mercury level stabilises, the temperature of the thermometer is considered to have the same value as that inside the mouth. Why? When the thermometer is in thermal contact with the tongue in the mouth, the heat will flow from the tongue to the thermometer. This only happens when the temperature of the tongue is higher than the temperature of the thermometer. On the other hand, if the temperature of the thermometer is lower than the temperature of the tongue, the heat will flow from the tongue to the thermometer. For example, if somebody has fever, his or her temperature is higher than normal. Therefore, the heat will flow from his or her tongue to the thermometer until both reach the same temperature. When physical properties are no longer changing, the objects are said to be in thermal equilibrium. Two objects are in thermal equilibrium if both are in thermal contact and have the same temperature. Therefore, if we know the temperature of the thermometer, we then know the temperature of the object which is supposed to be measured by the thermometer.

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THERMAL EQUILIBRIUM

Temperature is the measure of the degree of hotness of an object. The hotter the object gets the more internal energy it possesses. If you hold an ice cube, your hand feels cold because the heat is transferred from your hand to the ice cube, reducing the internal energy of your skin. On the other hand, if you place your hand in warm water, it gains internal energy due to heat transfer. However, if the water is the same temperature as your hand, the internal energy of your hand remain constant as there is no overall heat transfer between the hand and the water. When there is no overall heat transfer between two objects of the same temperature. The two objects are said to be in tthermal equilibrium. If two objects A and B are in thermal contact at different temperatures, they are not in thermal equilibrium. Heat will be transferred from the hotter object to the colder object. The hotter object will lose internal energy while the colder object will gain internal energy. Heat transfer is always from hot to cold, provided there is no external work done. It was also found experimentally than when two bodies A and B are in thermal equilibrium with a third body C, A and B are also in thermal equilibrium with each other. This is called the ZZeroth Law of Thermodynamics.

5.2

Take a small red hot steel marble and throw it into a warm swimming pool. Although the warm water in the swimming pool has more internal energy than the small red hot steel marble, the heat will not flow from the warm water in the swimming pool to the marble. As we have learnt before, heat will flow from the marble to the surrounding water in the swimming pool because the marble is at a higher temperature than the water in the swimming pool.

What happens to a glass and a jar of hot milk with different volume but same temperature? Which one will transfer more heat? Discuss and share your idea and the reasons behind your idea with the class.

ACTIVITY 5.2

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THERMOMETRY

Thermometry, refers to ttemperature measurement. It is important to a wide range of activities, including manufacturing, scientific research and medical practice. Do you know that the accurate measurement of temperature was developed only recently? (a) Temperature (like mass, length, time) is a chosen fundamental quantity.

Therefore, arbitrarily chosen units (such as degrees Celsius, degrees Fahrenheit or Kelvin) are used to measure temperature.

(b) Temperature is measured quantitatively by constructing a thermometer which makes use of a physical property of matter that varies with temperature.

(c) A physical property that changes continuously with temperature can be used to measure temperature and is usually referred to as its thermometric property.

The first thermometer was invented by Galileo in the 16th century (see Figure 5.1).

Figure 5.1: First thermometer

5.3

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In his instrument, the changing temperature of an inverted glass vessel produced the expansion or contraction of the air within it, which in turn changed the level of the liquid with which the vesselÊs long, open-mouthed neck was partially filled. This general principle was perfected in succeeding years by experimenting with liquids such as mercury and by providing a scale to measure the expansion and contraction brought about in such liquids by rising and falling temperature. For calibration of any temperature scale, it is necessary to have two ffixed points. These are standard degree of hotness that can be accurately reproduced. For example, the melting point for pure ice is 0�C, and steam point is 100�C. At least two fixed points are needed to define the scale of a thermometer. With these two points, any thermometer can be calibrated to measure temperatures by dividing the distance between the fixed points into equal number of intervals or degrees. Figure 5.2 shows you how to do it.

Figure 5.2: Calibrating a thermometer

Source: http://www.physicsclassroom.com Some common fixed points to note are: (a) IIce point � temperature when pure water ice is in equilibrium with liquid

water at standard atmospheric pressure (76mm Hg).

(b) SSteam point � temperature when pure liquid water exists in equilibrium with water vapour at standard atmospheric pressure.

(c) TTriple point � temperature when pure water ice, pure liquid water and pure water vapour exist in equilibrium.

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The thermometric properties of a thermometer are the physical properties which can be used to determine temperature. Examples of thermometric properties are: (a) Length for a liquid-in-glass thermometer where the length of liquid in the

stem of the thermometer is measured.

(b) Resistance for resistance thermometer where the electrical resistance is measured.

(c) Voltage for a thermocouple thermometer, where the e.m.f of the thermocouple is measured.

5.3.1 Temperature Scales – Celsius Scale and Kelvin Scale

The thermometer calibration process in the previous Subtopic 5.3.1 produced the centigrade thermometer, or more commonly known as the CCelsius scale. It is the most widely accepted temperature scale used throughout the world. It is the standard unit of temperature measurement in nearly all countries; only one country does not use this scale which is the United States. Using this scale, a temperature of 28 degrees Celsius is abbreviated as 28�C. In the United States, the FFahrenheit temperature scale is more commonly used. A thermometer can be calibrated using the Fahrenheit scale in a similar manner as was described above. The difference is that the normal freezing point of water is designated as 32 degrees and the normal boiling point of water is designated as 212 degrees on the Fahrenheit scale. As such, there are 180 divisions or intervals between these two temperatures when using the Fahrenheit scale. A temperature of 76 degrees Fahrenheit is abbreviated as 76�F. Temperatures in the Fahrenheit scale can be converted to the Celsius scale equivalent using the equation below:

�C = (ÀF � 32�)/1.8

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Similarly, temperatures expressed by the Celsius scale can be converted to the Fahrenheit scale equivalent using the equation below:

�F= (1.8����C) + 32� The Kelvin Temperature Scale The most common scales used to measure temperature are the Celsius and Fahrenheit scales. However, there is the KKelvin temperature scale, which is the standard metric system of temperature measurement and perhaps the most widely used temperature scale among scientists. The Kelvin temperature scale zero-degree mark (0 Kelvin) is equivalent to a temperature of -273.15ÀC. The degree symbol (À) is not used with this system. So a temperature of 300 units above 0 Kelvin is referred to as 300 Kelvin and not 300 degrees Kelvin; such a temperature is abbreviated as 300 K. Conversions between Celsius temperatures and Kelvin temperatures (and vice versa) can be performed using one of the two equations below:

ÀC = K � 273.15� K = �C�+ 273.15

The zero point on the Kelvin scale is known as aabsolute zero. It is the lowest temperature that can be achieved.

5.3.2 Different Types of Thermometers

A practical thermometer must have a thermometric property which varies smoothly with temperature. A thermometer can give accurate measurements if it is sensitive to small changes in temperature. In some situations, it needs to respond to a quick change in temperature such as in a nuclear reactor. Main types of thermometers and their specific uses are explained in the following Table 5.2.

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Table 5.2: Seven Types of Thermometers

Type Description

Liquid-in-glass thermometer

Liquid like mercury or alcohol is placed inside a bulb at the bottom of a sealed narrow glass tube. When temperature rises, mercury expands and rises up in the narrow glass tube. It responds to temperature and changes very quickly whether for recording and laboratory uses.

Resistance thermometer

Electrical resistance of a metal wire increases as temperature increases, so that a smaller current indicates a higher temperature measuring temperatures from 200 degree C to 1000 degrees C (such as engines and ovens, etc).

It can measure temperatures of over 1000 degrees Celsius and can be used in industry to measure the temperatures of ovens and furnaces. Resistance thermometer measure changes in the electrical resistance of metal materials or thermistors, made from semiconducting material. The change in electrical resistance is shown in the reading of the meter.

Thermocouple thermometer

Its wires are made from two different metals. They are joined together to form two junctions. Temperature difference at the two junctions causes a potential difference across the circuit.

A microvoltmeter is used to record the potential difference. It is very sensitive and can measure a wide range of temperatures. It can measure temperatures of over 1000 degrees Celsius and can be used in industry to measure the temperatures of ovens and furnaces.

Thermistor thermometer

It is an electronic component using a thermistor. Resistance in the thermistor decreases as temperature increases, so that a larger current indicates a higher temperature.

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Rotary thermometer

This thermometer makes use of a bimetallic strip that consists of two strips of different metals joined together surface to surface. The strip bends as one metal expands more than the other under temperature change. As temperature increases, the coiled bimetallic strip bends more to rotate a pointer around on a scale measuring the temperature of ovens and freezers.

Infra-red thermometer

Source: http://www.omega.com

The most basic design consists of a lens to focus the infrared (IR) energy on to a detector, which converts the energy to an electrical signal that can be displayed in units of temperature after being compensated for ambient temperature variations. This configuration facilitates temperature measurement from a distance without contact with the object to be measured.

As such, the infrared thermometer is useful for measuring temperature under circumstances where thermocouples or other probe type sensors cannot be used or do not produce accurate data for a variety of reasons. Some typical circumstances are where the object to be measured is moving; where the object is surrounded by an EM field, as in induction heating; where the object is contained in a vacuum or other controlled atmosphere; or in applications where a fast response is required.

Liquid crystal thermometer

It is for measuring the temperature of the human body and fish tanks. The colour of liquid crystal changes with temperature.

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SPECIFIC HEAT CAPACITY

If you need to boil a kettle of water, you will need to heat the kettle filled with water. Heat will be absorbed by the water to increase its temperature. To increase the temperature of 1kg of water by 1ÀC, a certain amount of heat must be absorbed by the water. This heat is called the specific heat capacity.

Specific heat capacity is expressed with units Jkg-1ÀC or Jkg-1K-1. The specific heat capacity of water is 4200 Jkg-1ÀC-1, while iron is 452Jkg-1ÀC-1. This means that 4200J of heat is required to increase the temperature of 1kg of water by 1ÀC while 452J of heat is required to raise temperature of 1kg blocks of iron through 1ÀC. This shows that it is easier for an iron to get hot compared with water as iron has a lower specific heat capacity. Specific heat capacity is a physical property of a substance. Some substances have high specific heat capacities while others have lower specific heat capacities. Specific heat capacity (c) can be calculated from the amount of heat supplied (Q) to the mass (m) of the substance and the increase in the temperature, �. Thus, specific heat capacity:

c = Q/m�

SPECIFIC LATENT HEAT

Certain substances may exist in many phases, for example, water can exist as solid, liquid or gas. The amount of heat required to change the phase of a substance depends on the mass and the type of material that makes up the substance. A small ice cube melts quickly but a large block of ice melts very slowly. 100J of heat energy can melt a large amount of wax, but the same amount of heat can only melt a small amount of another substance say, copper.

5.5

Specific heat capacity is the amount of heat needed to increase the temperature of a mass of 1kg by 1ÀC.

5.4

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Specific latent heat can be represented as,

L = Q/m where Q = latent heat absorbed or released by the substance and m = mass of the substance. The SI unit for specific latent heat is J/kg or Jkg-1. The latent heat absorbed or released when a substance of mass, m changes from one phase to another is represented by:

Specific latent heat can be written as

Q = ml The specific latent heat of fusion of a substance is usually smaller than the specific latent heat of vaporisation. This is due to the extra work done against atmospheric pressure during the change of phase from liquid to gas.

Specific latent heat of vaporisation of substance is defined as the amount of heat required to change 1kg of the substance from the liquid phase to the gaseous phase without a change in temperature.

Specific latent heat of fusion of a substance is the amount of heat required to change 1kg of the substance from the solid phase to its liquid phase without a change in temperature.

The sspecific latent heat of a substance is the amount of heat that is required to change the phase of 1kg of the substance at a constant temperature.

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GAS LAWS

In this subtopic, we are going to examine three types of gas laws which are BoyleÊs Law, CharlesÊs Law and Pressure Law.

5.6.1 Boyle’s Law

We live in 1atm of pressure, but we rarely even notice the pressure on us because the human body is primarily made up of liquid and liquids are basically non-compressible. However, we sometimes notice the changes in pressure, primarily in our ears for example, when flying, driving in the mountains, or even going up and down in elevators where our ears pop. This is because our ears have an air space in them and air, like all other gases, is compressible. A gas compresses in proportion to the amount of pressure exerted on it. For example, if you have a 10cm3 balloon and double the pressure on it, it will be compressed to 5cm3. If the pressure is increased four times, the volume will drop to 1/4 the original size etc. This theory was discovered by Sir Robert Boyle, a 17th century scientist.

From BoyleÊs Law, at constant temperature pressure in a closed container, pressure will decrease when the volume increases (see Figure 5.3).

Figure 5.3: BoyleÊs Law

Source: http://www.preceden.com

BoyleÊs Law states that if the temperature remains constant, the volume of a given mass of gas is inversely proportional to the absolute pressure.

5.6

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We can write this relationship mathematically as

�1

PV

or PV = constant As we reduce the volume further, the pressure will increase appropriately, so we can also write BoyleÊs Law as

P1V1 = P2V2 We can use this relationship to solve problems related to BoyleÊs Law. Example 5.1: The volume of the lungs is measured by the volume of air exhaled or inhaled. If the volume is 2,400 litres during exhalation and the pressure is 101.7kPa, and the pressure during inhalation is 101.01kPa, what is the volume of the lungs during inhalation? Solution: Consider the volume during inhalation as V1, volume during exhalation as V2 and the pressure during inhalation as P1 and pressure during exhalation as P2. Thus, V1 = ? V2 = 2.400l P1 = 101.01kPa P2 = 101.70kPa Using BoyleÊs relationship P1V1 = P2V2

101.01kPa � V1 = 101.70 � 2.400l

l�

1

101.70 2.400= = 2.416

101.01V

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Imagine if you have a balloon with a volume of 20cm3 at the surface of the water. This balloon is under 1atm of the atmospheric pressure. If we push the balloon into the water, for example to a depth of 10m, it is now under 2atm of pressure (1atm of pressure from the air, 1atm of pressure from the water). Boyle's Law then tells us that since we have twice the absolute pressure, the volume of the balloon will be decreased to one half. It follows then, that taking the balloon to

1. Draw a face on one side of the marshmallow and place it in the plastic syringe so the face can be seen from the side.

2. Place your thumb over the end of the syringe where the needle is usually located. Holding your thumb in place, push in the plunger. Observe what happens to the marshmallow as you do so.

3. With your thumb still in place, pull the plunger out and observe what happens.

Follow-up questions: 1. Marshmallows have bubbles of air trapped inside. What happened

to the marshmallow when you pushed in the plunger? What happened when the plunger was pulled out?

2. Relate this demonstration to the definition of Boyle's Law. How did this demonstration verify the accuracy of that law?

Source: http://www.education.com/reference/article/boyle-gas-law/

ACTIVITY 5.3

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20m, the pressure would compress the balloon to one third its original size, 30m would make it 1/4 etc. If we bring the balloon in the previous example back up to the surface, it would increase in size due to less pressure acting on it, until it reached the surface and returned to its earlier 20cm3 volume. The air in the balloon is compressed from the pressure of the water on it when submerged, but returns to its normal size and pressure when it returns to the surface. Taking BoyleÊs Law into consideration is very important in diving. The most important rule in scuba diving is „Never hold your breath!‰ Your lungs act like a pair of balloons in your chest. As a breath-hold diver (skin diver), if you fill your lungs with air at the surface, hold your breath and dive to a depth of 10m, the surrounding pressure will double to 30psi, so your lungs will be compressed to half of their original size. And if you take a full breadth of air at 10m deep, the volume of air will double when you head back to the surface. ThatÊs why you have to exhale on the return trip or else your lungs will explode!

5.6.2 Charles’s Law

There is another way to make a balloon smaller other than pushing it underwater. You can put it in the freezer. When you heat up a gas, the molecules that the gas is made up of move faster. In our balloon example, this increase in molecular motion causes the molecules to hit the sides of the balloon more often and with more force, making the balloon expand. Cooling the gas would have the inverse effect, making the balloon smaller. This situation can be explained by another gas law called CharlesÊs Law.

This significant study of gases came in the early 1800s in France when hot air balloons were extremely popular. At that time scientists were eager to improve the performance of their balloons. Two prominent French scientists, Jacques Charles and Joseph-Louis Gay-Lussac, made detailed measurements of how the volume of a gas was affected by the temperature of the gas. See Figure 5.4.

CharlesÊs Law states that if the pressure remains constant, the volume of a given mass of gas is directly proportional to the absolute temperature.

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Figure 5.4: CharlesÊs Law

Source: http://www.aculator.com

Mathematically, CharlesÊs Law can be represented as �V T

or V = kT ,

which can be rewritten as v

k =T

(where k is a constant)

For a fixed mass of gas, CharlesÊs Law can be written as

1 2

1 2

=V VT T

Example 5.2: A 30cm3 balloon is heated from 27ÀC to 127ÀC. If the pressure remains constant, what is the final volume of the balloon? Solution: From the information given:

Initial volume of the balloon is V1 =30cm3

Final volume V2 = ? To use the relationship of �V T , the temperature must be in the Kelvin scale. Convert to the Kelvin scale (K) by adding 273 to the temperature in the Celsius scale.

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T1 = (27 +273)K = 300 K T2 = (127+ 273)K = 400 K Using CharlesÊs Law

1 2

1 2

2

=

30=

300 400

V VT T

V

3�2

3.0 400= = 40 cm

300V

The final volume of the balloon is 40cm3.

5.6.3 Pressure Law

The relationship between temperature and pressure was investigated by the French chemist, Joseph Gay-Lussac (1778-1850) and for that, Pressure Law is also known as GGay-LussacÊs Law.

Pressure Law states that if the volume remains constant, the pressure of a given mass of gas is directly proportional to the absolute temperature.

Take a used soda can and fill it with about 10ml of water. Heat it on a hot plate so that steam rises from it for a few minutes. Next, fill a large beaker with water and set it near the hot plate. Pick up the soda can from the hot plate and quickly invert it into the water. What did you observe? Explain using CharlesÊs Law.

ACTIVITY 5.4

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The temperature of the gas trapped in the flask is increased gradually. The volume remains constant and increase in pressure can be observed using a pressure gauge. A graph of pressure versus temperature (in Kelvin) can then be plotted as shown in Figure 5.5.

Figure 5.5: Pressure law

Source: http://www.kentchemistry.com It shows that pressure is directly proportional to temperature, so the relationship can be written mathematically as

�P T

P = kT (where k is a constant)

Arranging the formula, �P

= Constant

or

1 2

1 2

=P PT T

Example 5.3: The pressure of a car tyre is 22kPa at 30ÀC. After a long journey, the pressure has increased to 25kPa. What is the final temperature of air in the tyre after the journey, assuming the volume of the tyre remained unchanged?

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Solution: From the information given: Initial pressure, P1 = 22kPa Final pressure, P2 = 25kPa Initial temperature, T1 = 30kPa = (30 + 273)K = 303K Final temperature, T2 = ?

2 2

2 2

=P PT T

Using

�

2

2

22kPa 25kPa=

303K

25kPa 303K= = 335.23K

22kPa

T

T

The final temperature of the air inside the tyre is 335.23 � 273 = 71.32ÀC One example of the application of Pressure Law is a scuba tank. A full scuba tank is left in the sun; the temperature of the gas inside it will increase. This causes the air molecules in the tank to move rapidly. Unlike the balloon which could expand, the tank is a rigid container that will not expand or increase its volume. This increase in motion then raises the pressure inside the tank. In fact, a full scuba tank will gain about 35 to 40kPa for every degree of temperature increase. This is one reason that full tanks should not be left in trunk of a car on a hot day. If the tank is filled to a pressure of 20000kPa, it could easily reach 25000kPa if the temperature is increased substantially. There are several cases where full scuba tanks are involved in boat fires when they exploded.

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• When there is no overall heat transfer between two objects of the same

temperature, the two objects are said to be in thermal equilibrium.

• Temperature is the degree of hotness of an object.

• Heat is the amount of thermal energy that can be transferred from one object to another and is measure in joules (J).

• Thermometry refers to temperature measurement. Temperature can be measured in degrees Celsius (C), degrees Fahrenheit (F) or in Kelvin (K).

• There are various types of thermometers which can be used to measure temperatures in different situations.

• Different types of thermometer are liquid-in-glass thermometer, resistance thermometer, thermocouple, thermistor thermometer, rotary thermometer, infra-red thermometer and liquid crystal thermometer

• The amount of heat that must be supplied to increase the temperature by 1ÀC for a mass of 1kg of the substance is known as its specific heat capacity.

• The specific latent heat of a substance is the amount of that heat required to change the phase of 1kg of the substance at a constant temperature.

• Specific latent heat of fusion of a substance is the amount of heat required to change 1kg of the substance from the solid phase to its liquid phase without a change in temperature.

• Specific latent heat of vaporisation of substance is defined as the amount of heat required to change 1kg of the substance from the liquid phase to the gaseous phase without a change in temperature.

• BoyleÊs Law states that if the temperature remains constant, the volume of a given mass of gas is inversely proportional to the absolute pressure. Its application can be seen in diving activity.

• CharlesÊs Law states that if the pressure remains constant, the volume of a given mass of gas is directly proportional to the absolute temperature. This law's application can be seen in hot air balloons.

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• Pressure Law states that if the volume remains constant, the pressure of a given mass of gas is directly proportional to the absolute temperature. One example of the application of Pressure Law is a scuba tank.

BoyleÊs Law

CharlesÊs Law

Degrees Celsius

Degrees Fahrenheit

Heat

Kelvin

Pressure

Pressure Law

Specific heat capacity

Specific latent heat

Temperature

Thermal equilibrium

Volume

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Walker, P., & Wood, E. (2010). The science teacher's activity-a-day, grades 5-10: Over 180 reproducible pages of quick, fun projects that illustrate basic concepts. San Francisco: John Wiley & Sons.

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