# PHYSICS FORM THREE-Topic 5: THERMAL EXPANSION

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THERMAL ENERGY

Heat – Is the transfer of energy due to temperature differences.

Temperature – Is the degree of hotness or coldness of a body.Or heat is a form of energy which raises the temperature of the substance.

SI Unit of Temperature is Kelvin (K).Conversion of centigrade into fahrerinheit given by:f = 9/5ºC + 32

Conversion of Fahrenheit into centigrade given by C = 5/9/ ( F – 32). Thermometer used for measurement of temperature. Maximum thermometer is the one which is used to measure the highest temperature obviously filled with mercury.

A Minimum thermometer is used to measure the lowest temperature and it is filled with alcohol. Combined maximum and minimum thermometer (Six’s thermometer) is used to measure highest and lowest temperature at the same time.

SI Unit of Heat is Joule (J) mathematically heat energy given by:

• H = MC (Q2 – Q1)
• M = Mass of substance
• C = Specific heat capacity
• Q= Final Temperature
• Q1 = Initial Temperature

Source of Thermal Energy in Everyday Life

There are numerous sources of energy such as the sun, fuels, nuclear sources, geothermal, electricity among others. The most important source of thermal energy is the sun. The sun generates its energy by a process called thermonuclear fusion.

Most sources of thermal energy derive their energy from the sun. Thermal energy from the sun makes life on earth
possible.

Difference between Heat and Temperature

Heat and temperature are related and often confused. More heat usually means a higher temperature.

Heat(symbol:Q) is energy. It is the total amount of energy (both kinetic and potential) possessed by the molecules in a piece of matter. Heat is measured in Joules.

Temperature(symbol:T) is not energy. It relates to the average (kinetic) energy of microscopic motions of a single particle in the system per degree of freedom. It is measured in Kelvin (K), Celsius (C) or Fahrenheit (F).When you heat a substance, either of two things can happen: the temperature of the substance can rise or the state of substance can change.

THERMAL EXPANSION OF SOLIDS

When a solid is heated one or more of the following may occur:

• Its temperature may rise
• Its state may change
• It may Expand

Expansion of solids is the increase in dimensions of a solid when heated.Contraction of solids is the decrease in dimensions of a solid when is cooled.

DEMONSTRATION OF EXPANSION OF SOLIDS

In order to demonstrate the expansion of solid we can use following method

1. The ball and Ring Experiment
2. The Bar and Gap Experiment

The ball and Ring Experiment 1st Case: When the ball is not heated then it will pass through the ring very easily because it has a small volume.

2nd Case: When the ball is heated, it will expand and increase in volume, so itwill not pass through the ring.

The Bar and Gap experiment 1st Case: When the Bar not heated (Not raised with temperature) then the dimension will remain constant.2nd Case: When the Bar is heated (raised with temperature) then the dimension of the Bar will increase and eventually will not pass thought the Gap.

Expansion of Solids in terms of Kinetic Theory of Matter

When a solid is heated, its atoms vibrate faster about their fixed points. The relative increase in the size of solids when heated is therefore small. Metal railway tracks have small gaps so that when the sun heats them, the tracks expand into these gaps and don’t buckle.

Forces due to expansion Normally Expansion and contraction is accompanied by tremendous forces; The
presence of force indicates the expansion and contraction is Resisted.

Bar breaker

• Consists a strong metal blocker with a pair of vertical jaws J and a strong metal Bar R. The metal bar has a wing nut N at one end and an eye at the other end.
• The bar is placed between the two pair of Jaws
• A short cast iron C is inserted in the eye of the bar.
• The bar is then heated it expands and the wing not screwed to tighten the bar R against the jaws.
• The bar is then allowed to cool as it cools, it contracts the short cast Iron rod C which presses against the jaws of the bar breaker, Resists
the contraction of the Metal bar R.
• The resistance to the contraction of the bar sets up very large forces which breaks the short cast Iron rod C in the eye of metal bar, Because the contracting bar is trying to pull itself through the small gap in the frame.

Expansivity of Different Solids

The coefficient of linear expansion or linear expansivity (x)The amount by which the linear dimension of a given solid expands depends on:

• The length of the solid
• The temperature to which the solid is heated
• The nature of solid

Coefficient of linear Expansivity (x) is the fractional increase in length of the solids per original length per degree rise in temperature.

Mathematical formula

Thus

SI Unit of coefficient of linear expansivity (X) is per degree centigrade ºC -1Example 1A copper rod has a length of 40cm on a day when the temperature of the room is 22.3ºC. What will be its length become on a day when the temperature of the room is 30ºC ? The linear expansivity of copper is 0.
000017/ºCSolutionTable which shows the coefficient of Expansivity Constant.

The Application of Expansion of Solids in Daily Life

There is a large number of important practical applications of thermal expansion of solids; While laying the railway tracks, a small gap is left between the successive lengths of the rails. This will allow expansion during a hot day. The iron tyre is to be put on a wheel, the tyre is first heated until its diameter becomes more than that of the wheel and is then slipped over the wheel.

Thermal Expansion of Liquids

Liquids expands when heated and contracts when cooled. It is easier to observe expansion in liquids than in solids. Different liquids expand at different rates in response to the same temperature change. Liquids expand much more than solids for equal changes of temperature.

Apparent expansion of liquids is always less than the true expansion of the liquid.

Liquids unlike solids can be poured. If a liquid is poured into a vessel, it takes the shape of the vessel. For this reason a liquid can’t have linear and aerial expansivity, thus liquids have only volume expansivity. Liquids molecules have kinetic energy. This energy
increases if the temperature of the liquid is raised by heating. Heating causes the molecules of liquid to move faster.

Activity 1

Items Needed

• Large heat safe glass bowl
• Cooking Oil
• Food Coloring
• Two 2×4 blocks
• Candle
• Match or Lighter

Instructions

1. Begin by filling a large glass bowl with cooking oil.
2. Next, add between 5-10 drops of food coloring into the oil. Helpful Tip: Place the drops near the center of the bowl.
3. Prop the bowl up off the table using two 2×4 blocks.
4. Light a candle and carefully place it under the bowl. The flame of the candle should touch the bottom of the glass bowl.
5. Look through the side of the glass bowl and watch carefully to observe what happens. Helpful Tip: It will likely take 5 minutes before you see anything happen to the liquid/food coloring.

You can alternatively follow the experiment through the following vedio

Verification of Anomalous of Water

The instrument used to demonstrate anomalous expansion of water is called hope’s apparatus. it consists of a brass cylinder, jacket J with a mixture of ice and salt and two thermometers A and B at regular intervals upward and at the bottom.The hope’s experiment shows that water contracts as it cools down to 4 degree centigrade and then expands as it cooled further below 4 degree centigrade.In the year 1805, the scientist T. C. Hope devised a simple arrangement, known as Hope’s apparatus, to demonstrate the anomalous behaviour of water.

Hope’s apparatus consists of a long cylindrical jar with two openings on the side, one near the top and the other near the bottom to fit thermometers in each of these openings. A metallic cylindrical air-tight trough with an outlet is also fitted onto the jar, on its central portion. Two thermometers are fitted air-tight in the two openings of the cylindrical jar. The thermometer near the bottom of the jar is T1, and the one near the top of the jar is T2.
Now the cylindrical jar is filled with water. The cylindrical trough at the central portion of the jar is filled with a freezing mixture of ice and common salt.

The Application of Expansion of Liquids in Everyday Life

Water in lakes and ponds usually freezes in winter. Ice, being less dense floats on the water. This insulates the water below against heat loss to the cold air above. Water at 4 degree centigrade being most dense, remains at the bottom of the lake, while ice, being less dense than water floats on the layers of water. This enables aquatic animals to survive in the water below the ice.

THERMAL EXPANSION OF GASES

The Concept of Thermal Expansion of Gases

Gases expand when heated just like solids and liquids. This is because the average kinetic energy of the molecules in a gas is directly proportional to the absolute temperature of the gas. Heating the gas increases the kinetic energy of its molecules, making them vibrate more vigorously and occupy more space.

The Relationship between Volume and Temperature of Fixed Mass of Air at Constant Pressure

Three properties are important when studying the expansion of gases. These are; pressure, volume and temperature. Charles law states that the volume of a fixed mass of gas is directly proportional to the absolute (Kelvin) temperature provided the pressure remains constant.
Mathematically V1T2 = V2T1.Example 2the volume of gas at the start is recorded as 30 cm3with a temperature of 30°C.

The cylinder is heated further till the thermometer records 60°C.
What is the volume of gas?Solution:We know,V/T = constanttherefore, V1/T1=V2/T2V1 =30 cm3T1 =30°C = 30+273 = 303K(remember to convert from Celsius to Kelvin)T2 =60°C = 60+273 = 333KV2 =?V1/T1=V2/T2V2=V1xT2/T1V2=30×333/303= 32.97 cm3

The Relationship between Pressure and Volume of a Fixed Mass of Air at Constant Temperature

The relationship obtained when the temperature of a gas is held constant while the volume and pressure are varied is known as Boyle’s law.
Mathematically, P1V1 = P2V2. Boyle’s law states that the volume of a fixed mass of gas is inversely proportional to its pressure if the temperature is kept constant.PressurexVolume = constantpxV = constant

Example 3 The volume of gas at the start is 50 cm3with a pressure of 1.2 x 105Pascals. The piston is pushed slowly into the syringe until the pressure on the gauge reads 2.0 x 105Pascals. What is the volume of gas?

Solution:We knowp x V = constanttherefore,p1xV1= p2xV2p1=1.2 x 105PascalsV1=50 cm3p2=2.0 x 105PascalsV2=?p1xV1= p2xV2V2=p1xV1/p2V2=1.2×105x50/2.0 x 105V2= 30 cm3The Relationship between Pressure and Temperature of a Fixed Mass of Air at Constant VolumeInvestigate the relationship between pressure and temperature of a fixed mass of air at constant volumeTo
investigate the relationship between the pressure and the temperature of a fixed mass, the volume of the gas is kept constant. The pressure is then measured as the temperature is varied. P1/T1 = P2/T2 ,this is called pressure law. The pressure law states that the pressure of a fixed mass of a gas is directly proportional to the absolute temperature if the volume is kept constantExample 4Pressure of gas is recorded as 1.0 x 105N/m2at a temperature of 0°C. The cylinder is heated further till the thermometer records 150°C. What is the pressure of the gas?Solution:We know,p/T = constanttherefore,p1/T1= p2/T2p1=1.0 x 105N/m2T1=0°C = 0+273 = 273K(remember to convert from Celsius to Kelvin)T2=150°C = 150+273 = 423Kp2 =?p1/T1= p2/T2p2=p1xT2/T1p2=1.0×105x423/273= 1.54 x 105N/m2The General Gas Equation from the Gas LawsIdentify the general gas equation from the gas lawsThe three gas laws give the following equations:

1. pV = constant(when T is kept constant)
2. V/T = constant(when p is kept constant)
3. P/T= constant(when V is kept constant)

These 3 equations are combined to give the ideal gas equation:

Where,

• p = the pressure of the gas
• V = the volume the gas occupies
• T = the gas temperature on the Kelvin scale

From this equation we know that if a fix mass of gas has starting values of p1, V1 and T1, and then some time later has value p2, V2 and T2, the equation can be written as:

Exercise 1 Sabah pumps up her front bicycle tyre to 1.7 x 105Pa. The volume of air in the tyre at this pressure is 300 cm3. She takes her bike for a long ride during which the temperature of the air in the tyre increases from 20°C to 30°C. Calculate the new front tyre pressure assuming the tyre had no leaks and so the volume remained constant?

Absolute Scale of Temperature

Absolute zero is the lowest temperature that can be attained theoretically. It is not possible to attain this temperature because all gases liquefy before attaining it. The kelvin scale of temperature is obtained by shifting the vertical axis to -273 degrees Celsius and renaming it 0 K.
On the scale 0 degrees Celsius becomes 273 K and 100 degrees Celsius corresponds with 373 K.

Convertion of Temperature in Degrees Centigrade (Celsius) to Kelvin Convert temperature in degrees centigrade (celsius) to kelvin

The Kelvin temperature scale takes its name after Lord Kelvin who developed it in the mid 1800s. It takes absolute zero as the starting point and temperature measurements are given the symbol K (which stands for “Kelvin”). Temperature differences on the Kelvin scale are no different to those on the Celsius (°C) scale. The two scales differ in their
starting points. Thus, 0°C is 273K.Converting from Celsius to Kelvin

• Temperature in °C + 273 = Temperature in K

Converting from Kelvin to Celsius

• Temperature in K – 273 = Temperature in °C

Example 5The temperature of a gas is 65 degrees Celsius. Change it to the kelvin scale.

SolutionT(K) = degrees Celsius + 273, T(K) = 65+273therefore T(K) = 338 K.Standard Temperature and Pressure (S.T.P)Explain standard temperature and pressure (S.T.P) The standard temperature and pressure (S.T.P) is a set of conditions for
experimental measurements to enable comparisons to be made between sets
of data. The standard temperature is 0 degrees Celsius (273 K) while the
standard pressure is 1 atmosphere (101300 Pa or 760 mm of mercury).Expansion of Gas in Daily LifeApply expansion of gas in daily lifeLand
and sea breezes are the result of expansion of air caused by unequal
heating and cooling of adjacent land and sea surfaces. The piston engine
and firing bullets from guns work under principles of expansion of
gases.

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