THERMAL EXPANSION

Thermal Energy

‘The Concept of Heat Heat — Is the transfer of energy due to temperature differences. Temperature ~ Is the degree of hotness or coldness ofa body, SI Unit of Temperature is Kelvin (K),Conversion of centigrade into fahrerinheit given by:f = o/s +32

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 iti filled with alcohol and lowest temperature at the same time SI Unit of Heat is Joule (J) mathematically heat energy given by

. H=MC(Q-Qi)

+ Qo Final Temperature

© Qy= Initia! Temperature

Source of Thermal Energy in Everyday Life State the 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 eneray fom the sun. Thermal eneray from the sun makes life on earth possible.

Difference between Heat and Temperature

Distinguish between heat and temperature Heatandtemperatureare related and often confused. More heat usually means higher temperature Heat(symbol:Q) is energy. It isthe total amount of energy (both kinetic and potential) possessed by the molecules in a piece of matter. Heat is measured in Joules, Temperature(symbol:7) 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 inKelvin (K),

Celsius (C) or Fahrenheit (F), When you heat a substance, either of two things can happen: the temperature of the substance an rise or thestatcof substance can change. feat Temperature efinition Heats» energy thats transfered from one Temperature « measure of hotness or codecs expressed in body to another asthe tesll ofa difference terms of any of several arbitrary seales ike Celsius and sn temperature Fabrenhost fymbor ° 1

nit Soules Kevin, Casas oc Fahrenheit

unit Joule Kelvin

particles Heat is a measure of how many atoms there Temperate 4 relaled to how fist the atoms within a are in a substance multiplied by how mach substance are moving. The ‘temperature’ of an object i like ‘energy cach atom possesses the water level — it determines the divetion in which *hea wil ow bility to

Thermal Expansion of Solids

Expansion of Solids

• its temperature may nse
• Its statemay change

. Itimay Expand

DEMONSTRATION OF EXPANSION OF SOLIDS

1 The ball and Ring Experiment

• ‘The Barand Gap Experiment

The ball and Ring Experiment 1° Case: When the ball is not heated then it will pass through the ring very easily because it has asmall volume. 2 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 "Case: When the Bar not heated (Not raised with ternpersture) then the dimension wall remain constant 2 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 Explain expansion of solids in terms of Kinetic theory of matter When asolidis 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 imo these gaps and don’t buckle

Forces due tocxpansion Normally Expansion and contraction is accompanied by tremendous forces; The presence of force indicates the expansion and contraction is Resisted, a a“ 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 baris placed between the two pair of Jaws
• Asshort 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 fron rod © 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

Identify expansivity of different solids The coefficient of linear expansion oF linear expansivity (3) The amount by which the linear dimension ofa 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) isthe fractional increase in length ofthe solids per original length per degree rise in temperature Mathematical formula x= SL LoAQ Where SS 1 – Change in length (Ho) lo – Original length Q — Change in Temperature(Q:—Q:) L – Final length

Qo Final Temperature

Qi — Initial Temperature

Thus

X= L=lo

Lo (Q2- Qi)

SIUnit of coefficient of linear expansivity (X) is per degree centigrade *C* Eeaailed will be its Length become on a day wien the temperature of the room is 30°C ? The linear expansivity of copper is 0. 000017°C

Solution

The increase in length 4 L is given by

La Q

AL =XLo49

AL =XLo(Q2-Q)

Aluninar (AD) .on0026 Bas 000019 Copper 100017 ra c.oona2 Stel 0.00012 Coase o.oon01 Gis c.onneoss Invar (Alloy of non and Nickel) o.oo: The Application of Expansion of Solids in Daily Life Explain the applications of expansion of solids in day ife laying the alway tracks, a small gap is lft 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 fist heated

until its diameter becomes more than that ofthe whee! and is then slipped over the wheel

Thermal Expansion of Liquids

The Apparent Expansion of Liquids

liquids then in solids. Different liquids expand at different rates in response to the same Demonstrate the Effects of Heat on Liquids Demonstrate the effect of heat on liquids Liguids unlike solids can be poured. Ifa 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 faster.

• Lange heat safe glass bow!

+ Cooking Oil

+ Food Coloring

• Two 24 blocks

. Candle a

• Match or Lighter

Instructions

• Begin by filling a large glass bowl with cooking ol

2 Next, add between $-10 drops of food coloring into the oil. Helpful Tip: Place the drops near the center ofthe bowl

• Prop the how! up offthe table using two 2:4 blocks.
• Light 2 candle and carefully place it under the bowl. The flame of the candle should

touch the bottom of the glass bowL

• Look through the side of the glass bow! and watch carefully to observe what happens.

Helpful Tip: It will likely take $ minutes before you see anything happen to the liquid/Tood coloring. You can alternatively follow the experiment through the following vedio Verification of Anomalous of Water Verify the anomalous expansion of water The instrument used to demonstrate anomalous expansion of water i called hope's apparatus. i consists ofa brass eylinder, jacket J with a mixture of ice and salt and two thermometers A and B

at regular imervals upward and at the bottom The hope's experiment shows that water contracis 4s 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 airtight trough with an outlet is also fitted onto the jer, 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 T,, and the one near the top of the jar is T;. 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 Explain the applications of expansion of liquids in everyday life Water in lakes and ponds usually freezes in winter. lee, 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.

Fy

Thermal Expansion of Gases

The Concept of Thermal Expansion of Gases

Explain 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 ternperature of the gas. Heating the gas inereases the kinetic energy of its molecules, making them vibrate more vigorously and ‘oceupy more space The Relationship between Volume and Temperature of Fixed Mass of Air at

Constant Pressure

Investigate the relationship between volume and temperature of fived 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 direetly proportional to the absolute (Kelvin) temperature provided the pressure temains constant

Mathematically Vj T= VsT

Example2

the volume of gas at the statis recorded as 30 em3with a temperature of 30°C. The eylinder is heated further till the thermometer records 60°C. What is the volume of gas?

Solution

therefore, Vives

cy v2~

VeVixtTy

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

Constant Temperature

Investigate the relationship between pressure and volume of a fexed mass of air at consiant temperamure The relationship obtained when the temperature of a gas ts held constant while the volume and

that the volume of a fixed mass of gas is inversely proportional to its pressure if the temperature is kept constant

pxV = constant

Example3

The volume of gas at the start is SO em'with a pressure of 1.2 x 10°Pascals. The piston is pushed slowly into the syringe until the pressure on the gauge reads 2.0 x 10°Pascals, What is the volume of gas?

Solution

We know

therefore PIXVi= paxVi 8s

Vir50 em

Ve?

VepaVilp2

Ver 30 om" The Relationship between Pressure and Temperature of a Fixed Mass of Air

at Constant Volume

Investigate the relationship between pressure and temperature of a fixed mass of air at constant volume To 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

mass of a gas is directly proportional to the absolute temperature ifthe volume is kepr constant

Example

Pressure of gas 1s recorded as 1.0 x 10*Nim“at a temperature of O'C. ‘The cylinder is heated further till the thermometer records 150°C. What isthe pressure of the gas?

Solution

We know.p'T = constant therefore, pT pT Pr-O 10sNim*

p=?

pepaxl/t peo} Ox10°%423/273,

The General Gas Equation from the Gas Laws Identify he general gas equation from ihe gas laws The three gas laws give the following equations:

• pV=constant(iien Tis kept constam)

2 WT constant(ivhen p is kepe constand)

• PT=constantivhen 11s kept constant)

These 3 equations are combined to give the ideal gas equation pv —_ = constant i Where

• p> the pressure ofthe gas

+P =the volume the gas accupies

• T= the gas temperature on the Ketvin scale

a7 From this equation we know that ia fix mass of gas has starting values of pl, VI and 1, and then some time later has yalue p2, V2 and T2, the equation can be writen as:

PY; Pa

y t Sabah pumps up her front bieyele tyre to 1.7 x 10SPa. The volume of air inthe tyre at this pressure ix 300 cm3, She takes her bike fora long ride during which the temperature ofthe air in the tyre increases ffom 20°C t0 30°C. Calculate the new front tyre pressure assuming the tyre tid no leaks and so the volume remained constant?

Absolute Scale of Temperature

Explain absolute scale of emperanure Absolute zero 1s the lowest temperature that can be attained theoretically. It is not possible to attain this temperature because all gases liquely before attaining it. The kelvin scale of temperature is obtained by shifting the vertical axis to -273 degrees Celsius and renaming i 0 K (On the scale 0 degrees Celsius becomes 273 K and 100 degrees Celsius comresponds with 373 K Convertion of Temperature in Degrees Centigrade (Celsius) to Kelvin

Comerttemparature in degrees centigrade (celsts) to kelvin The Kelvin temperature scale takes its name after Lord Kelvin who developed it in the mid 18005. It takes absolute zero as the starting point and temperature measurements are given the symbol K (which stands for "Kelvin"). ‘Temperature dificrences on the Kelvin scale are no <ifferent to those on the Celsius (°C) seale. The two scales differ in their staring points. Thus,

OPC 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 5

The temperature ofa gas is 65 degrees Celsius. Change itt the kelvin scale

Solution

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 dats. The standard temperature is O degrees Celsius (273 K) while the standard pressure is 1 atmosphere (101300 Pa oF 760 mm of mercury).

Expansion of Gas in Daily Life Apply expansion of gas in daily life Land and sea breezes are the result oFexpansion of ar caused by unequal heating and cooling of adjacent land and sea surfaces. The piston engine and firing bullets ftom guns work under principles of expansion of gases