FORM THREE PHYSICS STUDY NOTES TOPIC TOPIC 5: THERMAL EXPANSION & TOPIC 6: TRANSFER OF THERMAL ENERGY
TOPIC 5: THERMAL EXPANSION
Thermal Energy
Thermal Expansion of Solids
Expansion of Solids
Demonstrate 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
- The ball and Ring Experiment
- 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
1stCase: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
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 into these gaps and don’t buckle.
Forces due toexpansion
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
Identify 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 -1
Example 1
A 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/ºC
Solution
Table which shows the coefficient of Expansivity Constant.
| Substance | Linear Expasivity (PerºC) |
| Aluminum (Al) | 0.000026 |
| Brass | 0.000019 |
| Copper | 0.000017 |
| Iron | 0.000012 |
| Steel | 0.000012 |
| Concrete | 0.000011 |
| Glass | 0.0000085 |
| Invar ( Alloy of Iron and Nickel) | 0.000001 |
The Application of Expansion of Solids in Daily Life
Explain the applications 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
The Apparent Expansion of Liquids
Explain the apparent 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.
Demonstrate the Effects of Heat on Liquids
Demonstrate the effect of heat on liquids
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
- Begin by filling a large glass bowl with cooking oil.
- Next, add between 5-10 drops of food coloring into the oil. Helpful Tip: Place the drops near the center of the bowl.
- Prop the bowl up off the table using two 2×4 blocks.
- Light a 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 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
Verify the anomalous expansion 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
Explain the applications 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.
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 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
Investigate 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 2
the 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 = constant
therefore,
V1/T1=V2/T2
V1 =30 cm3
T1 =30°C = 30+273 = 303K(remember to convert from Celsius to Kelvin)
T2 =60°C = 60+273 = 333K
V2 =?
V1/T1=V2/T2
V2=V1xT2/T1
V2=30×333/303
= 32.97 cm3
The Relationship between Pressure and Volume of a Fixed Mass of Air at Constant Temperature
Investigate 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 = constant
pxV = 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 know
p x V = constant
therefore,
p1xV1= p2xV2
p1=1.2 x 105Pascals
V1=50 cm3
p2=2.0 x 105Pascals
V2=?
p1xV1= p2xV2
V2=p1xV1/p2
V2=1.2×105x50/2.0 x 105
V2= 30 cm3
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. 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 constant
Example 4
Pressure 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 = constant
therefore,
p1/T1= p2/T2
p1=1.0 x 105N/m2
T1=0°C = 0+273 = 273K(remember to convert from Celsius to Kelvin)
T2=150°C = 150+273 = 423K
p2 =?
p1/T1= p2/T2
p2=p1xT2/T1
p2=1.0×105x423/273
= 1.54 x 105N/m2
The General Gas Equation from the Gas Laws
Identify the general gas equation from the gas laws
The three gas laws give the following equations:
- pV = constant(when T is kept constant)
- V/T = constant(when p is kept constant)
- 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
Explain 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 5
The temperature of a gas is 65 degrees Celsius. Change it to the kelvin scale.
Solution
T(K) = degrees Celsius + 273, T(K) = 65+273
therefore 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 Life
Apply expansion of gas in daily life
Land 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.
TOPIC 6: TRANSFER OF THERMAL ENERGY
Conduction
The Concept of Conduction of Heat
Explain the concept of conduction of Heat
Conduction is the transfer of heat energy through solids, for example, metals. Generally solid substances contain particles which are close together. Each particle vibrates at one position but cannot move to another position.
Solid materials differ greatly in their ability to conduct HEAT.
Good and Bad Conductors of Heat
Identify good and bad Conductors of Heat
Solid materials differ greatly in their ability to conduct HEAT.
Good conductors
These are the substances which allows the passage of heat energy easily example all metals.
Metals contain tiny particles called electrons (particles that carry electricity through metals) which are free to move inside the metal and carry energy from hotter places to colder places.
Bad conductors
These are materials which does not allow the passage of heat and electricity e.g Non – metals, woods.
| GOOD CONDUCTOR | BAD CONDUCTOR |
|
|
How to Minimize Heat Losses due to Conduction
Explain how to minimise Heat losses due to Conduction
There are some simple ways to reduce heat loss, including fitting carpets, curtains and draught excluders.
Heat loss through windows can be reduced using double glazing. The gap between the two panes of glass is filled with air. Heat loss through conduction is reduced, as air is a poor conductor of heat. Heat transfer by convection currents is also reduced by making the gap is very narrow.
Heat loss through walls can be reduced using cavity wall insulation. This involves blowing insulating an material into the gap between the brick and the inside wall, which reduces the heat loss by conduction. The material also prevents air circulating inside the cavity, therefore reducing heat loss by convection.
Knowledge of Conduction in Daily Life
Apply knowledge of conduction in daily life
The difference in conductivity of various materials can be demonstrated using Edser’s apparatus
The apparatus consists of copper can with identical rods of aluminum, copper, lead and iron fixed to the bottom of the can.
The can is supported by a metal ring which is clamped to a retort stand. When hot water is poured inside the copper can, heat will be passed along the rods by conduction.
After some time, it will be observed that wax coatedon the rods will melt and move down the rods. Note how far along the rods the wax has melted when the apparatus reaches a steady state.
This indicates that the materials from which the rods are made have different thermal conductivities. Of the four metal rods, the copper rod is observed to conduct heat more quickly than the rest.
Conduction of Heat Energy through Liquids
- All liquids expect mercury and gases are poor conductors of heat.
- Gases are far worse conductors of heat than liquids.
- Fluids are bad conductors of heat. They transfer heat by means of convection.
Convection
The Concept of Convection of Heat
Explain the concept of convection of heat
Convection is the transfer of Heat through the fluids (Liquids or Gases)
Convection in Fluids in Terms of Kinetic Theory of Matter
Explain convection in fluids in terms of kinetic theory of matter
Convection currents are the currents of a liquid that move from the bottom to the top of the liquid container when the liquid is heated.
The heated liquid expands and becomes less denser and so can float upwards and replaced by colder denser liquids that sinks.
Convection in gases.
Convection air current occurs due to the unequal Heating of the Earth’s atmosphere by the sum. (Thus current called strong convection current).
How to Minimize Heat Losses due to Convection in Daily Life
Explain how to minimise heat losses due to convection to daily life
When you understand the effects of cold water on the body, and how the body responds, you are far more prepared to make life-saving decisions, either for yourself or in a rescue situation.
It’s actually quite simple: the body attempts to maintain a constant core temperature (homeostasis) through a balance of heat loss and heat gain. Body heat is normally gained through activities such as exercise and shivering, and also with the application of external heat sources such as heat packs.
Convection is the process of air or water flowing by the skin and carrying away body heat. It’s convective heat loss that you try to prevent by staying as still as possible in the water. Staying still, the boundary layer of water next to the skin is heated by the body and remains undisturbed. If you move around in the water, you disrupt that boundary layer of warmer water, and that increases heat loss.
Once a body has been in cold water for an extended period of time, most of the skin is cool with little blood flow. However, there are critical areas that are lighter (warmer) than the surrounding tissue. This is because blood is flowing through major blood vessels, which are near the skin surface. These areas in the neck, armpits and groin are areas of high heat transfer. That means that these areas have high heat loss in the cold but allow heat gain in the heat. This is why, in a rescue scenario, the most effective rewarming often consists ofapplying external heat directly to the armpits as well as the chest.
As a final note, it’s important to realize that the activity of swimming (which is naturally thought of as producing a heat GAIN), in cold water conditions will result in increasing the blood flow to blood vessels close to the skin, and because of conduction and convection, it can actually increase the rate of heat LOSS and expedite the onset of hypothermia.
Knowledge of Convection to Daily Life
Apply knowledge of convection to daily life
Domestic hot water system
- Convection currents are used to circulate hot water from a boiler in a domestic hot water system. The system consists of aboiler B, a hot water storage tank, H and cold water supply tank (cistern) C all connected by pipes.
- When water is heated (electrically or by fire) at the button of the boiler, it expands and become less dense, and so rises to the top.
- The hot water in the boiler passes through the outlets at the top of the boiler into the upper part of the hot water storage tank.
- The lower portion of the storage tank is filled with cold water from the cistern, which is high enough to drive the hot water out when the hot water tap T is open.
- The cistern is fitted with a ball-cock which maintains the level of water in the cistern by allowing water in when the level falls.
Radiation
The Concept of Radiation
Explain the concept of radiation
Radiation is transfer of heat energy from one point to another without the requirement of any material medium.
The stars including the sum illuminate the world by radiation.
Radiant energy from the sun Reaches the Earth through the Vast empty space ?(vacuum) existing between the atmosphere and the sun.
This energy travels with the speed of light and has similar properties to light i.e. Radiant energy can be reflected absorbed and Transmitted.
The body which absorbs radiant energy becomes heated up and its temperature rises.
Good Absorbers and Emitters of Radiant Heat
Identify good absorbers and emitters of radiant heat
Radiant energy can be detected by means of a thermopile.
Thermopile is an instrument which convents radiant energy ( radiant heat energy) into electrical energy.
If the terminals of the thermocouple are connect to a galvanometer by connecting wires, a current flows in the galvanometer G when the thermopile is directed towards a hot body, such as an electric lamp.
An increase in deflection of Galvanometer G is observed when the current thought the electric lamp is increased. Comparison of Radiant energy
The amount of Heat energy radiated by a body depends on:
- The Temperature of the body.
- The Nature of surface the body.
- The surface area for the body
To demonstrate the fact that the amount of Heat energy radiated from a body depends on the nature and area of its surface (Leslie’s cube) can be used.
The figure below shows Comparison son of Radiant energy from different – substance.
- Leshe’s cube is a cube – shaped metal Box which has Three of its sides painted with different colours e.g Green, Black and Grey.
- One side is highly polished serve as a reflecting surface.
- The cube is placed on a Turn table R and Maintained Hot by Running steam into it.
- Thermopile, T connected to a galvanometer G is placed at a fixed distance from the cube by Turning the Turn table.
- The black side of the cube will produce the largest deflection of the Galvanometer G, While the polished surface will produces the leats deflection.
- The alternative demonstration of the absorption of radiant Heat by a surface can be per formed by using two tiny plates and Ban sern burner.
Heat Losses due to Radiation
Minimize heat losses due to radiation
The vacuum flask was designed by sir James Dewar for purpose of stoning condenser air in the liquid state.
Now days used for keeping liquids hot over a period of Time. It would also keep liquids Cold for a long time.
The vacuum flask consists of the double walled glass vessed with a vacuum between the walls.
The walls are silvered on the vacuum side. The flask controls convection, conduction and radiation of Heat energy.
Convection is prevented by the vacuum space between the walls and by closing the flask at the top.
Conduction is reduced by having the container made of glass, which is a bad conductor of heat. The stopper is made of a bad conductor e.g. cork or rubber.
The vacuum is also a non – conducting space. The outer glass wall is supported by a pad of felt or cork attached to a plastic case.