School Science Lessons
Physics
2025-11-16
Heat radiation
Contents
23.8.0 Heat radiation
23.2.0 Liquid expansion caused by heat
23.3.0 Solid expansion caused by heat
23.8.0 Heat radiation
23.8.1 Absorption of radiation
23.8.3 Bichsel boxes
23.8.4 Colour temperature
23.8.7 Feel radiation through glass
23.8.8 Feel radiation with your hand and cheek
23.8.9 Focus radiant heat waves
23.8.10 Heat radiation decreases with distance
23.8.11 Heat transferred by radiation. black body radiation
23.8.12 Leslie's cube
23.8.13 Light a match with reflectors
23.8.14 Non-linear absorption of soot and flour mixes
23.8.15 Plate in a furnace
23.8.16 Radiant heat passes through glass
23.8.17 Radiant heat using parabolic reflectors and a thermopile
23.8.18 Radiation from shiny surface and black surface
23.8.19 Reflection of radiant heat waves
23.8.20 Surface colour and the heat absorbed
23.8.21 Surface radiation from an engine
23.8.2 Surfaces affect radiation
23.8.23 Thermopile
23.8.24 Transfer heat by radiation
23.8.25 Thermoscope to compare absorption of radiation
23.8.26 Teapot experiment
23.8.27 Black body radiation
23.8.28 Melt ice blocks
23.8.29 Holes in carbon blocks
23.2.0 Liquid expansion caused by heat
23.2.1 Fluid expansion, coefficient of volume change, thermal expansion of water
23.2.2 Expansion and contraction of liquids, thermal expansion of different liquids
23.2.3 Coefficient of expansion of liquid in flask and U-tube
23.2.4 Expansion and contraction of liquids
23.2.5 Expansion of liquid in a thermometer
23.2.6 Expansion of water and kerosene
23.2.7 Freezing water expands
23.2.8 Heat one litre of water
23.2.9 Heat water in a sealed flask
23.3.0 Solid expansion caused by heat
23.3.1 Solid expansion caused by heat
23.3.2 Coefficient of thermal expansion
23.3.3 Compensated balance wheel of a watch
23.3.4 Motor vehicle flashing lights
23.3.5 Thermal shock
23.3.6 Trevelyan rocker
23.3.7 Ball and ring
23.3.8 Bar breaker
23.3.9 Bend glass by expansion
23.3.10 Bimetallic strip
23.3.11 Expansion of solids when heated apparatus
23.3.12 Expansion tube
23.3.13 Expanding wire
23.3.14 Expanding quartz and glass
23.3.15 Expanding solids when heated
23.3.16 Expansion gauge
23.3.17 Shrink fit
23.3.18 Microwave ice
23.8.1 Absorption of radiation
* Expose the lettered side of a white card with letters in India ink (China ink) to a hot source charring it where the letters are.
* Put a radiant heater midway between two junctions of a demonstration thermocouple and cover the junctions with black or white caps.
23.8.2 Surfaces affect radiation
1. Black and white surfaces affect radiation
See diagram 23.8.7: Shiny cans and black cans.
To compare the influences of surfaces with different quality and colour in emitting and absorbing thermal radiation use three empty flat cans.
Remove their caps and clean them then dry them.
Paint their insides with white lacquer and outsides with black lacquer and white quicklime solution uniformly.
Choosing bright lacquers to paint them is better and do not paint the second layer of lacquer until the first one is fully dry.
Use a piece of white foam board for packing instruments.
Make three caps and pads for the three cans with the board.
Insert a thermometer into each cap.
Fill the 3 tin cans with the same volume of cold water.
Cover the cap on each can and put the pad under each can.
Place each can with the cap and the pad in the sunlight far from each another.
Record the original temperatures.
Then record their temperatures every 5 to 15 minutes.
Draw a temperature time curve with the 5 groups of data recorded.
The ideal distance between the bulb and cans is where your hand feels the heat from the bulb.
Repeat the experiment with hot water more than 80oC and in a cool room.
Record the temperatures.
2. Use three same size metal drink-cans.
Paint the first can white.
Paint the second can black.
Let the third metal drink-can remain shiny.
Fill the cans to the same level with warm water at the same temperature.
Record the initial temperature.
Put cardboard covers with holes for thermometers over each can.
Put cans in a cool place.
Record the temperature of the water in each can at five minute intervals.
Describe the difference in the rate of cooling.
The second can cools fastest, because a black surface is the best radiator of heat.
3. Use a metal with width greater than a 100 W incandescent light bulb.
Paint one half of the inside of the can black.
Leave the other half shiny.
Put two blobs of petroleum jelly on opposite sides of the outside of the can.
Put one opposite the middle of the black interior and the other opposite the middle of the shiny interior.
Stick two coins on the blobs of petroleum jelly.
Fix a 100 watt light globe over the middle of the can and turn on the light.
The coin nearest the black interior falls first, because its blob of petroleum jelly melts first.
4. Wear a pair of old shoes.
Paint the left shoe black and the right shoe white.
Your left foot becomes your hot foot.
5. Wear a dark coloured sleeve and a light coloured sleeve of the same weave.
Your arm in the dark-coloured sleeve feels warmer.
If one sleeve is made of loosely woven material. it has many air spaces compared with a tightly woven material. and air is a heat insulator.
6. Different surfaces affect heat radiation and absorption
See diagram 4.36: Heat radiation and absorption.
Use three same size metal drink-cans.
Paint the first can white.
Paint the second can black.
Let the third metal drink-can remain shiny.
Fill the cans to the same level with warm water at the same temperature.
Record the initial temperature.
Put cardboard covers with holes for thermometers over each can.
Put cans in a cool place.
Record the temperature of the water in each can at five minute intervals.
Describe the difference in the rate of cooling.
The second can cools fastest, because a black surface is the best radiator of heat.
7. Fill the same metal drink-cans with very cold water and record the initial temperature.
Put cardboard covers with holes for thermometers over each can.
Put the cans in a warm place in the sun.
Record the temperature of the water at five minute intervals.
The black metal drink-can is the best absorber of heat.
8. Use a pair of old shoes.
Paint the left shoe black and the right shoe white.
Your left foot becomes your hot foot.
23.8.3 Bichsel boxes
See diagram: Bichsel boxes.
A "black body" is a hypothetical perfect absorber and radiator of electromagnetic radiation.
Holes in black boxes are blacker than the boxes themselves, even though one box is painted white on the inside.
A box with a black interior and another box with a white interior show that the radiation coming from a cavity is determined by the temperature inside the cavity.
The two holes appear equally dark. although the inside of one box is painted white and the other is painted black.
So the radiation emerging from the holes is a function only of temperature.
Bichsel boxes demonstrates Wien's law of radiation:
The density energy of radiation Uv. which corresponds to the frequency of radiation v. depends on v and the absolute temperature T.
Bichsel boxes
1. A light tight box has two small identical holes in one face.
One of the holes is backed by a black piece of paper.
The other hole has no backing and appears much darker.
Open the box to show that the inside is painted white.
An ideal black surface absorbs. rather than reflects. all radiation that hits it.
If the hole in the box is small enough. most radiation that hits the hole enters the box. bounces around the box. most getting absorbed on each bounce, and never leaves the box through the hole.
So the hole is perfectly black.
The small hole also emits radiation. with a spectral distribution of frequencies that depends only on the temperature of the walls of the box.
The description of this radiation led directly to the discovery of quantum theory.
2. Two identical boxes are painted black on the outside, can be opened or closed, and have an identical small hole in the middle of the wall.
One box is painted black inside and the other box is painted white inside.
For both boxes, the holes appear blacker than the outside wall of the boxes.
This observation demonstrates that the radiation coming from a cavity is determined by the temperature inside the cavity.
3. A light tight oven with a tiny hole in the side. emits "cavity radiation" through the hole.
23.8.4 Colour temperature
Colour temperature is a measurement in degrees Kelvin that indicates the hue of a light source.
The colour temperature of a light source is the temperature of an ideal black body radiator that radiates light of comparable hue to the light source.
Colour temperatures over 5,000 K are called cool colours (bluish white) and lower colour temperatures (2000 K) are called warm colours, (yellow-white to red).
Within visible light, the shorter the wavelength the higher the colour temperature.
The hottest stars radiate blue (cool) light, and the coolest radiate red (warm) light.
Approximate ranges of colour temperature:
Infrared, candle 1800 K. tungsten incandescent bulb 2800 K. tungsten-halogen bulb (quartz bulb) 3200 K.
fluorescent lamp 4500 K. noon sunlight 5800 K. clear sky light 27,000-30,000 K, Ultraviolet
Trade descriptions used by the "Light Bulbs Direct" company:
Colour Temperature. "Designation". Application
2700 "Extra Warm White": Similar light to normal incandescent bulbs, giving a warm cosy feel.
3000 "Warm White": The colour of most halogen lamps.
Appears slightly "whiter" than ordinary incandescent lamps.
3500 "White": The standard colour for many fluorescent and compact fluorescent tubes.
4000 "Cool White": Gives a more clinical or high tech feel.
6000 "Daylight": Fluorescent or compact fluorescent lamps simulating natural daylight.
6500 "Cool Daylight": Extremely white light used in specialist daylight lamps.
23.8.7 Feel radiation through glass
1. Stand near an open window to feel the radiation from the sun onyour cheek.
Close the window.
You can still feel the radiation from the sun on your cheek.
2. Hold your cheek 25 cm from a hole in a wooden sheet placed in front of a heating element.
Feel the radiation on your cheek.
Put a piece of glass between your cheek and the hole.
Feel the radiation on your cheek.
Repeat the experiment using more sheets of glass.
23.8.8 Feel radiation with your hand and cheek
1. Hold your hand under an unlighted electric light bulb. the palm upward.
Turn on the electricity and feel the heat from the light bulb.
The heat could not reach your hand so quickly by conduction, because air is a very poor conductor of heat.
The heat could not reach your hand so quickly by convection, because convection carries the heat upward and away from your hand.
The heat came to your hand carried by short electromagnetic waves of wavelengths longer than light.
Radiation carries heat in every direction from the source.
2. Stand near an open window to feel the radiation from the sun on your cheek.
Close the window.
You can still feel the radiation from the sun on your cheek.
3. Hold your cheek 25 cm from a hole in a wooden sheet placed in front of a heating element.
Feel the radiation on your cheek.
Put a piece of glass between your cheek and the hole.
Feel the radiation on your cheek.
Repeat the experiment by using more sheets of glass.
4. Hold the palm of your hand very close to., but not touching. your cheek.
Feel the radiation from your hand.
Heat travels by radiation almost instantaneously.
5. Place a piece of glass between an incandescent light bulb and your hand to block any movement of air.
Feel the radiated heat.
23.8.9 Focus radiant heat waves
See diagram 23.3.7: Focus sun's rays.
1. Use a magnifying glass to focus the rays of the sun on a piece of paper tissue.
Observe that the tissue paper chars. then catches fire from the focussed heat rays.
2. Repeat the experiment with tissue paper blackened with Indian ink or soot.
The blackened tissue paper catches fire sooner than the white paper in the previous experiment.
3. Focus the sun's rays on your arm.
A bright spot forms and you can feel the hot spot.
Note the distance of the lens from your arm when the light spot is smallest and brightest.
This distance is the focal length of the lens.
Notice the distance of the lens from your arm when the spot feels hottest.
The two distances are different.
23.8.10 Heat radiation decreases with distance
Radiation shadow. radiation to and from the earth. clear cold night
See diagram 23.3.3: Radiation and distance.
Put 4 thermometers at two different distances as two groups of two with both thermometers in the same group at the same level distance from a heat source,, but at different heights.
Group 1. (distance 1. from heat source) t1 upper, t1 lower
Group 2. (distance 2. from heat source) t2 upper, t2 lower
Different groups are at different level distances from the heat source., e.g. electric household radiator.
Measure the distances from the heat source.
Turn on the heat source.
Record the reading on the thermometer at each position when the reading stabilizes.
The intensity of thermal radiation from the heat source is dependent on the distance and independent on the direction.
23.8.11 Heat transferred by radiation. black body radiation
Stefan-Boltzmann law. Wien's law. KircHoff's law
The Stefan-Boltzmann law states that the total energy radiated from a black body is proportional to the fourth power of the temperature of the body.
(Joseph Stefan 1835 - 1893. Ludwig Boltzmann 1844 -1906)
Heat can be transferred by wave motion. even across a vacuum.
This is called radiation.
Heat travels by radiation almost instantaneously.
A "black body" is an imaginary body that absorbs all the thermal radiation onto it and is a perfect emitter of thermal radiation as a continuous spectrum.
So the radiation includes all the wavelengths of electromagnetic radiation.
The intensity of the radiation is greatest at a wavelength that depends only on the temperature of the body.
Energy = σ × T4. ( σ (sigma) = 5.67 × 10-8 Joules second-1 metres Kelvin-4. and T = absolute temperature.
Total energy radiated = E × surface area × time.
A full radiator would absorb all the radiant energy falling on it.
Lampblack is close to being a full radiator.
Wien's law (Wilhelm Wien. Germany 1864-1928) states the product of the absolute temperature of a body and the wave length of maximum radiation is a constant.
T × absolute temperature = constant.
The wavelength at which the maximum energy is radiated from a source is inversely proportional to the absolute temperature of the source.
So as temperature rises. maximum radiation decreases.
Hotter objects emit most of their radiation at shorter wavelengths
and appear to be blue-white. white hot.
Cooler objects emit most of their radiation at longer wavelengths and appear red, because of infrared radiation, i.e. red hot.
KircHoff's law of radiation (Gustav KircHoff 1824-1887) refers to the observation that black clothes are good absorbers of heat and good emitters of heat.
However. on a hot day. the body wearing black clothes receives more heat than it can emit. so white clothes are preferred, because they are good reflectors of heat and poor absorbers of heat.
1. Hold your hand under an unlighted electric bulb. the palm upward.
Turn on the electricity.
Feel the heat almost as soon as you turn on the bulb.
The heat could not have reached your hand so quickly by conduction, because air is a very poor conductor of heat.
The heat could not reach your hand by convection, because convection
carries the heat upward and away from your hand.
The heat came to your hand carried by short electromagnetic waves of
wavelengths longer than light.
23.8.12 Leslie's cube
A Leslie's cube. invented by John Leslie. (1766 – 1832), Scotland. shows that surfaces at the same temperature do not radiate equally.
The cube has three different surface areas: black, white, and two are smooth brass. or one grey and one silvered.
The original was said to have side made of gold. silver. copper and white varnish.
1. Fill a Leslie's cube with water and heat with a Bunsen burner.
Compare the heat radiation from the surfaces with a thermopile or thermometer or just use your hand to feel the difference.
The heat energy radiated from the surfaces is at the same temperature,, but different surfaces emit different amounts of heat.
The black surface radiates the most energy. then the white surface, then the brass surface. or grey surface then silvered surface.
Move the thermopile to show the inverse square law. the magnitude of the quality is proportional to the reciprocal of the distance from the source.
2. Put a Leslie cube with opposite faces blackened between two bulbs of a differential thermoscope.
3. A brass container coated on half of one surface with a matte black paint and highly polished on the other.
Hot water is placed inside the cube and each surface presented in turn, at the same distance to a thermopile.
4. PASCO'S Apparatus consists of a cube internally heated by a temperature controlled light globe with black. white. shiny and matte surfaces.
5. Place a Leslie's cube on a turntable so that alternate faces emit radiation to a sensor to show that the radiant heat is greater from the black surface.
23.8.13 Light a match with reflectors
See diagram 28.3.6: Radiation.
Two reflectors are set at opposite ends of the lecture bench.
One contains a heater controlled by a variac.
The other has a match at the focal point of the reflector.
Turn the variac all the way up and wait.
The match will light in about 1 minute.
If it takes longer. something is wrong.
Alignment is critical!
23.8.14 Non-linear absorption of soot and flour mixes
Add different amounts of carbon to flour and measure the reflectivity.
23.8.15 Plate in a furnace
A white plate with a black pattern on it appears as a dark plate with a grey pattern on it when placed in a furnace.
Good reflectors are bad absorbers and bad radiators.
The white plate is a good reflector. therefore when heated in the furnace it is a poor radiator compared with its surroundings and so appears dark.
The black pattern will. as it is a bad reflector. be a good radiator compared with the plate at the same temperature. so appears relatively white.
being a glazed black. however. it is probably a better reflector. and hence a slightly worse radiator. than all other black portions of the furnace.
23.8.16 Radiant heat passes through glass
1. Hold your cheek about 25 cm away from the hole in a plastic sheet fixed in front of a heating element or the sun's rays.
The hole should be level with the glowing part of the heating element.
Insert a glass plate between your cheek and the hole.
Take it out and put it back. noting what you feel.
Repeat the experiment using two sheets of glass plate held together.
2. On a sunny day. feel the warmth from the sun through a clear glass window.
However. if you light a fire and place a sheet of glass between you and the fire. you cannot feel the warmth of the fire.
The energy distribution curve for the sun has its maximum in the visible region. and the sun emits also considerable energy in the infrared and in
the region of short heat waves.
This energy passes through glass with little absorption.
The energy radiated by the fire mainly consists of heat rays of long wavelengths. and these wave lengths are almost completely absorbed by the glass.
23.8.17 Radiant heat using parabolic reflectors and a thermopile
1. Use a heat source at the focal point of one concave reflector to direct heat at a thermopile mounted at the focus of a second concave reflector
2. A thermopile mounted at the focus of a parabolic mirror detects radiation differences from different coloured beakers of water.
3. Show transmission of radiant heat with a match at the focus of one parabolic reflector lit by a heating element placed at the focus of another reflector.
Use two parabolic mirrors to transmit radiation to light matches.
23.8.18 Radiation from shiny surface and black surface
1. Paint one side of a copper sheet black, so that it has a dull black surface, and polish the other side until it is bright and shiny.
Attach the copper sheet horizontally to a retort stand.
Heat the copper sheet with Bunsen burners until it is very hot.
Remove the Bunsen burners and turn the copper sheet vertical.
Hold the back of the hand near the bright and shiny side of the copper sheet, then near the dull black side of the copper sheet.
Be careful! The back of the hand must not touch the hot copper sheet!
You can bring the back of the hand much closer to the shiny side than to the black side.
The two sides have the same temperature,, but more radiation comes from the black side of the copper sheet.
2. Hold a sheet of paper near a stove heating element painted half white and half black.
Paper held close to a stove element is not scorched where the element is painted white.
23.8.19 Reflection of radiant heat waves
Heat tissue paper with a magnifying glass.
Note the distance from the reading glass to the tissue paper.
Put a tilted mirror half way between the lens and the paper.
Feel with your hand above the mirror until you find the point where the heat waves are focussed.
Hold a piece of paper tissue at this point.
The paper ignites.
23.8.20 Surface colour and the heat absorbed
See diagram 23.8.8: Surface colour and the heat absorbed.
Cut two vertical slits opposite each other on the side of a cylindrical tin can. so that the surface of the tin can is divided into two parts.
Blacken inside one half with ink or "dead black" paint. or paste apiece of black paper.
Leave the other half shiny.
Put a lighted candle inside the tin can at the centre.
The surface of the two parts of the tin can will have different temperatures.
Test by touching them with hands.
Fix matchsticks with wax on the outer surface of the tin can so that the matchstick on the half that has a black surface inside the tin falls first.
23.8.21 Surface radiation from an engine
A paper-covered tin can cools faster than a shiny can.
In the radiator of a water-cooled engine, the water, heated by passing round the engine, passes through a hollow metal tubes.
They conduct the heat through them to be taken up by the surrounding air, which is usually forced through the metal tubes by a fan.
The radiator should be black to radiate best.
The water is either pumped through the metal reticulation. or passes round it by convection currents.
In a motor cycle. heat flows out through the metal cylinder to the metal flanges. whence it is radiated. or passed on to the surrounding air currents.
The flanges ensure a big radiating surface. and big area of contact with the cooler air.
They should be kept black.
23.8.23 Thermopile
Electromotive force, emf
A thermopile is a set of joined thermocouples.
A thermopile is made of thermocouple junction pairs connected electrically in series.
The absorption of thermal radiation by one of the thermocouple junctions.
called the active junction. increases its temperature.
Differential temperature between an active junction and a reference junction at fixed temperature produces an emf proportional to the differential temperature.
This effect is called a thermoelectric effect.
For more sensitivity. thermocouples are joined in series to make a thermopile.
Thermopiles do not respond to absolute temperature., but generate an output voltage proportional to a local temperature difference or temperature gradient.
A thermopile consists of four iron and four copper wires twisted to form seven junctions to produce a thermoelectric emf.
The end terminals connect to a galvanometer.
Use a hand held hair drier is a suitable source of heat to activate the thermopile.
23.8.24 Transfer heat by radiation
Hold the palm of your hand very close to., but not touching. your cheek.
Feel the radiation from your hand.
Heat travels by radiation almost instantaneously.
Hold your hand under an unlighted electric light bulb. the palm upward.
Turn on the electricity and feel the heat from the light bulb.
The heat could not reach your hand so quickly by conduction, because air is a very poor conductor of heat.
The heat could not reach your hand by convection, because convection carries the heat upward and away from your hand.
The heat came to your hand carried by short electromagnetic waves of wavelengths longer than light.
Radiation carries heat in every direction from the source.
Put a piece of glass between a light bulb and your hand to block any movement of air.
Feel the radiated heat.
23.8.25 Thermoscope to compare absorption of radiation
See diagram 23.116: Simple thermoscope
Practise with different materials before doing this experiment, because for most cloths the absorption of infrared is almost independent of colour.
The amount of surface area pointing towards the source is also a variable.
Use two identical clear plastic bottles.
Put a dark coloured piece of cloth or plastic in one bottle.
Put an identical amount of white cloth or shiny metal foil in the other bottle.
Fit the bottles with one-hole stoppers with 20 cm of glass tubing.
Into each glass tube introduce a bead of water or oil.
Place each bottle in the sun. or about 50 cm from a bright light bulb or 1 metre from a fire or 20 cm from a burning lamp or candle.
Note the rate at which the beads of water or oil rise in the tubes.
1. Paint two thermoscopes. one thermoscope white the other black and illuminate both by a lamp.
2. Two thermoscopes have a black surface and a white surface.
The pressure inside the thermoscopes is less than atmospheric pressure and is equalized by the connecting tubes and valve A.
Close valve A so that the two thermoscopes are independent.
Shine a 150 W spotlight on the thermoscopes and observe the difference in fluid height showing a difference in pressure between the two thermoscope tubes caused by different temperatures.
So the black surface has absorbed more heat than the white surface.
3. Use flasks. or cut off light bulbs.
Fit both flasks or bulbs with corks and tubes about 15 cm in length.
Make holes 22 cm apart in a base board.
Pass the lower ends of the tubes through flat corks. glue the tubes in a vertical position and connect the open ends by rubber tubing.
Remove one bulb and blacken the other bulb in a candle flame.
Pour liquid into the U-tube so formed until the level is about 7 cm above the baseboard.
Replace the clear bulb and slide the tube in or out so that the liquid remains level.
Place a candle equidistant between the bulbs and note the levels of the liquid in the U-tube.
4. Experiment with different materials before doing this experiment, because for most cloths the absorption of infrared is almost independent of colour.
The amount of surface area pointing towards the source is also a variable.
Use two identical clear plastic bottles.
Put a dark coloured piece of cloth or plastic in one bottle.
Put an identical amount of white cloth or shiny metal foil in the other bottle.
Fit the bottles with one-hole stoppers with 20 cm of glass tubing.
Into each glass tube introduce a bead of water or oil.
Place each bottle in the sun. or about 50 cm from a bright light bulb or 1 metre from a fire or 20 cm from a burning lamp or candle.
Observe the rate at which the beads of water or oil rise up the tubes.
5. Show selective absorption of radiation using a thermoscope.
Place different screens between a heat source and a thermopile detector.
Focus a large light on a blackened match head the clear glass bulb of a thermoscope and the bulb covered with black paper.
6. Thermoscope to compare absorption of radiation
Experiment with different materials before doing this experiment, because for most cloths the absorption of infrared is almost independent of colour.
The amount of surface area pointing towards the source is also a variable.
Use two identical clear plastic bottles.
Put a dark coloured piece of cloth or plastic in one bottle.
Put an identical amount of white cloth or shiny metal foil in the other bottle.
Fit the bottles with one-hole stoppers with 20 cm of glass tubing.
Into each glass tube introduce a bead of water or oil.
Place each bottle in the sun. or about 50 cm from a bright light bulb or 1 metre from a fire or 20 cm from a burning lamp or candle.
Note the rate at which the beads of water or oil rise in the tubes.
23.8.26 Teapot experiment
Use two identical teapots.
Fit a woollen tea cosy to one teapot.
Put the same volume of hot water and tea leaves in each teapot.
Put a thermometer in each teapot and compare the loss of heat due to radiation.
23.8.27 Black body radiation
Bichsel boxes
Use two identical teapots.
Fit a woollen tea cosy to one teapot.
Put the same volume of hot water and tea leaves in each teapot.
Put a thermometer in each tea pot and compare the loss of heat due to radiation.
23.8.28 Melt ice blocks
Place blocks of ice as follows:
* (1) in the sun and sheltered from the wind.
* (2) in the sun and in the wind.
* (3) sheltered from the sun and wind.
* (4) in an ice chest or insulated portable cooler. e.g. "Esky".
List the blocks of ice in order of complete melting.
The ice will melt most rapidly in (2). then (1). then (3). then (4).
1. The ice absorbs most heat directly from the sun by radiation and lesser heat from its surroundings by conduction and radiation,
but chiefly by convection currents.
Some of the ice has melts to form a layer of water over the ice.
Water is a bad conductor of heat so the ice will melt more slowly if the layer of water remains.
When the air is still. a layer of cold air forms round the ice and
reduces the amount of heat received from the air by convection.
2. The layer of water over the ice evaporates
more freely than in (1) so that the ice is dried and so melts more quickly.
Unlike (1). new air is continually coming into contact with the ice.
so the amount of heat received by convection is not reduced.
3. No heat is received by radiation from the sun or by wind convection.
Some heat is received by conduction and radiation from the shaded surroundings and some very small convection currents.
4. No loss of heat by convection except from within the container.
When the temperature of the interior of the container falls below room temperature, it receives heat from surroundings by convection, conduction and radiation.
The rate depends on the temperature difference.
The temperature of the container falls until the heat received by the container equals the heat used in melting the ice.
The temperature difference for the container and air is less than for the ice and air. and the container is made of a bad conductor of heat.
So melting in (4) is the slowest.
23.8.29 Holes in carbon blocks
1. A carbon block with a hole bored in it is heated red hot with a torch.
The hole glows brighter.
Bore a hole in an old carbon arc rod and heat electrically.
The hole glows brighter.
2. Two holes are drilled in a carbon block.
One is filled with a porcelain insulator and the block is heated red hot with a torch.
Graphite and porcelain heated red hot look the same.
A pattern on a porcelain dish shows brighter when heated.
23.2.1 Fluid expansion, coefficient of volume change, thermal expansion of water
All of the above formula are applicable only if α has a small value and do not apply to substances where α changes with temperature.
When a volume change with temperature occurs, the fraction by which he volume at 0 oC changes per oC is the coefficient of volume change,
e.g. mercury = 180 × 10-6, air = 3400 × 10-6.
Liquids generally increase in volume as the temperature increases and have coefficients of cubic expansion about 10 times that of solids.
Water is an exception, because as you heat water from 0 oC, it contracts rather than expands.
At 4 oC, water occupies its smallest volume, i.e. it has the highest density.
So water obeys the general laws of thermal expansion, except in the temperature interval from 0 oC to 4 oC.
The cubic expansion formula does not apply to expansion of gases, because all gases expand by 1/273 of their volume at 0 oC as in Charles's law.
For expansion of gases, you must use Charles's law (The law of volumes):
The volume of an ideal gas at constant pressure is directly proportional to the absolute temperature.
Air, and most other gases at atmospheric pressure, have a coefficient of cubic expansion of 0.0034 (oC)-1.
23.2.2 Expansion and contraction of liquids, thermal expansion of different liquids
See diagram 23.4.2 : Heated liquids expand.
1. Use two identical small flasks with one hole stoppers and tubes passing through into the liquid.
Fill the bottles with different liquids.
Put the bottles in a container of hot water.
The different rise of liquids inside the tubes shows the difference in expansion of the liquids.
2. Put some coloured water in a small bottle or flask fitted with a one hole stopper and glass tube that extends into the bottle.
Heat the bottle.
The water level initially falls as the bottle expands then rises as the liquid is warmed and expands.
Cool the bottle.
Depending on the rate of cooling the liquid will initially rise as the bottle contracts and then drop as the liquid cools and contracts.
This experiment shows the principle of the liquid in glass thermometer.
Note that the water level drops at first when you begin the heating and then it rises, because the glass starts to expand before the water inside.
If a long tube filled with red water is immersed in a boiling water bath, the level of the red water will drop before rising.
3. Use two identical small plastic bottles.
Insert a thin long glass tube into the stopper of each bottle.
Fill each bottle with different liquids, e.g. water and alcohol, or vinegar and machine oil.
Place the two bottles simultaneously into a beaker of hot water.
Observe the difference between the heights increased of liquids in the two glass tubes.
At the same temperature, the expansion of different liquids is different, the increases of their volumes are different.
4. Fill a conical flask full of coloured water and plug its mouth with a stopper with a glass tube inserted in it.
Dip the glass tube into the water so that the height of the water in the glass tube is 30 mm.
Place the flask in a large beaker.
Pour hot water on the surface of the flask.
Observe the change in height of the water column at the glass tube. Pour cold water on the surface of the flask.
Observe the change in height of the water column in the glass tube again.
23.2.3 Coefficient of expansion of liquid in flask and U-tube
1. Flask
A flask is filled with a liquid such that the upper level of liquid is in the neck of the flask and can be marked.
When the flask is heated, the xpands and the new level of liquid in the neck of the flask can be marked.
However, this difference of levels does not represent the true expansion of the liquid, because the glass in the flask has also expanded.
The apparent increase in volume of the liquid is the difference between the true increase in volume and the increase in volume of the flask.
Observe the exact position of the mercury meniscus in a mercury-in-glass thermometer.
Plunge the bulb of the thermometer into boiling water and observe the immediate drop in level of the mercury meniscus cause by the expansion of the glass.
Later, the level of the meniscus rise as heat is conducted into the mercury.
2. U-tube
Find the true coefficient of expansion of a liquid, by using the method balancing columns in a U-tube.
Put into a U-tube mercury or any other liquid that does not dissolve in the liquid to be tested.
Pour the liquid to be tested into both arms of the U-tube so that the level of mercury is the same in both arms.
Immerse both arms of the U-tube in a liquid at temperature t1 and not the height h1 of the columns above the mercury.
Immerse both arms of the U-tube in a liquid at temperature 1, higher than t1, and not the height h2 of the columns above the mercury.
23.2.4 Expansion and contraction of liquids
See diagram 23.108 : Expansion and contraction of liquids.
See diagram 4.6 : Expansion and contraction of liquids 1.
See diagram 4.7 : Expansion and contraction of liquids 2.
1. Fit a flask with a one-hole stopper and a 30 cm length of glass tubing that extends into the flask.
Add coloured water to the flask so that it extends 5 cm up the glass tubing.
Slowly heat the flask while carefully watching the level of coloured water in the glass tubing.
When you heat the flask, the water level initially falls as the glass in the flask expands then rises as the water expands.
Cool the flask under the tap.
The level of coloured water in the glass tubing first rises as the glass in the flask contracts then drops as the coloured water cools and contracts.
So the expansion of liquid you see in a thermometer is really the expansion of liquid less the expansion of the glass tube.
2. Use two identical small bottles fitted with one-hole stoppers and glass tubing passing though into the bottles.
Fill the bottles with different liquids.
Put the bottles in a container of hot water.
The different rise of liquids inside the glass tubing shows the difference in expansion of the different liquids.
3. Place some coloured water in a flask.
Insert a one-hole stopper and glass tube so that it extends downward into the fluid and upward.
Pour warm water over the flask and the coloured water rises in the tube.
Pour cold water and the coloured water drops inside the tube.
4. Use a hydrometer to measure the density of olive oil as it cools.
23.2.5 Expansion of liquid in a thermometer
Fill a flask with coloured water.
Insert a one hole stopper carrying a 30 cm length of glass tubing until the water rises 5 cm in the tubing.
Put the flask in a beaker of water.
Heat the beaker and observe the water level in the tubing.
The water rises in the tubing.
However, if you carefully observe the water level in the tubing when the heating begins, you will see that it falls slightly and then begins to rise!
It falls, because the glass in the flask starts to expand before the water inside.
When the heat energy reaches the water it expands.
So the expansion of liquid you see in a thermometer is really the expansion of liquid less the expansion of the glass tube.
23.2.6 Expansion of water and kerosene
1. Note the level of water in a vertical tube at room temperature.
Heat the water in the beaker until it is a constant 20 oC above the previous room temperature and note the level water in the tube again.
2. Repeat the experiment using kerosene instead of water.
Be careful! Kerosene is inflammable!
So heat the beaker with an electric hot plate.
Compare the expansion of kerosene with the expansion of water.
23.2.7 Freezing water expands
You can do this experiment at home.
Fill an ice cube tray exactly with water to make separate ice cubes.
Put the ice cube tray in the freezer.
The next day the level of the ice cubes is higher than the former level of the water.
So water expands when it freezes to form ice.
Take out some of the ice cubes and put them in water.
The ice cubes can float in water.
So when water changes to ice, it expands.
23.2.8 Heat one litre of water
Heat one litre of water from room temperature to 100 oC.
Before the experiment, set up a tripod, a heating mat, and place the beaker on the mat.
Design a table of results.
Hold the thermometer vertically and slowly put it into the water until the liquid bulb of the thermometer immerses into the water completely.
Do not stir water with the thermometer.
The thermometer must remain in the water while observing and should not touch the bottom or wall of the beaker.
Then read the value of the temperature of water with eyes being the same level of the liquid column.
The temperature of the water should the same as the room temperature.
Light the Bunsen burner and turn the sleeve around to get a non-luminous flame.
Slide the Bunsen burner under the beaker to heat the beaker evenly.
Keep stirring and steadily heat the water while recording the temperature every 30 seconds.
Draw a graph of variation of temperature in water with the time.
Plot temperature on the vertical axis and time on the horizontal axis.
Connect each data point to get a smooth graph.
Reach a conclusion according to the shape of the graph.
Repeat the experiment with a fan blowing slowly on the apparatus.
The temperature rises rapidly at first heating, because the rate of evaporation is slow at that temperature and loss of heat to the surroundings is slow as long
as the temperature difference between the water and room temperature is small.
As the temperature of the water rises, the rate of rise of temperature diminishes at an increasingly rapid rate.
23.2.9 Heat water in a sealed flask
See diagram 23.4.6 : Heat water in a sealed flask
1. Fill the flask of some cold water of height 1-2 cm.
Seal the mouth of the flask with a one hole rubber stopper.
Insert a straight capillary through the stopper so that the lower end of the capillary enters the water and is about 1-2 mm from the bottom of the flask.
The upper end of the capillary remains outside the flask.
Heat the coloured water in the beaker to the temperature of 80 oC more.
Place the flask into the hot water in the beaker to heat the water in the flask to 70 oC.
During heating, tightly press the mouth of the flask with your hand to seal the air in the flask.
After 2 minutes, suddenly take your hand off the mouth of the flask and observe a stream of water spurting out of the upper end of the capillary tube.
2. Place a wet coin on the upper end of the capillary tube.
It will move up and down gently to produce some vibration sound.
When you heated the air in the flask, its volume did not increase, because you sealed the flask with your hand.
So the air pressure increased and a stream of water current spurted out of the upper end of the capillary tube when you take your hand off the mouth of the flask.
23.3.1 Solid expansion
See diagram 23.4.7 : Expansion of a solid.
Expansion due to heat, thermal expansion, expansivity, coefficient of expansion
Most bodies increase their volume upon heating under normal pressure.
Solids retain their shape during temperature variations,.so distinguish between linear expansion, area expansion and volume expansion (cubic expansion).
Applications of solid expansion include shrink fitting, riveting, expansion gap, expansion roller, bimetallic strip, fire alarm, thermostat.
Put the cover on the pot before heating the pot, because the pot will expand on heating and then you cannot put the top on the pot.
Linear expansion
The length of a solid changes with temperature.
The coefficient of linear expansion, α, is the fraction by which
the length at 0 oC changes per oC change in temperature.
For example, for Aluminium, α = 23 × 10-6, but most tables just show Aluminium = 23, Copper 16.7, Iron 11.8, Glass 8.5.
If a solid at temperature t1, width length L1, expands at temperature t2 to length L2, then L2 =L1 [1 + α (t2 - t1)], OR
L = Lo (1 + α T), where α = the coefficient of linear expansion, L = final length, Lo = original length, T = change in temperature,
Surface expansion (superficial expansion, area expansion)
Similarly A2 = A1 [1 + 2 α (t2 -t1)], OR
A = Ao (1+2 α T)
α A = 1 / A × dA / dT, where A = area and dA / dT is the rate of change of that area per unit change in temperature.
Surface expansion has been likened to expansion of a photographic print.
Cubic expansion
V2 = V1 [1 + 3 α ([t2 - t1)]
The coefficient of cubic expansion for a solid, is about three times the coefficient of linear expansion.
A cube of edge 1 cm at 0 oC and volume 1 cc would become a cube of edge (1+ α ) cm at 1 oC,
so its volume would become (1 + α )3 = (1 + 3x +3x2 + α3 ) cc.
However, for solids, α is very small, so x2 and x3 are negligible, hence the formula V2 = V1 [1 + 3 α ([t2 - t1)].
23.3.2 Coefficient of thermal expansion, negative thermal expansion (NTE)
See diagram 23.107 : Bimetallic strip, compound bar, invar.
Thermal expansion
Most substance expand when heated as distances between atoms increase.
The coefficient of thermal expansion characterizes the expansion of various bodies as the degree of expansion divided by the change in temperature.
The coefficient of linear thermal expansion is the ratio of the change in length per degree K to the length at 273 K.
The coefficient of volume expansion is about three times the linear coefficient.
Negative thermal expansion
Negative thermal expansion (NTE) (not called "thermal contraction"), occurs in some substances, e.g. zirconium tungstate (ZrW2O8), zirconium,
vanadate (ZrV2O7), scandium trifluoride (ScF3), forms of silicon between 18 and 120 Kelvin, and rubber bands.
Glass-ceramic cooktops are non-porous mixtures of MgO, Al2O3, SiO2 glass with positive coefficient of thermal expansion and crystals with negative
coefficient of thermal expansion, a material that experiences no thermal shock.
Water
The coefficient of thermal expansion of water drops to zero as it is cooled to 4 oC (3.983 oC), then becomes negative.
Water has a maximum density at this temperature.
In sub-zero temperatures, the ice on the surface of a pond may have a lower temperature than the water underneath it, so fish can survive below the ice.
Tooth fillings
If tooth fillings had the same coefficient of thermal expansion as tooth they would not expand to cause toothache when drinking a very hot cup of tea.
Bimetallic strips
Materials with compensating coefficients of thermal expansion are used in bimetallic strips and invar.
23.3.3 Compensated balance wheel of a watch
See diagram 23.107 : Compensated balance wheel of a watch.
Examine the compensated balance wheel in a watch.
As the temperature rises, the radius arm of the balance wheel expands to increase the moment of inertia about the axis and increase the period.
The increasing temperature also reduces the elasticity of the hair spring to also increases the period.
To compensate for these effects, the balance wheel is made of two strips of dissimilar metals fastened together, bimetallic strips, so that the metal with
the smaller coefficient of expansion is on the inner side of the bimetallic strip.
When the temperature increases, the radius of curvature of the bimetallic strip decreases, because of the lesser increase in length of the inside strip
and P and Q are fixed, so R and S move in towards the axis, the moment of inertia of the balance wheel is lessened and the corresponding decrease in period
compensates exactly for the increase in period caused by the change in elasticity.
23.3.4 Motor vehicle flashing lights
Flashing lamp direction indicators current heats the hot wire, so it elongates and allows the armature assisted by its spring to move towards the iron core
and close the contacts.
Blinking lights on cars use a small unit containing is a bimetallic strip that heats up as current flows through it.
The strip bends and opens the circuit.
On cooling, the strip straightens and closes the circuit.
You can adjust the timing of the cycle with a screwdriver.
23.3.5 Thermal shock, borosilicate glass
Thermal shock is differential expansion where at places on a material stress expansion causes a crack to form and the structure to fail.
Thermal shock can often be avoided by changing temperature more slowly, i.e. reducing the thermal gradient, and during manufacture, reducing the
coefficient of thermal expansion, and reducing the Young's modulus.
Borosilicate glass has a coefficient of thermal expansion less than any other glass, so is used in test-tubes.
Be careful! Turn on the electricity to a light bulb.
Turn off the electric power then immediately spray water on the hot light bulb.
23.3.6 Trevelyan rocker
See diagram : Trevelyan rocker.
The Trevelyan rocker is a brass or copper bar and an extension.
The brass bar has an S-shaped cross-section so that the bottom surface has two parallel knife edges.
Heat the Trevelyan rocker and place the brass bar on a cold lead block with the end of the extension resting on the bench.
The rocker starts to vibrate due to the rapid expansion of the lead causing the rocker to tip from edge to edge and emit a musical note.
Press on the rocker with a pencil point to change the pitch of the note.
The action is related to other rockers, e.g. the "celt" or rattle back.
23.3.7 Ball and ring, ring and plug
See diagram 23.105 : Ring and plug.
See diagram 23.105A : Ball and ring.
1. The experiment demonstrates the diameter expansion of metal caused by heat.
At room temperature a ball that is slightly larger than the ring will not pass through it.
Heat the ring over the Bunsen burner.
The ball can now pass through the ring.
2. The apparatus consists of a ball and ring constructed
so that at room temperature the ball just passes through the ring.
On heating the ball in the bunsen flame, expansion is demonstrated by the ball being unable to pass through the ring.
3. The apparatus consists of a heavy metal ball that at room temperature just passes through a hole in the base plate of the support.
Expansion is demonstrated by heating the ball in the bunsen flame, whereupon the ball is unable to pass through the hole.
4. Use a large metal screw and a screw-eye through which the head of the screw just passes.
Alternatively, use a metal ball that just passes through a metal ring, or a bar that will just pass through a gauge.
Attach the screw and screw eye into the ends of a stick.
Hold the stick to heat the head of the screw in a burner flame.
Try to pass the screw through the screw eye.
The screw cannot pass, because of expansion caused by heating.
Keep the screw hot and heat the screw eye in the flame simultaneously.
Now the screw head can pass through the screw eye.
Keep the screw head in the flame and cool the screw eye in cold water.
The screw head cannot pass through the screw eye.
5. If you cannot open a glass jar with a metal screw top, hold the jar upside down so that the metal screw top is touching hot water.
The metal screw top expands more than the glass and you can open the glass jar.
23.3.8 Bar breaker, the force of contraction
1. Heat an iron bar then tighten it in a yoke so it breaks a cast iron
bar when the bar cools.
2. Bar breaker
Construct a strong iron bar so that it rests in two yokes on a cast iron base.
Pin the bar on one end by a thin cast iron pin, and thread it on the other end so that it can be tightened.
Heat the bar with the gas jets located directly beneath the bar.
Tighten the bar as it is heated.
After the bar is fully tightened, dowse it with water.
As the bar contracts the forces present are large enough to snap the cast iron pin.
There is a delay between initial cooling and fracture of up to 30 seconds.
23.3.9 Bend glass by expansion
Heat one edge of a strip of plate glass with a Bunsen burner to cause the glass to bend towards the cooler side.
23.3.10 Bimetallic strip
Bimetallic strip, compound bar, invar, thermostat
See diagram 23.107 : Bimetallic strip
Coefficient of liner expansion of brass = 19 × 10-6 K-1 at 20 oC.
Coefficient of liner expansion of invar steel = 1.2 × 10-6 K-1 at 20 oC.
"Invar" is trade name for an alloy composed of iron 63.8%, nickel 36%, carbon 0.2%.
"Invar" is abbreviation of "invariable".
It is used in surveyors' measuring tapes, pendulums, and tuning forks.
Bimetallic strips are used to switch thermostats and fire alarms on or off when a small bimetallic strip acts as a switch by bending away
from an electrical contact when heated.
1. The experiment demonstrates the unequal expansion of different metals.
Strips of dissimilar metals bonded together bend when heated.
Use a bimetallic strip with brass on one side and steel on the other side.
When this strip heated over a Bunsen burner, the strip curves toward the steel side.
When cooled in liquid nitrogen, the strip curves toward the brass side.
The bimetallic strip suffers appreciable curvature within a few seconds of being placed in the flame of the bunsen burner.
Leave the bimetallic strip in a container of liquid nitrogen.
The bimetallic strip curves towards the brass side, because the brass contracts more.
2. A pair of iron and brass strips riveted together bends when heated, because of the difference of expansion of the two metals.
The strip curves towards the steel side, because the brass expands more.
Mount a pointer on the end of a bimetallic strip.
3. Use two 25 cm strips of brass and invar steel welded together as a bimetallic strip.
Make holes in the metal strips with a nail and fix small tacks as rivets.
Fasten the strips together by cutting them with projections at equal intervals and bend the projections over to interlock.
The strip curves towards the steel side, because the brass expands more.
23.3.11 Expansion of solids when heated apparatus
See diagram 23.106 : Expansion of a solid when heated
Use a 2 m piece of stout copper tubing, A.
Put it on a table and fix one end with a clamp, B.
Underneath the other end put a bicycle spoke to act as a roller, C.
Fix a drinking straw to the roller by wax to show any movement of the rod resting on it, D.
Blow steadily down the tube between the fixed end and the middle.
This arrangement detects the expansion of the tube caused by the hot breath.
Pass steam through the tube and note the motion of the pointer.
Repeat the experiment with different types of tubing.
23.3.12 Expansion tube
See diagram 23.4.7 : Expansion of a solid.
Pass steam through an aluminium tube with a dial indicator to show the change in length.
One end of a tube rests on a needle attached to a pointer that moves as the tube is heated.
23.3.13 Expanding wire
Expanding wire, sagging wire
Heat electrically a long iron wire or nichrome wire with a small weight hanging at the midpoint and see it sag.
Pass one end of a heated wire is passed over a pulley to a weight.
The pulley has a pointer attached.
23.3.14 Expanding quartz and glass
Heat both quartz and glass tubes with a high temperature torch and plunge into water.
Heat a piece of quartz tube and quench it in water.
Try the same thing with Pyrex and soft glass.
23.3.15 Expanding solids when heated
See diagram 23.106 : Expansion of solid A = copper tubing, B = clamp, C = bicycle spoke roller, D = straw.
1. To show and compare thermal expansion of different metals.
The expansion apparatus consists of a cast iron base with two vertical supports that hold the metal expansion rod.
The pointer is zeroed by the adjusting screw illustrated and the burners lighted beneath the rod.
Use aluminium, brass, copper and mild steel expansion rods.
Expansion of the rod causes deflection of the pointer and this deflection may be compared for the different metals for the same time interval.
2. Use a 2 metre piece of stout copper tubing.
Put it on a table and fix one end by a clamp.
Underneath the other end put a bicycle spoke to act as a roller.
A drinking straw fixed to the roller by wax will show any movement of the rod resting on it.
Blow steadily down the tube between the fixed end and the middle.
This arrangement detects the expansion of the tube caused by the hot breath.
Pass steam through the tube, and note the motion of the pointer.
Repeat the experiment with different types of tubing.
3. Heat a 60 cm copper rod for five minutes with a Bunsen burner.
Note the movement of the pointer.
The rod rests on a knitting needle so when the rod moves it rolls the needle.
If the expanding rod caused the needle to do one complete turn of 360 degrees, the hot copper rod has
expanded a distance equal to the circumference of the knitting needle.
23.3.16 Expansion gauge
Commercial: Bar and gauge
See diagram 23.4.10 : Expansion gauge
Engineers use expansion gauges to check whether metal parts are no larger than a certain size.
23.3.17 Shrink fit
Heat a brass ring and slip it onto a slightly tapered steel bar.
23.3.18 Microwave ice
Put water in a plastic dish
Dry two ice cubes with a tea towel and put them in another plastic dish.
Put the plastic dishes in a microwave oven and turn on the oven for one minute.
Take out the plastic dishes then feel the temperature of the water and ice cubes.
The water feels hot.
A little ice has melted, but the ice feels cold.
The water in the ice cannot turn around, so it is difficult to defrost food in the microwave oven.