School Science Lessons
2024-09-17
(UNPh23.1)
Heat transfer, Radiation
Contents
23.8.1 Absorption of radiation
23.8.2 Black and white surfaces affect radiation
23.8.4 Colour temperature
23.8.6 Different surfaces affect heat radiation and absorption
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
23.8.23 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, Bichsel boxes
23.8.28 Melt ice blocks
23.8.29 Holes in carbon blocks
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 Black and white surfaces affect radiation
See diagram 23.8.7: Shiny cans and black cans.
1. 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.
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.
23.8.6 Different surfaces affect heat radiation and absorption
See diagram 4.36: Heat radiation and absorption.
1. 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.
2. 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.
3. Use a pair of old shoes.
Paint the left shoe black and the right shoe white.
Your left foot becomes your hot foot.
23.8.7 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.