School Science Lessons
23. Heat transfer, expansion, conduction, convection, radiation, heat and temperature
2012-01-27 SP
Please send comments to: J.Elfick@uq.edu.au
Table of content
23.0.0 Heat transfer
23.0.0 Coefficient of thermal expansion
23.7.0 Conduction of heat, thermal conductivity
23.6.0 Convection
23.8.0 Heat radiation
22.3.0 Heat transfer
23.2.0 Liquid expansion caused by heat
23.4.0 Materials at low temperature
23.3.0 Solid expansion caused by heat
23.7.0 Conduction of heat, thermal conductivity
Order online: Ice Melting Blocks
23.7.4 Boiling water in aluminium pot and stainless steel pot
4.16.0 Conduction of heat experiments, UNESCO
4.21 Conduction of heat by coin on paper
23.7.3 Conduction of heat by different metals
23.7.2 Conduction of heat by metal bar
23.7.5 Conduction of heat by metals, Davy lamp
4.22 Conduction of heat by different metals
23.7.11 Conduction of heat by wood, anisotropic conduction
23.7.12 Cook an egg on a piece of paper
23.7.6 Copper coil candle snuffer
23.7.9 Dropping wax
2.1.5 Heat insulation properties of common materials
23.7.7 Heat paper without burning
23.7.14 Hit a hardwood peg with a hammer
23.8.23 Melting blocks of ice
23.7.1 Reduce heat loss with heat insulation materials
23.7.10 Relative conductivity
23.7.8 Water is a poor conductor of heat, boil water in a balloon
4.23 Water is a poor conductor of heat, boil water in a paper cup, heat water in a paper bag
23.7.13 Wood and iron in the sun
23.6.0 Convection
23.6.0 Convection
4.24.0 Convection experiments, UNESCO
23.6.10 Barnard cell
37.13 Convection box
4.27 Convection box, convection currents in air
23.6.6 Convection box with two chimneys, smoke house
23.6.2 Convection currents between jars of water
4.30 Convection currents and ventilation
4.25 Convection currents in a container
4.24 Convection currents in a test-tube
4.29 Convection disc, heat snake, convection wheel
3.39 Convection disc, heat snake (Primary)
23.6.4 Convection disc, heat snake, revolving picture lamp
23.6.1 Convection currents in water
4.26 Convection currents from an ink bottle
23.6.8 Convection tube
23.6.3 Feel convection currents in a test-tube
23.6.5 Lava lamps, cumulus cloud, convection cells, Hadley cells, miso soup
23.6.9 Model heating system
2.2.5 Newton's law of cooling
2.2.5.1 Rate of heat transfer
4.12 Smoke moves up and down (Primary)
4.31 Temperature of water at maximum density, 4ºC
4.28 Trace convection currents
37.14 Trace convection currents
5.23 Wind speed and direction
37.2.0 Wind speed indicator, rotation anemometer
23.8.0 Heat radiation
23.8.16 Absorption of radiation
36.49 Angle of the Sun's rays on the Earth
23.8.7 Black and white surfaces affect radiation
2.8 Dull and bright in the sun (Primary)
4.35 Feel heat radiation
23.8.2 Feel radiation with your hand
4.33 Focus radiant heat waves
23.8.4 Focus radiant heat waves
23.8.3 Heat radiation decreases with distance
23.8.0 Heat transferred by radiation, black body radiation, Stefan-Boltzmann law, Wien's law, Kirchhoff's law
23.8.12 Infrared radiation using iodine in alcohol
23.8.13 Leslie's cube
37.43 Model greenhouse to simulate the "greenhouse effect"
23.8.19 Non-linear absorption of soot and flour mixes
23.8.25 Plate in a furnace
23.8.5 Reflection of radiant heat waves
23.8.9 Radiant heat lights a match
23.8.6 Radiant heat passes through glass
23.8.10 Radiant heat using parabolic reflectors and a thermopile
23.8.14 Radiation from shiny can and black can
23.8.24 Radiation through glass
23.8.17 Surface absorption
23.8.8 Surface colour and the heat absorbed
23.8.20 Surface radiation from the engine of a motor car and a motor bike
23.8.22 Tea pot experiment
4.15 Thermoscope to compare absorption of radiation
23.8.1 Thermoscope, Simple thermoscope
23.2.0 Liquid expansion caused by heat
23.2.8 Coefficient of expansion of oil
23.2.9 Coefficient of expansion of a liquid in a flask and in a U-tube
4.6 Expansion and contraction of liquids
23.2.4 Expansion of water and kerosene
23.3.01 Fluid expansion
23.4.6 Heat water in a sealed flask
6.8 Heated liquids expand (Primary)
23.2.7 Hope apparatus
23.2.1 Liquid expansion, expansion and contraction of liquids, simple thermometer
11.2.2 Maximum density of water, negative expansion coefficient of water
4.31 Temperature of water at maximum density, 4oC
23.2.5 Torricelli tube, barometer tube
23.4.0 Materials at low temperature
23.4.1 Properties of materials at low temperature, liquid helium
23.4.2 Reactions in liquid oxygen
23.3.0 Solid expansion caused by heat
23.3.0 Solid expansion
4.3 Ball and ring, plug and ring
23.3.9 Bend glass by expansion
4.5 Bimetallic strip, compound bar
23.3.8 Break the bolt, forces caused by change of length
23.3.16 Compensated balance wheel of a watch
4.4 Expansion of a solid when heated
23.3.12 Expansion tube
23.3.13 Expanding wire, sagging wire
23.3.11 Expanding quartz and glass
23.3.3 Expansion gauge
23.3.12 Expansion tube
2.21 Heat different substances (Primary)
23.3.15 Motor car flashing lights
32.5.2.6 Motor vehicle thermal circuit breaker
23.3.7 Shrink fit
3.4.1.1 Stretched rubber band
23.3.5 Thermostat
23.3.10 Trevelyan rocket
2.1.5 Heat insulation properties of common materials
See diagram 23.1.5
Use 4 big beakers and 4 small beakers. Put a small beaker into each big beaker. Put 3 kinds of heat insulators, e.g. polyester plastic, paper and shredded wood, in the space between a big beaker and a small beaker. The fourth large beaker contains a small plastic stopper and the small beaker so the beakers are separated mostly by air as a control. Pour the same volume of hot water into each small beaker. Put a thermometer in each small beaker. Record the temperature in each small beaker at one minute intervals for 10 minutes. Plot a graph of temperature against time on one sheet of graph paper for all beakers.
2.2.5 Newton's law of cooling
See diagram 23.2.5
Newton's Law of Cooling states that the rate of loss of heat from a body both by radiation and convection is proportional to the difference between the temperature of the body and the temperature of the surroundings. It applies only to small ranges in temperature. Test whether a hot cup of coffee cools faster than a warm cup of coffee. Record the room temperature, e.g. 17.5oC. Use identical coffee cups. Put the same volume of hot coffee or warm coffee in the coffee cups. Insert a thermometer and use it to keep stirring gently. Record the temperature every two minutes for twenty minutes while still stirring. In the second column, record the temperature of the cooling water every two minutes. In column D, record the difference between the temperatures every two minutes and the room temperature. Calculate F / D for each two minute interval. The mass of coffee in the coffee cup is constant so the rate of heat loss of the coffee is proportional to the fall in temperature. The rate of fall of temperature is proportional to the mean difference of temperature between the coffee and the surroundings. So the fall in temperature during time interval / mean difference in temperature between the coffee and surroundings = constant. As the temperature of the body is higher and the temperature of surroundings is lower, the difference of the two temperatures is greater, so the rate of heat loss of the body is faster.
Time in
minutes		 Temp. of coffee F = fall in temp. in the last 2 minutes Mean temp. in last 2 minutes
(to nearest 0.1oC)		 D = difference between
water temp.
and room temp.		 F / D
(constant)
0 44.7oC .
 .
 . .
2 41.4oC 3.3oC 43.1oC 25.6oC 0.13
4 38.7oC 2.9oC 40.1oC 22.6oC 0.13
6 36.1oC 2.6oC 37.4oC 19.9oC 0.13
8 33.7oC 2.4oC 34.9oC 17.4oC 0.13
2.2.5.1 Rate of heat transfer
1. Use two identical thermos flasks containing (a) 700 g water at 40oC and (b) 100 g ice + 200 g water at 0oC. Which reaches room temperature 20oC first? The loss or gain of heat is greatest when the difference in temperature between the contents of the flask and the surroundings is greatest. In thermos flask (a), the temperature difference with room temperature is continually decreasing from its original temperature difference of 20oC. In thermos flask (b) the temperature difference remains the same at 20oC when latent heat is absorbed to convert the ice to water. More than half the total heat is received when the temperature difference remains at 20oC. So (a) reaches room temperature first.
2. Add water at 90oC to tea in a teapot and and leave it to stand for 5 minutes. If you want the tea to be as cool as possible before drinking it, do you add milk immediately after pouring out the tea or just before drinking it? The rate of loss of heat depends on the temperature difference between the body and the surroundings. If the milk were added immediately after pouring the temperature of the tea would fall and the rate of loss of heat would be less than if the milk had not been added. So the milk should be added just before drinking the tea.

4.3.0 Ball and ring, plug and ring
See diagram 23.105: Ball and ring
1. Use an iron ring with a set of two balls one over size and one under size. Heat the ring and slip over both metal balls. A ball passes through a ring only when the ring is heated.
2. Use a large metal screw and a screw eye through which the head of the screw just passes. Alternatively use a metal ball which 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 due to 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. If you cannot open a 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 and you can open the jar. 3. Leave the over size ball in liquid nitrogen for ten minutes then try to pass the ring around it.
Commercial
Ball and ring
4.5.0 Bimetallic strip, compound bar
See diagram 23.107: Bimetallic strip
Coefficient of liner expansion of brass = 19 X 10-6 K-1 at 20oC.
Coefficient of liner expansion of invar steel = 1.2 X 10-6 K-1 at 20oC.
Invar" is trade name for 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.
1. Strips of dissimilar metals bonded together bend when heated. Heat a bimetallic strip of brass and steel in a Bunsen burner flame. 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.
2. Mount a pointer on the end of a bimetallic strip. Use two 25 cm strips of brass and invar steel welded together as a bimetallic strip.
3. Make holes in the metal strips with a nail and fix small tacks as rivets.
4. Fasten the strips together by cutting them with projections at equal intervals and bend the projections over to interlock.
5. Leave a brass / steel bimetallic strip in a container of liquid nitrogen. The bimetallic strip curves towards the brass side because the brass contracts more.
Commercial Bi-Metallic strip, for heat conductivity testing.
4.6.0 Expansion and contraction of liquids
See diagram 23.108 Expansion and contraction of liquids 1 | See diagram 23.109: 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.
4.21 Conduction of heat by coin on paper
Hold a piece of paper above a candle flame: it will char if brought near. Place a metal coin on the paper and repeat the experiment: the metal will conduct the heat away and leave a pattern on the paper.
4.23 Water is a poor conductor of heat, boil water in a paper cup, heat water in a paper bag
See 22.2.7.1: Heat transfer coefficient, 1 / thermal insulation
1. Use your bare fingers to hold the bottom of a test-tube containing water. Tilt the test-tube over a flame so that you can heat the water in the upper part of the test-tube. You can hold the bottom of the test-tube until the water in the upper part boils because water is a poor conductor of heat.
2. Boil water in a paper cup. Pour some water in a paper cup and hold it over a flame. The water boils without burning the paper cup. As a control, heat a paper cup not containing water or use a propane torch to burn away the top part of the cup above the water level.
3. Boil water in a paper pan. Draw two concentric squares on copy paper with sides 13 cm and 18 cm. Cut out the outer square and fold along the edges of the 13 cm square to make right angle corners. Staple the flap at each corner. Heat a sheet of metal gauze over a stove or Bunsen burner on a tripod until the metal gauze is red hot.. Fill the paper pan one third full of water. Lift each end of the paper pan and place it on the hot metal gauze. Observe steam coming from the surface of the water before it boils. Some teacher add a raw egg to the water in the pan. Water absorbs the heat without the temperature being high enough to scorch the paper because of its high heat capacity. Also, when the water turns to steam latent heat of vaporization is absorbed by the water.
4. Put small pieces of ice in the bottom of a test-tube containing water. Heat the water near the top of the test-tube with a spirit burner. The water will start to boil, yet the ice will not melt. The warmed water is already at the top, so no convection takes places, and the conduction by water is very small. Little heat transfers to the ice.
5. Put a small fish in a test-tube full of water. Tilt the test-tube and heat the top 1 cm of water. The water will boil and not harm the fish. However, this experiment upsets some students.
6. Put 120 mL of water in a rubber balloon and tie the inlet. Suspend the balloon over a lighted candle but do not let the rubber touch the hot wick. The balloon will explode after a few minutes. . Inflate another balloon with air. and suspend it over la lighted candle. This balloon explodes almost immediately. Water at has a higher specific heat capacity, about 4.2 J.g-1 K-1, than air, slightly above 1.0 J.g-1 K-1, so it can absorb more heat than air. for any degree rise in temperature.
7. Pour some water in a paper bag. Agitate the paper bag to coat the inside with water, then pour out the excess water. Put a small soft chocolate, e.g. "Chocolate Kiss", in the paper bag. Heat the paper bag over a 100 W light globe. The chocolate melts, but the paper bag does not get hot. The chocolate was melted by the radiant heat from the light globe.
4.24 Convection currents in a test-tube
See diagram 23.1.8
Fill a test-tube with cold water. When the water is still, add a very small crystal of potassium manganate (VII) and let it fall to the bottom leaving little colour trace. Hold the test-tube in the bare fingers near the top but not above water level. Heat with a very small burner or candle flame at the bottom of the tube. You can hold the warm test-tube with bare fingers. Note the movement of the coloured dye from the crystal in the convection current. Repeat but heat very gently near the top of the water surface, while holding the test-tube near the bottom.
4.25 Convection currents in a container
See diagram 23.1.8
Weigh an empty container. Fill a container exactly with cold water and weigh it again. Empty the container and fill it exactly again with the same volume of hot water and weigh it again. The same volume of hot water weighs less than cold water. When you heat water the lighter warm water displaces the heavier cold water and convection currents occur. Hot water is less dense than cold water. This is the cause of convection currents.
4.26 Convection currents from an ink bottle
See diagram 23.126: Convection currents from an ink bottle
Use a small ink bottle, fitted with a two-holes stopper. Cut two pieces of glass tubing. One piece should extend from the stopper almost to the bottom of the bottle. The other piece should extend 5 cm up from the stopper. Fill a large container with cold water. Fill the small bottle with hot coloured water. Put the small bottle in the bottom of the large container while holding the fingers over the ends of the tubing. The hot coloured water rises in the large container as the cold water enters the bottle.
4.27 Convection currents in air, convection box
See diagram 23.2.6: Convection box
To make a convection box, cut away one side of a box and replace it with glass. Cut two holes 2 cm diameter and 10 cm apart in the top of the box. Attach two tubes above the holes to be chimneys. Put a candle in the box under one chimney. Light the candle. Hold the smoking paper above each chimney. See the convection currents through the glass side of the box.
4.29 Convection disc, heat snake, convection wheel
See diagram 23.127: Convection disc, heat snake
1. Use a disc of thin tin from the end of a cylindrical metal can. Cut four blades all round the disc and pivot it on a bent knitting needle. Hold the disc above a candle flame, and it will revolve rapidly. A paper spiral supported on a knitting needle will revolve in a similar way.
1. Use a disc of tin cut from the top of a metal can. Make four radial cuts and bend the tin to form four propeller blades. Balance the disc on the end of a bent wire. Hold the disc above a candle flame. The disc revolves as rising air hits the blades.
2. Make a more sensitive convection wheel from the metal foil top of a milk bottle.
3. Cut paper into a spiral. The centre of the spiral is like the head of a snake. Support the head of the snake on a wire over a candle. The heat snake turns around the candle.
4. Look at an object on the other side of a hot engine or a hot road. The object will appear distorted because the refractive indexes of warm and cold air are different. This is one cause of mirages in the desert.
4.30 Convection currents and ventilation
See diagram 23.128: Convection current ventilation
Use a box with grooves for a lid and cut a glass window that slides in the grooves to make an airtight fit. Bore four holes in each end. Each end represents a window. The top holes of each side are the top halves of each window. Put four candles in the box, light them and close the sliding glass. To study the best conditions for ventilation, put solid corks in the openings, close completely both windows, and note the candles.
Try the following different combinations of opening:
1. one window open at the top and bottom, i.e. all four holes in one side open,
2. one window open at the top and the other at the bottom,
3. both windows open at the top, one window open at the bottom,
4. both windows open at the bottom, one window open at the top. Find which window openings provide the best ventilation.
4.31 Temperature of water at maximum density, 4oC
1. Fill a bottle with water and put the top on securely. Wrap the bottle in a cloth, to prevent the shattered glass from falling. Put the bottle into the freezing compartment of a refrigerator. After 24 hours, remove the bottle and examine it. The bottle may be cracked because of pressure from the expanding ice.
2. Put a large piece of ice into a glass of water. Arrange two thermometers so that they measure the temperatures near the top and the bottom of the water. The water cooled by the ice falls to the bottom. This fall continues until the water at the bottom of the glass reaches a temperature of 4oC. The water stays at this temperature for a long time, the colder water remaining higher up near the ice. So water at 4oC is denser than the water at 0oC, so a pond freezes from the surface downwards while the bottom seldom falls below 4oC.
3. To study the expansion of freezing water, use two identical drinking cups. Fill the first cup with tap water at room temperature so that the water heaps up to form a meniscus. Put the second cup in the freezing compartment of the refrigerator then add extra water to the cup to get the highest possible meniscus. When the water in the cup is frozen, compare the meniscus of the frozen water with the meniscus at room temperature. The frozen water heaped up because it had expanded. Water has a maximum density at 4oC. When water cools from room temperature to 4oC, it contracts in volume. When water cools from 4oC to 0oC, it expands in volume. At 4oC the density of water is 1000 kg m-3 (1 g per cc). At 0oC the density of water is 999.87 kg m-3 and the density of ice is 918 kg m-3, so ice floats on water.
4.33 Focus radiant heat waves
Use a magnifying glass to focus the rays of the sun on a piece of paper tissue. The paper chars and catches fire. Repeat the experiment with paper tissue soaked in black ink. The black paper catches fire sooner than the white paper. Repeat by focussing 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 spot is smallest and brightest. This distance is the focal length of the lens. Notice the distance when the spot feels hottest. The two distances are different.
4.35 Feel heat radiation
1. 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.
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.
23.0.0 Coefficient of thermal expansion
The coefficient of thermal expansion characterizes the expansion of various bodies as the degree of expansion divided by the change in temperature. Most substance expand when heated as distances between atoms increase. However, the coefficient of thermal expansion of water drops to zero as it is cooled to 4 °C
23.2.1 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 though 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.
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.
23.2.4 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 20oC 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.
23.2.5 Torricelli tube
Immerse a long tube filled with red water in a boiling water bath. The fluid will drop before rising.
23.2.7 Hope apparatus
Hope's apparatus is a glass cylinder with a copper trough fitted around the middle of the cylinder. Stand the cylinder vertically, fill it with water and put an ice water freezing mixture in the trough. You can insert thermometers through holes in the top and bottom of the cylinder or put a small thermometer in the bottom of the cylinder. Leave to stand until the more dense water collects at the bottom of the cylinder at a temperature of 4oC, while ice form on the surface of the water in the cylinder. A tall cylinder of water with a collar of salt / ice around the middle will freeze at the top and remain at 4oC at the bottom. In a jar of water 35 cm high with 15 cm of ice floating on top, the temperature at the bottom does not fall below 4oC.
23.2.8 Coefficient of expansion of oil
Use a hydrometer to measure the density of olive oil as it cools.
23.2.9 Coefficient of expansion of a liquid in a flask and in a U-tube
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 liquid expands 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.
U-tube
Find the true coefficient of expansion of a liquid, β, 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.
h1ρ1g = h2ρ2g
ρ2 / ρ1 = h1 / h2
ρ2 = ρ1/ (1 + β t)
so 1/(1+ β t) = h1 /h2, (where t = t2-t1)
23.3.0 Solid expansion
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 you 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
Linear expansion
The length of a solid changes with temperature. The fraction by which the length at 0oC to changes per oC is called the coefficient of linear expansion, α. For example for Aluminium, α = 23 X 10-6 but most tables just show Aluminium = 23, Copper 16.7, Iron 11.8, Glass 8.5. If a solid at temperature t1 has length L1 has expanded 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.
Surface expansion (superficial expansion, area expansion)
Similarly A2 = A1 [1 + 2α (t2 -t1)] or A = Ao (1+2α∆T)
αA = 1 / A X 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
and V2 = V1 [1 + 3α ([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 0oC and volume 1 cc would become a cube of edge (1+α) cm at 1oC, 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 + 3α ([t2 - t1)]}
23.3.01 Fluid expansion
All of the above formula are applicable only if α has a small value and do not apply to substances whereα changes with temperature.
When a volume change with temperature occurs, the fraction by which the volume at 0oC changes per oC is called the coefficient of volume change, e.g. mercury = 180 X 10-6, air = 3400 X 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 0oC it contracts rather than expands. At 4oC, water occupies its smallest volume, i.e. it has the highest density. Water obeys the general laws of thermal expansion except in the temperature interval from 0oC to 4oC. The cubic expansion formula does not apply to expansion of gases because all gases expand by 1/273 of their volume at 0oC as in Charles' law. So for expansion of gases you must use Charles' law - 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.
23.3.1 Expanding solid when heated
See diagram 23.106: Expansion of solid
A = copper tubing, B = clamp, C = bicycle spoke roller, D = straw
1. 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.
2. 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.
23.3.3 Expansion gauge
See diagram 23.4.10: Expansion gauge
Engineers use expansion gauges to check whether metal parts are no larger than a certain size.
23.3.5 Thermostat
A small bimetallic strip acts as a switch in a thermostat. Bimetallic strip bends away from an electrical contact when heated to turn off a light.
23.3.7 Shrink fit
Heat a brass ring and slip it onto a slightly tapered steel bar.
23.3.8 Break the bolt, forces caused by change of length
Heat an iron bar then tighten it in a yoke so it breaks a cast iron bar when the bar cools.
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 Trevelyan rocker
The Trevelyan rocker is a brass or copper bar and an extension. The brass bar has an S-shape cross-section so that the bottom surface has two parallel knife edges. Heat the 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.
23.3.11 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.
23.3.12 Expansion tube
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, sagging wire
Heat a length of nichrome wire electrically and watch it sag. 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.
23.3.15 Motor car flashing lights
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.
23.3.16 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.
23.4.1 Properties of materials at low temperature
Ethyl alcohol becomes very viscous at liquid nitrogen temperatures.
23.4.2 Reactions in liquid oxygen
Drop a piece of potassium cooled in liquid oxygen into water.
23.4.6 Heat water in a sealed flask
See diagram 23.4.6
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 80oC more. Place the flask into the hot water in the beaker to heat the water in the flask to 70oC. 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.
23.6.0 Convection
Convection is movement of heat energy through a liquid or gas that involves the flow of the medium itself. Convection is caused by the expansion of the medium as its temperature rises; the expanded material being less dense, rises above colder and denser material. Smoke from a fire rises because the air above the fire is heated, expands, and therefore becomes lighter than the surrounding air, and hence is pushed up, carrying with it the particles of carbon which constitute the smoke. Ice wrapped in a blanket melts slowly because the blanket is a bad conductor of heat so little heat is conducted to the ice from the surroundings. Also, the blanket prevents the outside air from coming into contact with the ice so little heat is conveyed to the ice by convection.
23.6.1 Convection currents in water
See diagram 23.2.1a
1. Use two small plastic bottles. Fill one bottle with cold coloured water and fill the other bottle with hot coloured water. Completely cover the mouths of the bottles with plastic film or cling film, then fasten the plastic film under the mouths of the bottles with elastic. Stand upright each plastic bottle in a large beaker. Put tap water in each beaker to cover the plastic bottles standing in them completely. Use a long straight wire or spike to make a hole in each film covering the mouths of the plastic bottles. Observe the movement of coloured water in each beaker.
2. Use two 200 mL beakers. Place one beaker on each pan of an adjusted beam balance. Readjust the balance accurately to balance the two empty beakers. Put 200 mL of tap water in one beaker and put 200 mL of hot water at 90oC in the other beaker. Observe whether the beakers still balance.
3. Use a large beaker full of tap water on a tripod stand. Drop a few large crystals of potassium permanganate, potassium manganate (VII), from above the centre of the beaker. Heat the beaker with a spirit burner placed under the centre of the beaker. Observe the movement of the purple water.
4. Fill a big pot with icy water. Put a few heavy objects in a small jar, e.g. glass marbles, lead sinkers, steel washers. Pour hot water and a dye, e.g. black ink, into the small jar. Drop the small jar into the big pot of cold water. Observe the "undersea volcano" when the warm water from the small jar mixes with the hot water in the big pot to form convection currents.
23.6.2 Convection currents between jars of water
See diagram 23.2.2
Use four similar wide mouth jars with screw-on lids. Fill jar 1 with tap water and jar 2 with hot water, 90oC. Add the same number of drops of red ink to each jar. Close the jars and turn them upside down repeatedly to make the red colour even. Stand the jars on the bench. Fill jar 3 with tap water and jar 4 with hot water, 90oC. Cover the mouths of jar 3 and jar 4 with a card. With your first two fingers pressing on the card, turn each bottle upside down to be ready to place them over the jars on the bench. Put jar 3 over jar 2 and put jar 4 over jar 1. Remove the cards between the jars and observe any change in colour of the water. The less dense hot coloured water in jar 2 mixes with the more dense cold water in jar 3. The more dense cold coloured water in jar 1 does not mix with the less dense hot water in jar 4.
23.6.3 Feel convection currents in a test-tube
1. Fill a test-tube with cold water. When the water is still, add a very small crystal of potassium manganate (VII) and let it fall to the bottom leaving little colour trace. Hold the test-tube in the bare fingers near the top but not above water level. Heat with a very small burner or candle flame at the bottom of the tube while holding the warm test-tube with bare fingers. Observe the movement of the coloured dye from the crystal in the convection current.
2. Repeat the experiment but heat very gently near the top of the water surface, while holding the test-tube near the bottom.
23.6.4 Convection disc, heat snake, revolving picture lamp
See diagram 23.2.7: Convection currents in air
1. To make a convection wheel, use a disc from the end of a cylindrical tin can. Make four radial cut and bend the tin to form four propeller blades. Cut four blades all round the disc and pivot it on a bent knitting needle. Hold the disc above a candle flame. The disc revolves as rising air hits the blades. A paper spiral supported on a knitting needle will revolve in a similar way.
2. Make a more sensitive convection wheel from the metal foil top of a milk bottle. Cut the foil into a spiral so that the centre of the spiral is like the head of a snake. Support the head of the snake on a wire over a candle. The "heat snake" turns.
3. Look at an object on the other side of a hot engine or a hot road. The object will appear distorted because the refractive indexes of warm and cold air are different. This is one cause of mirages in the desert.
4. Stand a short candle in a flat dish of water. Light the candle. Lower a cylinder of glass or plastic until it stands on the dish and surrounds the candle. The candle flame trembles, becomes weaker and goes out. The candle is extinguished by the carbon dioxide product of its own burning. Repeat the experiment so that when the candle flame starts to tremble you lower a long strip of metal or plastic into the cylinder to nearly touch the candle and divide the cylinder into almost two equal parts. The candle flame becomes strong again because air rising up one side of the divider is replaced by fresh air from the outside.
5. Hang a T-shape piece of cardboard from the rim of a large jar to reach half way down the jar. Lower a lighted candle down one side of the jar. Use smoking paper to find the convection currents in the jar.
6. Use smoking paper to trace the air currents, e.g. around a candle, in a room heated with a stove, at different levels above the floor with windows open at the top and open at the bottom, in a doorway between a warm and cold room.
7. Another way of showing air current is by making use of the difference in refractive indexes of warm and cold air. A car bulb without a reflector will cast "shadows" of convection current from an electric heater.
23.6.5 Lava lamps, cumulus cloud, convection cells, Hadley cells, miso soup
A lava lamp contains coloured water, phenylamine or oil or wax slightly less dense than water and an incandescent light bulb surrounded by the oil at the bottom of the container. When the switch is turned on the incandescent lamp becomes hot, heats the oil at the bottom of the lamp so that it becomes less dense and rises through the coloured water. Near the top of the lamp the rising oil cools, becomes more dense and sinks down towards the incandescent bulb. So what you see is a convection current of oil in water. Similarly, damp ground heated by the sun warms the air above it that expands, becomes less dense and rises as a thermal, carrying water vapour with it to form cumulus cloud.
The photosphere, shining surface, of the Sun consists of regions of hot larva that rise to the surface, cool, and drop back into the interior again. Similarly, Hadley cells in the atmosphere occur where air warms and rises near the equator and descend towards the poles.
1. Put water coloured with a vegetable dye in a tall beaker. Add vegetable oil and baby oil. Put the beaker on a low heat source. Note the time taken by globs of oil to reach the surface and return to the bottom of the beaker. Not the time taken again after increasing the heat from the heat source.
2. Heat water in a large boiler heated by a ring of gas jets. Note the convection cells in the water above the gas jets.
3. Observe convection cells in heated soup containing small particles, especially the Japanese miso soup.
4. Sometimes round stones come to the surface of loose soil and this may be caused by a type of convection cell in the soil.
23.6.6 Convection box with two chimneys, smoke house
See diagram 23.2.6: Convection box
1. A candle burns under one chimney in a two chimney convection box the use smoke to show convection in the two chimneys. Use a box with a lid and glass wall. Make 2 holes in the lid of the box to allow you to insert 2 cardboard cylinders A and B for chimneys. Cut two thin pieces of thin paper and paste one piece on the top edge of cylinder B and the other piece on the lower edge of cylinder B. Let both pieces of paper hang down. Place a small birthday cake candle directly under the chimney A inside the box. Light the candle and close the lid of the box. Observe the direction of the moving pieces of paper on chimney B to show the direction of the flowing air inside the box.
2. Light a wad of newspaper then stamp out the flame to make smoke. Hold the smoking newspaper above the chimney A then above chimney B and observe the movement of smoke. The smoke moves up from over chimney A and down from over chimney B.
23.6.8 Convection tube
See diagram 23.29: Convection tube
Fill a square tube with water. Place a lighted Bunsen burner under one side. Use a dropper to drop ink into the top hole. The ink moves in the direction of the water flow. Move the Bunsen burner to the other side to reverse the water flow.
23.6.9 Model heating system
See diagram 23.29
Heat water in a loop of glass tubing. Use a model of a heating system with an expansion chamber and radiator.
23.6.10 Barnard cell
Paraffin with aluminium dust is heated in a small brass dish until convection cells are formed.
23.7.0 Conduction of heat, thermal conductivity
The process of transformation of energy from one object to another is caused by heat motion of molecules and atoms and is called heat transfer. Heat transfers from an object or a part of it in higher temperature to an object or a part of it in lower temperature. When the temperatures of the two objects are equal, they are in a state of heat equilibrium. Heat transfer can occur in solids, liquids and gases.
23.7.1 Reduce heat loss with heat insulation materials
Use identical cans of water, one wrapped with insulation. Do NOT use asbestos or any product containing asbestos.
1. Use four large tin cans of equal size and four smaller tin cans of equal size. Inside the first large can put a small can on two corks in a large can as the control. Select types of insulating material, e.g. sawdust, cork pieces, newspaper, plastic. Put a small can inside each large can. Pack one type of insulating material under and around each of the smaller cans. Put a cardboard cover on each large can. Make a hole in each cover for a thermometer. Fill each small can to the same depth with water that is nearly boiling. Record the initial temperature of the water in each can. Record the temperature of the water in each can at five minute intervals. Draw cooling curve graphs by plotting temperature against time for each tin can. Note which material is the best insulator.
Material Initial temp. Temp. after
5 minutes		 Temp. after
10 minutes		 Temp. after
15 minutes		 Temp. after
20 minutes
control (air) .
 .
 .
 .
 .
sawdust .
 .
 .
 .
 .
cork .
 .
 .
 .
 .
newspaper .
 .
 .
 .
 .
plastic .
 .
 .
 .
 .
2. Be careful! To avoid scalding, prepare a sponge to absorb overflowing water. Use 5 plastic fruit juice bottles. Punch a hole in each lid to insert a thermometer through it. Select a heat insulation material, e.g. paper, cloth, plastic cloth, sponge. Cut the materials into a shape that you can wrap around the bottles. Pour hot water into the bottles, close the lids tightly, and insert the thermometers. Wrap bottles with three layers of heat insulation materials and attach the outer layers with adhesive tape. Record the temperature in each bottle in equal time intervals. Draw a temperature / time graph. The horizontal axis is for time. The vertical axis is for temperature of water.
23.7.2 Conduction of heat by metal bar
See diagram 23.1.2: Heat conduction of different metals
1. Use a bar of copper, brass or aluminium at least 30 cm long. Place blobs of melted paraffin wax at 3 cm intervals. While the paraffin blobs are still soft, push the pointed ends of nails or tacks into them. Heat one end of the box with a flame. Note the evidence that heat moves along the bar by conduction.
2. Use lengths of metal bars with the same lengths and diameters. The metals should have big differences in heat conduction coefficient, e.g. lead, iron, aluminium and copper. Remove the bottom of a metal can and cut out three legs. Punch several holes in the wall of the can and insert the metal bars so that they are all in contact at the centre of the can. Attach pins to the ends of the metal bars with paraffin wax. Place a spirit burner below the apparatus to heat the bars evenly. Observe the dropping of the pins.
23.7.3 Conduction of heat by different metals
See diagram 23.1.4: Conduction of heat by different metals
1. Use an iron rod, copper rod and glass rod that are the same length and diameter. Hold one end of each rod with the other end over a Bunsen burner flame.
2. Repeat the experiment with rods of different diameters. The bar that feels hot first shows the fastest rate of heat conduction.
3. Prepare metal wires with the same diameter, e.g. copper, iron and aluminium. Cut the wires the same length and twist them together but keep one end open. Put the open end of the wires into melted wax liquid, and take out to let the wax harden and form a wax drop at the end of the wires. Heat the other end of the wires over a Bunsen burner. Rotate the wires as you heat to heat each wire evenly. Note which wax drop at the end of a wire melts first.
4. Hold a wire coat hanger horizontally over a flame with your fingers, a small distance from directly above the flame. Soon the wire becomes too hot to hold. Move your fingers back but keep the coat hanger in the same position. Feel heat moving along the wire.
5. Use identical lengths of different metal bars, e.g. copper, brass, aluminium. Try to use rods of the same diameter. Put blobs of melted candle wax at intervals along the bars. Push small nails or metal pieces into the wax while the wax blobs are still soft. Heat one end of the bars. The blobs of wax melt and the nails fall down as heat moves along the bars. The metals do not conduct heat equally.
23.7.4 Boiling water in aluminium pot and stainless steel pot
Use similar sizes of aluminium pot and a stainless steel pot. Add the same volume of water. Heat the two pots simultaneously. Note the time to boiling in each pot. As stainless steel is a good conductor of heat, the temperature in the part of bottom and wall of pot not touching the flame is almost the same as the part that is directly heated. This allows convection of heated water to occur in many small regions so you can see steam bubbles in the whole surface of water, evenly distributed and similar in size. However, in the aluminium pot, you see only a raised boiling liquid column in the centre of an area on the surface of water just above to the bottom of pot heated by flame. In the aluminium pot, the small bottom of pot heated absorbs the heat of vaporization mainly and convection currents starting from this small area extend to all the liquid in the pot. Before the violent boiling appears, the original vaporization happens in a circle that the surface touches with the wall of the stainless steel, so you can see many small steam bubbles. This is because in such place the temperature is higher and the pressure inside the liquid is less.
23.7.5 Conduction of heat by metals, Davy lamp
See diagram 23.119: Davy lamp
1. Hold a sieve or a piece of metal gauze, e.g. 1 mm iron gauze or metal fly wire screen, over the flame of a small candle. (Some fly wire screens consist of fibreglass or plastic so do not use this type of screen!) As you lower the wire gauze on the flame, the flame becomes smaller because the wire conducts the heat away from the flame so the temperature is lowered. Also, as you lower the wire gauze on the flame, the flame does not go through the wire netting because heat is conducted away from the flame by the wires. Sir Humphry Davy in 1816 used this observation to invent the miners' safety lamp that has metal gauze around the flame in the lamp to conduct away the heat so that the flame is not hot enough to ignite explosive gas in the coal mine.
2. Put a spirit burner under a tripod stand and cover the stand with 1 mm iron gauze. Turn on the gas and ignite it above the metal gauze. The gas burns only above the wire gauze screen because the wire gauze conducts away the heat and prevents the gas below the gauze from reaching ignition temperature.
3. Hold a piece of paper above a candle flame. The paper chars. Put a metal coin or a key on the paper and hold it over the candle flame. The metal conducts the heat away from the paper and leaves a pattern where the metal touches the paper.
4. Every substance has own ignition temperature, i.e. the temperature to which you must heat it before it will burn in air. Hold wire netting or a wire sieve above a lighted candle. Move the wire netting downwards and observe any change of the candlelight. The candle flame becomes dim because wire netting transfers the heat energy from the candle. The candle flame not only becomes small but also is hindered crossing through the wire netting.
5. Be careful not to turn on the gas for too long time! Place a Bunsen burner under a tripod covered with wire netting.
6. Turn on the gas then try to light the gas above and below the wire netting with a lighted match. Only the gas above the wire netting can be lit because conduction of heat energy makes the gas under the wire netting unable to reach ignition temperature. In a model Davy lamp, a candle enclosed in a cylinder of wire gauze does not light a jet of gas played on it from a rubber tube. Use a block of wood or Plasticine (modelling clay) as a base. Be Careful! Do not leave the gas jet turned on for extended periods. Disperse the released gas by ventilating the room. Remember to turn off the gas!
7. Place a candle on a board and light the candle. Place wire netting in the shape of a column above the candle. Prepare a rubber tube to lead to a combustible gas. Place the nozzle of the gas on top of the wire netting then turn on the gas so that the gas flows on the top of the wire netting. The gas does not burn because the high conductivity of metal makes the temperature outside the wire netting not reach the ignition temperature of the gas.
8. A Bunsen burner will burn on top and bottom of two copper screens a few cm apart. A Bunsen burner flame will not strike through to the other side of fine copper wire gauze.
9. Heat platinum wire in a flask until it glows dull red then evacuate the flask and the wire will glow more brightly at the same voltage.
10. With your fingers hold a wire coat hanger horizontally over a flame a small distance from directly above the flame. Soon the wire becomes too hot to hold. Move your fingers back but keep the coat hanger in the same position. Feel heat moving along the wire.
11. Use identical lengths of different metal bars or rods with the same diameter, e.g. copper, brass, aluminium, iron. Put blobs of melted candle wax at the same intervals along the bars. Push small nails or metal pieces into the wax while the wax blobs are still soft. Heat one end of each metal bar. The blobs of wax melt and the nails fall down as heat moves along the bar. The metals do not conduct heat equally.
12. Put an unlit burner under a tripod stand and cover it with 1 mm iron gauze. Turn on the gas and ignite it above the metal gauze. The gas burns only above the wire gauze screen because it conducts away the heat and prevents the gas below it from reaching ignition temperature.
13. Hold a piece of paper above a candle flame. The paper chars. Put a metal coin or a key on the paper and hold it over the candle flame. The metal conducts the heat away from the paper and leaves a pattern where the metal touches the paper.
23.7.6 Copper coil candle snuffer
See diagram 4.20: Copper coil snuffer
The ignition temperature of a gas is the temperature at which total heat lost from conduction, convection and radiation is less than the heat produced by the combustion of the gas. To show that metal is a good heat conductor of heat energy and that a certain temperature is a necessary conditions for burning, make a screw coil by rolling with thick copper wire or brass netting.
1. Light a small candle. Hold the coil high above the candle flame and slowly move it down towards the flame. Observe the change in candle light. The candle light will reduce gradually then go out not because of absence of oxygen but because the wire transfers away the heat energy around the candle quickly the temperature around the candle is lower than the ignition temperature. If the candle flame is too big, it may produce enough heat energy to compensate for the heat energy transferred by the wires so that the flame will not go out. Note that the flame will not go out if you heat wire netting to a higher temperature so that its ability to transfer heat energy is lower.
2. Place a coil of heavy copper or aluminium wire over the flame of a candle. The flame goes out. You can snuff out a candle flame by depriving it of oxygen but here the oxygen can easily get to the flame. The fire goes out because the coil of heavy wire conducts the heat away from the flame so fast that the temperature is lowered below the ignition temperature. This shows that copper and aluminium are good conductors of heat. If the flame is too large, it will produce heat energy too rapidly to be carried away by the coil. If the coil is already hot before the experiment, the temperature of the flame may not be lowered enough to extinguish the flame.
23.7.7 Heat paper without burning
Coin on paper conducts heat, paper which cannot be lighted
See diagram 23.1.7
1. Place a coin on piece of paper and hold it high above a burning candle. Lower the paper and coin towards the candle flame. The paper in contact with the coin will not be burnt because the metal in the coin conducts away the heat. The paper not in contact with the coin will be burnt and leave a shape of the coin formed by the trace of burning. Stretch the paper level to contact keep good contact between paper and coin. Repeat the experiment with the same paper with no coin on it. All the paper will be burnt.
2. Wrap soft thread around a long screw. Leave a small length of thread hanging down. Set light to the end of the thread hanging down. The flame goes out at the place of contact with the screw because metal in the screw conducts away heat so the thread cannot reach the temperature needed for burning (ignition temperature). Repeat the experiment with a piece of wood roughly in the shape of the screw. The thread burns completely because wood cannot conduct heat away from the place of burning.
23.7.8 Water is a poor conductor of heat, boil water in a balloon
See diagram 23.1.8 .
1. Boil water in the top of a test-tube while ice is held at the bottom. Put small pieces of ice in the bottom of a test-tube containing water. Heat the water near the top of the test-tube using a spirit burner. The water will start to boil, yet the ice will not melt. The warmed water is already at the top, so no convection takes places, and the conduction by water is very small. Little heat transfers to the ice.
2. Boil water in a balloon. Make a tripod big enough to suspend a balloon full of water over a burning candle. Put aluminium foil on the table. Put the tripod on the foil for safety. Attach the balloon full of water so that the bottom of the balloon will just touch the candle flame.
3. Boil water in a paper cup. Use several disposable paper cups or make a square paper cup as in the diagram. Heat a paper cup with a spirit burner and the paper cup burns out instantly. Put two metallic rods over an iron heating stand. Put a paper cup containing water on the two metallic rods and heat with the spirit burner. The water boils without the cup catching on fire. You can try the experiment with a plastic cup but different plastics have different melting temperatures.
4. Fill a children's balloon with water, suspend a thermometer in the balloon and suspend the balloon over a burner. Observer the increased temperature of the water without damage to the balloon..
23.7.9 Dropping wax
See diagram 23.1.4
Waxed balls drop off different metal rods connected to a heat source as the heat is conducted along the metal rods. Dip metal rods in wax then watch as the wax melts off.
23.7.10 Relative conductivity
See diagram 23.1.7
Put matches on hot plates of different metals over burners. Use match head ignition when heating bars of metals attached to a common copper block. Hold one end of stainless steel, iron and aluminium rods in a Bunsen burner flame.
23.7.11 Conduction of heat by wood, anisotropic conduction
Conductivity is greater along the grain in wood so heat the centre of a thin board covered with a layer of paraffin and watch the melting pattern.
23.7.12 Cook an egg on a piece of paper
Cooking food keeps the temperature of the surface of the cooking vessel to the temperature of boiling water, 100oC. You will need a small camping gas stove, an A4 sized piece of clean white paper, a little cooking oil, an old metal coat hanger, a few large paper clips, a metal spatula and an egg.
Make a square paper frying pan from a wire coat hanger with a paper dish fixed with paper clips. Put drops of cooking oil on the paper to prevent the egg sticking to it. Break an egg into the paper frying pan then hold it above a burner so that the paper above the flame is covered by egg. The egg white and yolk contain water that turn into steam at 100oC that remains at that temperature. The paper may char around the edges of the egg.
23.7.13 Wood and iron in the sun
An object made of iron  may feel colder than an object made of wood at the same temperature even if both objects have been in the sunlight and the iron object appears hotter. Iron is a good conductor of heat, so when the finger touches the iron, heat is transferred from the body to the iron, and is distributed over the whole of the piece of iron, so there is only a very slight rise in the temperature of the iron, and it seems cold. Wood is a bad conductor of heat so when it is touched heat is transferred from the body to the wood, but the heat is concentrated in the touched region. The temperature in that touched region rises and the wood appears comparatively warm. However, heat has not spread throughout the bad conduction object made of wood so the other fingers may feel the wood to be cooler than the iron. If the iron and wood are placed in the sun so that the same amount of radiant energy falls on both of them, the iron may become hotter than the wood because the specific heat of the iron is much less than that of the wood so it is a better absorber of heat.
23.7.14 Hit a hardwood peg with a hammer
The face of the hammer feels hot but soon cools but the top of the hardwood peg still feels warm. Some of the work done by the hitter is turned into heat energy, parts going to the wood  and part to the iron. The wood is a bad conductor of heat so that most of the heat is localized in the top of the peg, so the temperature of the peg rises.
23.8.0 Heat transferred by radiation, black body radiation, Stefan-Boltzmann law, Wien's law, Kirchhoff's law
The Stefan-Boltzmann law (Joseph Stefan 1835 - 1893, Ludwig Boltzmann 1844 -1906) states that the total energy radiated from a black body is proportional to the fourth power of the temperature of the body. 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, i.e. 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, where constant 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 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 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, red hot.
Kirchhoff's law of radiation (Gustav Kirchhoff 1824 - 1887) refers to the observation that black clothes are good absorbers of heat and good emitters of heat, but 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.
2. 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. You will still feel the radiated warmth. Electromagnetic waves can transfer heat energy. Most of these waves have wavelengths slightly longer than visible light and you call them infrared waves or thermal radiation. An object may emit thermal radiation and absorb it simultaneously. Dull black surfaces emit more thermal radiation than shiny metallic or white surfaces and dull black surfaces are better than shiny or white surfaces at absorbing thermal radiation.
3. 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.
23.8.1 Thermoscope, simple thermoscope
See diagram 23.116: Thermoscope
1. 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.
2. You should 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.
3. 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.
4. Paint two thermoscopes, one thermoscope white the other black and illuminate both by a lamp.
5. Put a Leslie cube with opposite faces blackened between two bulbs of a differential thermoscope.
23.8.2 Feel radiation with your hand
Hold the palm of your hand very close to, but not touching, your cheek. You can feel the radiation from your hand. Heat travels by radiation almost instantaneously. Hold your hand under an unlighted electric bulb, the palm upward. Turn on the electricity. You can feel the heat when you turn on the 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 wavelength 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. You can still feel the radiated warmth.
23.8.3 Heat radiation decreases with distance, radiation shadow, radiation to and from the earth, clear cold night
See diagram 23.3.3: Radiation at 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. 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.
23.8.4 Focus radiant heat waves
See diagram 23.3.7
1. Hold a magnifying glass lens in the sun and focus the rays to a point on a wad of tissue paper. Observe that the tissue paper catches fire from the focussed heat rays. Try the effect of using tissue paper
blackened with Indian ink or soot. Does it catch fire more readily?
2. Use a magnifying glass or reading glasses to focus the rays of the sun on a piece of paper tissue. The paper chars and ignites. Repeat with paper tissue soaked in black ink. The black paper ignites sooner than the white paper.
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.
23.8.5 Reflection of radiant heat waves
See diagram 23.3.7
1. Heat tissue paper with a magnifying glass. Note the distance from the reading glass to the tissue paper. Place a tilted mirror about half way between the lens and the paper. Feel about with your hand above the mirror until you find the point where the heat waves are focussed. Hold a bit of crumpled tissue paper at this point with forceps and see if it will catch fire, ignite.
23.8.6 Radiant heat passes through glass
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.
23.8.7 Black and white surfaces affect radiation
See diagram 23.3.6: Different surfaces
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 a two blobs of petroleum jelly on opposite sides of the outside of the can, 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. Use a pair of old shoes. Paint the left shoe black and the right shoe white. Your left foot becomes your hot foot.
23.8.8 Surface colour and the heat absorbed
See diagram 23.3.6: Shiny and black surfaces
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.
23.8.9 Radiant heat lights a match by using a parabolic reflector
See 2.0.5: Conic sections, parabola | See 2.0.6: Parabola equation
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.
23.8.10 Radiant heat using parabolic reflectors and a thermopile
See diagram 23.3.3
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 the at focus of a parabolic mirror detects radiation differences from different coloured beakers of water.
23.8.12 Infrared radiation using iodine in alcohol
Iodine dissolved in alcohol gives a filter transmitting in the IR but absorbing in the visible.
23.8.13 Leslie's cube
A Leslie's cube shows that surfaces at the same temperature radiate do not radiate equally. The cube has three different surface areas, black, white and two are smooth brass, or one grey and one silvered.
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 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.
23.8.14 Radiation from shiny can and black can
See diagram 23.3.6
Measure the cooling rates of shiny unpainted black painted and white painted cans. Shiny and flat black cans filled with cool water warm up cool off when filled with boiling water two can radiation. paper held close to a stove element is not scorched where the element is painted white radiation from a shiny stove element. Hold a sheet of paper near a stove heating element painted half white and half black. Fill with boiling water 3 tin cans, black, insulation-covered and shiny, and leave to cool.
23.8.16 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.
23.8.17 Surface absorption
Put a radiant heater midway between two junctions of a demonstration thermocouple and cover the junctions with black or white caps.
23.8.19 Non-linear absorption of soot and flour mixes
Add different amounts of carbon to flour and measure the reflectivity.
23.8.20 Surface radiation from the engine of a motor car and a motor bike
See diagram 23.3.6
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 mesh (or system of tubes) which conducts the heat through it to be taken up by the surrounding air, which is usually forced through the metal mesh 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.
23.8.22 Teapot experiment
Use two identical teapots. Fit a woollen tea cosy to one tea pot. 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.
23.8.23 Melting blocks of ice
Place blocks of ice (a) In the sun and sheltered from the wind, (b) In the sun and in the wind, (c) Sheltered from the sun and wind, (d) In an ice chest or insulated portable cooler, e.g. “Eski”. List the blocks of ice in order of complete melting. The ice will melt most rapidly in (b), then (a), then (c), then (d).
(a) 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 in the air. 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.
(b) The layer of water over the ice evaporates more freely than in (a) so that the ice is dried and so melts more quickly. Unlike (a), new air is continually coming into contact with the ice so the amount of heat received by convection is not reduced.
(c) 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..
(d) No loss of heat by convection except from within the container. When the temperature of the interior of the container falls below the room temperature it receives heat from the surroundings by convection, conduction and radiation at a rate depending 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 (d) is the slowest.
23.8.24 Radiation through glass
See also 37.43: Greenhouse effect in a model greenhouse
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 fir. The energy distribution curve for the sun has its maximum in the visible region, and the sun emits also considerable energy in the infra red 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.
23.8.25 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.