School Science Lessons
Expansion, specific heat capacity,  conduction , convection, radiation, Joule's equivalent
2009-10-12
Please send comments to: J.Elfick@uq.edu.au
See: Interesting websites
Table of contents
23.00 Thermal properties of matter,  heat  as energy
23.2.0 Liquid expansion
23.3.0 Solid expansion
23.4.0 Materials at low temperature
23.5.0 Specific heat capacity (thermal capacity) C
23.6.0 Convection
23.7.0 Conduction, thermal conductivity
23.8.0 Radiation, Heat transferred by radiation, black body radiation
23.9.0 Heat transfer applications
23.10.0 Mechanical equivalent of heat, Joule's equivalent
22.7.0 Thermometers
20.1.0 Gas expansion
Topic 14 Thermochemistry, heat of reaction, chemical bonds
20.4.0 Thermodynamics, isothermal change and adiabatic change
23.00 Thermal properties of matter, heat as energy
4.1 Temperature rise and quantity of heat intake
4.2 Transfer kinetic energy to heat energy
4.3 Plug and ring experiment,  plate with hole, expansion
4.4 Expansion of a solid when heated
4.37 Heat and temperature
4.38 Calorific value of fuel
4.100 Angle of the sun's rays and how much heat and light received by the earth
23.2.0 Liquid expansion
4.6 Expansion and contraction of liquids
4.7 Expansion and contraction of a liquid
4.31 Temperature of water at maximum density, 4oC
6.8 Heated liquids expand (Primary)
11.2.2 Maximum density of water, negative expansion coefficient of water
23.2.1 Liquid expansion, expansion and contraction of liquids, bottle and tube, simple thermometer
23.2.4 Expansion of water and kerosene
23.2.5 Torricelli tube, barometer tube
23.2.7 Hope apparatus
23.2.8 Coefficient of expansion of oil
23.3.0 Solid expansion
2.21 Heat substances primary)
4.3 Plug and ring experiment
4.4 Expansion of a solid when heated
4.5 Bimetallic strip, compound bar
9.4.1.1 Stretched rubber band
23.3.1 Expansion of a solid when heated
23.3.3 Expansion gauge
23.3.5 Thermostat
23.3.7 Shrink fit
23.3.8 Break the bolt, forces caused by change of length
23.3.9 Bending glass by expansion
23.3.10 Trevelyan rocker
23.3.11 Expansion of quartz and glass
23.3.12 Expansion tube
23.3.13 Expanding wire, sagging wire
23.3.15 Motor car flashing lights
32.5.2.6: Motor Vehicle Thermal circuit breaker
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
23.5.0 Specific heat capacity, (thermal capacity), C
23.5.01 Specific heat capacity, shc
23.5.01a Specific heat of water
23.5.02 Molar heat capacity, Cm
23.5.1 Melting wax calorimeter, specific heat comparison of different metals, specific heat of lead shot
23.5.2 Specific heat of water by electrical method
23.5.2.1 Electrical determination of specific heat of aluminium block
23.5.3 Water and aluminium on the hot plate, heat capacity of metal and water, oil and water
23.5.4 Mixing heated water
23.5.5 Specific heat calorimeter.
23.5.6 Ice calorimeter
23.5.7 Heat of combustion, bomb calorimeter
23.6.0 Convection
2.2.5 Verify Newton's law of cooling, cups of coffee
3.39 Convection heat snake (Primary)
4.12 Smoke moves up and down (Primary)
4.24 Convection currents in a test-tube
4.25 Convection currents in a container
4.26 Convection current from an ink bottle
4.27 Convection currents in air, convection box
4.28 Trace convection currents from a lighted candle
4.29 Convection disc, heat snake, convection wheel
4.30 Convection currents and ventilation
4.31 Temperature of water at maximum density, 4oC
4.108 Wind speed indicator
4.119 Make a convection box
4.120 Tracing convection currents
23.6.1 Warm water is lighter than cold water, convection currents in water
23.6.2 Convection currents between jars of water, confused bottles
23.6.3 Feel convection currents in a test-tube
23.6.4 Convection currents of coloured water
23.6.5 Lava lamp
23.6.6 Two chimney convection box, smoke house
23.6.8 Convection tube
23.6.9 Model heating system
23.6.10 Barnard cell
23.6.11 Miso Soup
23.7.0 Conduction, thermal conductivity
2.1.5 Compare the heat insulation properties of common materials
4.16 Reduce heat loss with insulation
4.17 Conduction of heat by metals
4.18 Solids that conduct electricity
4.19 Liquids that conduct electricity
4.20 Copper coil snuffer
4.21 Conduction of heat by a coin on paper
4.22 Conduction in a metal bar
4.23 Water is a poor conductor of heat, boil water in a paper cup
23.7.1 Compare heat-insulating materials to reduce heat loss, thickness of material and heat insulation
23.7.2 Conduction in a metal bar, heat conduction of different metals
23.7.3 Different shapes of boiling water in aluminium pot and stainless steel pot
23.7.4 Conduction by different metals
23.7.5 Conduction of heat by metals, Davy lamp
23.7.6 Copper coil candle snuffer, brass wire netting extinguishes candle
23.7.7 Heat paper without burning, coin on paper conducts heat, paper that cannot be lighted
23.7.8 Water is a poor conductor of heat
23.7.9 Dropping wax
23.7.10 Relative conductivity
23.7.11 Anisotropic conduction with wood
23.7.12 Cook an egg on a piece of paper
23.8.0 Heat transferred by radiation, black body radiation
2.8 Dull and bright in the sun (Primary)
2.116 Thermoscope to compare absorption of radiation
4.32 Transfer heat by radiation
4.33 Focus radiant heat waves
4.34 Reflect radiant heat waves
4.35 Feel heat radiation
4.36 Different surfaces affect heat radiation and absorption
4.100 Effects of the angle of the sun's rays on the earth
4.150 Model greenhouse to simulate the "greenhouse effect"
23.8.1 Simple thermoscope
23.8.2 Feel radiation with your hand
23.8.3 Heat radiation decreases with distance
23.8.4 Focus radiant heat waves
23.8.5 Reflect radiant heat waves
23.8.6 Passage of radiant heat through glass
23.8.7 Different surfaces affect radiation
23.8.8 Colour of the surface and the heat absorbed
23.8.9 Light the match
23.8.10 Reflection of radiation
23.8.11 Beakers of water at a distance
23.8.12 Infrared radiation
23.8.13 Leslie's cube
23.8.14 Two can radiation, shiny and black cans
23.8.15 Selective absorption
23.8.16 Absorption of radiation
23.8.17 Surface absorption
23.8.18 Selective absorption
23.8.19 Non-linear absorption of soot and flour mixes
23.8.20 Surface radiation
23.8.22 Tea pot experiment
23.9.0 Heat transfer applications
23.9.0.1 The units of work and energy, joule and calorie
23.9.1 Thermos flask (vacuum flask, Dewar flask)
23.9.3 Insulation materials
23.10.0 Mechanical equivalent of heat, Joule's equivalent
23.10.1 Waterfall
23.10.2 Dropping lead shot
23.10.3 Hammer on lead
23.10.4 Heat by bending
23.10.5 Bow and stick, friction ignition, fire maker, drill and dowel
23.10.6 Flint and steel
23.10.7 Mechanical equivalent of heat, J, by an electrical method
23.00 Heat and temperature, internal energy and heat, heat and the first law of thermodynamics
Heat is a form of energy. The unit of work and energy is the joule, J, (i.e. newton.metre) (James Prescott Joule 1818 - 1889). The first law of thermodynamics states when other forms of energy are converted to heat, or when heat is converted to other forms of energy, there is no loss of total energy. The second law of thermodynamics state heat always flows from hot bodies to cold bodies.
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.
23.3.0 Solid expansion
Shrink fitting, riveting, expansion gap, expansion roller, bimetallic strip, fire alarm, thermostat
Expansion due to heat, thermal expansion, expansivity, coefficient of expansion
Most bodies increase their volume upon heating under normal pressure. The coefficient of expansion characterizes the expansion of various bodies. Solids retain their shape during temperature variations so you distinguish between linear expansion, area expansion and volume expansion (cubic 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, a, e.g. for Aluminium, a = 25 X 10-6. If a solid at temperature t1 has length L1 has expanded at temperature t2 to length L2, then L2 =L1 (1 + a [t2 - t1]), where a = the coefficient of linear expansion. Similarly A2 = A1 (1 + b [t2 -t1]), where b = the coefficient of area expansion, and V2 = V1 (1 + gamma [t2 - t1]), where gamma = coefficient of volume expansion. Note that the coefficient of cubic expansion for a solid is about three times the coefficient of linear expansion, i.e. gamma = about 3a. 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. Air and most other gases at atmospheric pressure have a coefficient of cubic expansion of 0.0034 (oC)-1. However, for expansion of gases you must use Charles' law.
23.3.1 Expansion of a solid when heated
See diagram 4.4: Expansion of solid
1. Use a 2 metre piece of copper tubing, A. Put it on a table and fix one end by a clamp, B. Underneath the other end put a bicycle spoke, C,  to act as a roller. A straw, D,  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, and this arrangement will detect the expansion of the tube caused by the hot breath. Now pass steam through, and note the motion of the pointer. Try 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. Heat an iron bar and place in a yoke to breaks a cast iron bolt as it 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 Expansion of 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.
23.4.1 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.
23.5.0 Heat capacity (thermal capacity) C, of a calorimeter
A calorimeter is an insulated vessel usually containing water and used to measure the thermal quantities of a process, heat changes.
Heat capacity, Cp, is the ratio: heat given to an object / rise in temperature of the object and is expressed in joules per kelvin, J K-1. The heat capacity of the calorimeter itself is usually measured as the amount of heat needed to raise the temperature of the calorimeter by 1 K. This value is usually found by experiment that involves transferring a known amount of heat into it and measuring its temperature increase. This experiment is done before measuring the heat capacity of an unknown substance. For example if the temperature of a calorimeter increases by 0.2 K when 8.0 J of electrical energy is used to heat it, the heat capacity of the calorimeter, C = 8 .0 / 0.15 = 53.3 J / K.
The heat capacity of the calorimeter is usually compared with the heat capacity of an amount of water.
The heat capacity of one mole of water, Cp,m = 18 g mol-1 X 1 cal g-1K-1 X 4.184 J cal-1 = 75.312 J mol-1K-1at 25oC.
23.5.01 Specific heat capacity, shc
1. The amount of heat absorbed by object per unit of mass as the temperature rises is called the specific heat capacity, symbol "c" or "shc". Specific heat is usually measured as the amount of heat required to raise the temperature of 1 kilogram of the substance by 1oC. Its unit is joule / kgoC. For water, shc = 4200 joule / kgoC (or 4.1813 J g-1K-1 at 250C). For copper, shc = 380 joule / kgoC. These values are the same if specific heat capacity is expressed using the Celsius scale or the Kelvin scale because the one degree interval has the same magnitude on each scale.
2. The heat required to raise the temperature of 15 kg mass of copper from 15oC to 25oC = mass X (t2 -t1) X specific heat = 15 kg x (25 - 15)oC x 380 joule / kgoC = 15 x 10 x 380 = 57000 joule, J (j).
3. Specific heat is the character of the material itself. The c values of a substance may be different in different states. The c values of the same gases are quoted as specific heat at constant volume (cv) for when only its internal energy is increased, or specific heat at constant pressure (cp), which requires more heat because the gas expands. For solids and liquids, the difference between specific heat values is very small.
23.5.01a Specific heat of water
Note the very high and unexplained specific heat of water, 4.1823 J g-1 K-1, (4.2 joules per gram per kelvin) at 25oC. The higher specific heat means that water is very suitable for use in central heating systems or cooling engines. Water has about five times the specific heat capacity of land keeping islands cooler in summer and hotter in winter. So continents have greater temperature variations than islands. The exceptionally high heat capacity of water slow temperature changes, allows heat to be transported around the world by ocean currents and influences climate change.
23.5.02 Molar heat capacity, Cm
1. Dulong and Petit's law states that relative atomic mass X specific heat = constant, approximately 25 J mol-1K-1
Molar heat capacity of a solid element, Cm = relative atomic mass X specific heat capacity = approximately 25 J mol-1K-1 (6.0 cal mol-1K-1) = 3R (where R = universal gas constant 8.314 J mol-1K-1) [3X 8.314 = 24.942]
If specific heat is expressed as gram heat capacity expressed as J g-1K-1, and specific heat of iron = 0.473 J g-1K-1, then the ratio: molar heat capacity / specific heat = 25 J mol-1K-1 / 0.473 J g-1K-1 = 52 .85 = approximately 55.847, the molar mass of iron. The molar heat capacity of non-metal compounds ot metallic salts is about 60-80% of the molar capacity of heavy metals.
23.5.1 Melting wax calorimeter
See diagram 24.1.1: Melting wax calorimeter
Prepare equal masses of aluminium, steel and lead. Tie a thread to each metal and put each into a copper beaker. Pour the same volume of boiling water on the metals. Use a smooth wooden board. Its size can meet the needs of all metals arranged one by one leaving space between each. Cover a thick layer of paraffin wax evenly on the board in advance. Lift the thread tied to the metal out of the boiling water, put it rapidly on the board. The hot metal produces a concavity on the layer of paraffin wax. After the paraffin wax stops melting, compare the width and depth of different concavities that can show that different metal has different specific heat. From this you can know roughly the values of specific heat of different metals.
23.5.2 Electrical determination of specific heat of water, c
1. Examine the electric jug or immersion heater for a power rating in watts. If power is not shown on an immersion heater, put immersion heater in water, connect to its power supply with an ammeter in the circuit, e.g. 12 volts DC. and note current used, e.g. 4 amps. power, P = VI = volts X amps = 12 X 4 = 48 watts. You can also use an ohmmeter to measure the resistance of the heating element and find the current drawn by the element using Ohm's Law, V = IR. Then calculate the power rating of the element.
2. Measure 1 litre of water. The heating element must be completely immersed in the water.
3. Measure the temperature of the water, t1
4. Switch on the electric power and record the time.
5. After a period of time when the temperature of the water has increased but before the water boils, i.e. below 100oC, switch off the power and record the time and the temperature of the water, t2.
6. Q = mc(t2 - t1), where Q is the energy absorbed, m is the mass of the water, "c" is the specific heat of water and t1 and t2 are the initial and final temperatures of the water. Assume that the water absorbs all of the energy output from the heating element. Thus, P = Q / t where P is the power rating of the element, t is the time taken to heat the water. Therefore, P = mc(t2 - t1) / t. Specific heat of water, c = 4186 J / kgoC.
If a 3 kW immersion heater raises the temperature of 60 kg water from 10oC to 60oC in 70 minutes.
Heat from immersion heater = heat gained by water.
3000 joules X 70 X 60 seconds = 60 kg X c X (60 -10)oC,
c = 4200 J / kgoC
23.5.2.1 Electrical determination of specific heat of aluminium block
1. Use a solid aluminium cylinder with 2 holes drilled into it and weighing 1 kg. Put a thermometer in one hole and an electric immersion heater, e.g. 12 V power supply, into the other hole. Record temperature when steady and time taken. Power of immersion heater, J X time immersion heater switched on, seconds, s = mass, m (1 Kg) X c X (t2 -t1).
2. Connect an immersion heater to the 12 volt supply in series with an ammeter and a rheostat. The immersion heaters are 12 volt, 60 watts. Adjust the rheostat to a current of about 4 amps. Insert the immersion heater in the aluminium block and the thermometer in its hole in the block. Use paraffin oil in the thermometer hole to ensure good thermal contact with the block. Wait for five minutes then record the temperature of the block. Close the switch. Start the clock and note the temperature change. Take the temperature every half minute and draw a graph. Connect the immersion heater to the 12 volt supply in series with an ammeter and a rheostat. The immersion heaters are 12 volt, 60 watts. Adjust the rheostat to give a current of about 4 amps. Switch on, start the clock and note the temperature change. Two methods can be used: 1. Take the temperature every half minute and plot a graph. 2. Take the total temperature rise over the known heating period. Continue recording temperature after the switch is opened. If the potential difference across the heater gave a current through it of 31 amps, and the temperature rose from 24.5oC to 37.8oC in six minutes when the electricity supply was turned off, the temperature may continue to rise to 40.1oC after 8.5 minutes. Close the switch, start the clock, record the temperature, open the switch after 10oC rise, record the time for which the heater was in operation, record the temperature after a further four minutes has elapsed. (temperature rise, oC x specific heat) / time, seconds = (current, amps x potential difference, volts) / J.
23.5.3 Water and aluminium on the hot plate, heat capacity of metal and water, oil and water
Put 1 litre of water in a beaker and 1 kg aluminium + water in another beaker and heat on the same hot plate then measure the temperature in each beaker. Heat two beakers one with 1 Kg water and the other with 5 Kg water and 5 Kg lead at the same rate. Heat two beakers on a single hot plate each contains the same mass of either water or oil, water and oil. Heat an iron plate and a beaker of water with the same mass on identical Bunsen burners then dip your hand in the water and sprinkle it on the iron plate where it will sizzle.
23.5.4 Mixing heated water
Mix different masses of hot and cold water and compare the final temperature to the calculated value. If the temperature of a 10 kg mass of copper, specific heat capacity 400 J / kgoC, rises from 20oC to 35oC, heat received by copper mass: H = mc(t2-t1) = 10 X 400 X (35 -20) = 60, 000 joules, J.
23.5.5 Specific heat calorimeter
Heat known masses of lead and copper are heated and put into calorimeters with a known mass of water then calculate specific heats of metals from initial and final temperatures.
If 1 kg aluminium in boiling water (100oC) put in 0.5 kg water at 10oC and temperature of water rises to 38.23oC.
Specific heat of water =4200 J / kgoC
Heat lost by aluminium = mass X specific heat X (final temperature - initial temperature) = 1 X c X (100 -38.23)
Heat gained by water = mass X specific heat X (final temperature - initial temperature) = 0.5 X 4200 X (38.23 -10)
heat lost = heat gained, so 1 X c X 61.77 = 2100 X 28.23, c = 959.7 J / kgoC (specific heat of aluminium = 960 J / kgoC)
23.5.6 Heat capacity of a metal with a Styrofoam cup calorimeter
A calorimeter made from two Styrofoam coffee cups is a constant pressure calorimeter in that measures the change in enthalpy of a reaction with the atmospheric pressure remaining constant.
Cp = [W X dH / (M X dT)], where dH = enthalpy of solution, dT = change of temperature, w = weight of solute, m = molecular weight of solute
In calorimetry, dH is the heat energy released at constant pressure and dE is the energy released at constant volume. dH= dE + [d(PV)], where
The enthalpy increase, dH, is the heat added to a system at constant pressure.
dH = mCpdT
where dH = change in enthalpy, m = mass of substance, Cp = heat capacity at constant pressure (J g-1K-1), dT = temperature change.
Styrofoam cup + cool water + hot water = 0
dHcal + dHcw +dHhw = 0
mCpdT + mcwCpdTcw + mhwCpdThw = 0
Let B, the calorimeter constant for the Styrofoam cup = MCp J /K
The calorimeter constant describes how the calorimeter responds to added heat.
So BdTcw + mcwCpdTcw + mhwCpdThw = 0
1. Measure the calorimeter constant, B
Use two Styrofoam cups, one inside the other, as a calorimeter. Weigh the two Styrofoam cups empty, m1, add 70 mL of water at room temperature and weigh the two Styrofoam cups again, m1 + 70, and record the temperature of the water in the calorimeter, T1. Boil water in a beaker, record the temperature, T2, and pour 30 mL of the boiling water into the calorimeter. Be careful! Gently stir the water with a thermometer with the bulb 3 cm above the bottom and record the highest temperature, T3 and mass M1 + 100.
B X (T3 - T1) + 70 X (T3 - T1) + 70 X (100 - T3) = 0
2. Measure the heat capacity of a metal, e.g. lead shot
Put a a test-tube containing lead shot in boiling water. Repeat the above experiment but add the hot lead shot to the calorimeter instead of the 30 mL of boiling water.
B X (T3 - T1) + 70 X (T3 - T1) + 70 X (100 - T3) = 0
3. The heat capacity of a metal in joules per gram per kelvin X molar mass of the metal in grams per mole = the constant, Cp X M = 25 J mol-1 K-1 (Dulong and Petit's law)
Heat capacity of metals expressed as joules per gram per degree Kelvin, J.g-1.K-1
Mg 1.04, Al 0.904, Fe 0.473, Ni 0.444, Cu 0.387, Zn 0.386, Ag 0.236, Sb 0.207, Au 0.129, Pb 0.128
23.5.6 Ice calorimeter
Heat different metals of the same mass to the same temp and lower into funnels filled with crushed ice then collect the melted water in graduated cylinders.
23.5.7 Heat of combustion, bomb calorimeter
See diagram 23.5.7: Bomb calorimeter
Use a bomb calorimeter to show heating value of foods and fuel.
dH = heat energy released at constant pressure, dE = heat energy released at constant volume, dH = dE + [d(PV)] = dE +dn RT (from ideal gas laws)
Measuring heat produced at constant volume, qv, = C dT (temperature change)
here qv = change in internal energy dE, so dE = qv = CdT
The heat capacity of a calorimeter can be calculated by burning a known weight of a standard substance, e.g. benzoic acid, dH = -3227 kJ mol-1.
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.
23.6.1 Warm water is lighter than cold water, 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.
23.6.2 Convection currents between jars of water, confused bottles
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, convection 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 currents in water
See diagram 4.26: Convection currents
1. Use a small bottle, fitted with a 2-hole stopper. Cut two pieces of glass tubing. Heat the end of one piece of tubing and draw it out to a jet like the end of a medicine dropper. Push this tube just through the cork to extend 5 cm above it. The other piece of tubing should be just level with the top of the cork and extend nearly to the bottom of the bottle. Fill the small bottle with hot water coloured deeply with ink. Use a jar large enough for you to put your hand in it and fill it with cold water. Rinse the small bottle under the hot tap and quickly place it on the bottom of the large jar while holding your fingers over the ends of the tubing. Remove your fingers and leave the small bottle at the bottom of the large jar. The hot coloured water rises in the large jar as the cold water enters the bottle.
23.6.5 Lava lamp
A lava lamp contains coloured water, oil 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.
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.
23.6.6 Two chimneys convection box., smoke house
See diagram 23.2.6:  Two chimneys
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.
23.2.5d Convection currents in air, revolving disk, 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.
23.6.8 Convection tube
Heat one side of a glass tube loop filled with water and insert some ink. Fill a rectangular glass tube with water is heated on one side.
23.6.9 Model heating system
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.
23.6.11 Miso Soup
Make miso soup and observe the convection patterns.
23.7.0 Heat conduction
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 Compare heat insulating materials to reduce heat loss, thickness of the material and heat insulation, how heat losses can be reduced
See diagram: 23.7.1 Speed of cooling
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.
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 in a metal bar, heat conduction of different metals
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. Observe 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 Different shapes of 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.
23.7.4 Conduction by different metals
See diagram 23.1.4
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.
23.7.5 Conduction of heat by metals, Davy lamp
See diagram 23.1.5: Model Davy lamp |  See diagram 4.17: A model 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. Direct a stream on gas at a lit Davy safety lamp.
10. 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.
11. 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.
12. 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.
13. 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, the flame gets smaller. The flame does not go through the wire netting. The flame becomes smaller because the wire conducts the heat away from the flame so the temperature is lowered. Sir Humphry Davy in 1816 used this observation to invent the miners' safety lamp. Metal gauze around the flame in the lamp conducts away the heat so that the flame cannot ignite explosive gas in the coal mine.
14. 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.
15. 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, brass wire netting extinguishes candle, snuffing out a candle flame with a copper coil
See diagram 23.1.6
1. 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.
2. 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. 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.
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
See diagram 23.1.8
1. Use your bare fingers to hold the bottom of a test-tube containing cold 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 f 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. Burn one paper cup and boil water in another paper cup. Burn away the top part of the cup with a propane torch.
3. 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.
4. See a swimming fish under boiling water! 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 you will not harm the fish!
5. 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.
6. 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.
7. 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
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 Show the relative conductivity
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 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.
23.8.0 Heat transferred by radiation, black body radiation
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.
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. Neither could it have reached your hand by convection because this would have carried the heat upward away from your hand. The heat came to your hand carried by short electromagnetic waves of wavelength 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.
23.8.1 Simple thermoscope
See diagram 23.3.1: 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.
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, radiant heat waves can be focussed
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 Reflect radiant heat waves, radiant heat waves can be reflected
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.
23.8.6 Passage of heat radiation 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 Different kinds of surfaces affect radiation
See diagram 23.3.7:  Different surfaces
1. Use three tin cans of the same size. Paint one white, inside and out, and another black; leave the third one shiny. Fill the three cans to the same level with warm water at the same temperature. Record the temperature. Place cardboard covers with holes for thermometers on each can, set them well apart on a tray, and then put them in a cool place. Record the temperature of the water in each can at 5 minute intervals. Was there a difference in the rate of cooling? Which surface was the best radiator of heat? Which was the poorest? Empty the cans to the same level. Next fill the tin cans with very cold water. Record the temperature, cover the cans and place them in a warm place or in the sun. Record the temperature of the water at 5 minute intervals. Note which surfaces were the best and worst absorbers of heat. The black metal tin can cools fastest because the black surface is the best radiator of heat. The black metal tin can is the best absorber of heat.
2. Use a pair of old shoes. Paint the left shoe black and the right shoe white. Your left foot becomes your hot foot.
3. 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.
23.8.8 Colour of the surface 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 Light the match
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 Reflection of radiation
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
23.8.11 Beakers of water at a distance
A thermopile mounted the at focus of a parabolic mirror detects radiation differences from different coloured beakers of water.
23.8.12 Infrared radiation
Iodine dissolved in alcohol gives a filter transmitting in the IR but absorbing in the visible.
23.8.13 Leslie's cube
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. Fill the 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.
23.8.14 Two can radiation, shiny and black cans
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.
23.8.15 Selective absorption
Various screens are placed 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.
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. Paint two thermoscopes, one thermoscope white the other black and illuminate both by a lamp.
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.
23.8.18 Selective absorption
Put a Leslie cube with opposite faces blackened between two bulbs of a differential thermoscope.
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
A paper covered tin can cools faster than a shiny can.
23.8.22 Tea pot 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.
23.9.0 Heat transfer applications
Heat transfer by conduction, convection and radiation, coefficient of expansion, the joule / calorie
1. First law of thermodynamics: When other forms of energy are converted to heat or when heat is converted to other forms of energy there is no loss of total energy.
2. Second law of thermodynamics: Heat always flows from hot bodies to cold bodies.
Heat is a form of energy measured in joules, J. Heat transfer is the process of transfer of energy from an object to another, or from a part of an object to another one. Heat energy can be transferred by conduction, convention, and radiation. The natural flow of heat is from higher temperature towards lower temperature. So heat energy spreads out from concentrations at high temperature. When you apply heat to one end of a solid conductor, the particles at that end, e.g. atoms and molecules vibrate more rapidly. This energy is passed from particle to particle through the material by conduction. All metals are good conductors of heat but many liquids and gases are poor conductors. Liquids and gases can transfer heat by convection when hot fluid rises and is replaced by colder surrounding fluid. Heat can be transferred through space as electromagnetic radiation. Rough or black surfaces are good absorbers and good emitters of radiation whereas polished or white surfaces are not.
23.9.0.1 The units of work and energy, joule and calorie
1 Joule of work done = 1 newton force moves object through 1 metre, Work done = force distance in direction of force, W = Fs, Work and Energy
Work = force X distance (displacement), joule (newton.metre). Work done on an object changes its energy that may be stored as potential energy or cause change in speed, kinetic energy. When a wheel is moved by a force, the work done = displacement X component of the force in the direction of the displacement
The joule, J, is the SI unit of work and energy. A joule is equal to the amount of work done when the point of application of a force of one newton moves one metre in the direction of the force.
1 joule = 107 ergs = 0.2388 calorie. The c.g.s. unit, the calorie, is the amount of heat required to raise the temperature of 1 gram of water by 1oC, i.e. 1 K. Nowadays the SI unit the joule, J, is used. 1 calorie (cal) = 4.184 J, commonly, 4.2 joules.
23.9.1 Thermos flask (vacuum flask, Dewar flask, Mariotte flask)
Draw a cooling graph for a vacuum flask, measure the temperatures of water in four thermos bottles.
See diagram 23.05: Dewar flask
1. The silver surfaces of the double glass walls or steel walls reduce radiation. The thin walls of the double glass flask, the vacuum between the double walls and the cork or rubber stopper reduces conduction and prevent evaporation. The case reduces convection.
2. Draw a cooling graph for a vacuum flask. Almost fill a vacuum flask with boiling water. Note the time and temperature of the hot water every half hour until it is cold. Draw a graph of your results. When the contents are hot, heat is lost at a greater rate so the temperature-time graph is a swooping curve rather than a straight line. Thus heat losses are faster when the difference in temperature between the hot object and the surroundings is greatest. Put an equal quantity of ice cold water in a second vacuum flask it and graph the rate of warming. A vacuum flask keeps heat from getting out from hot things and stops heat from getting in to cold contents.
23.9.3 Test insulation materials
Use 2 identical cans of water, one wrapped with insulation. Do NOT use asbestos or any product containing asbestos.
23.10.1 Waterfall
If 10 kg water falls 150 metres and all the energy converted to heat (silent waterfall!), and g = 9.8 m / s2
potential energy of water = mgh = 10 X 9.8 X 150 = 14700 joule, J
H = mc(t2-t1), where c = 4200 J / kgoC = 10 X 4200 X (t2 - t1)
14700 = 42000(t2-t1), so difference in temperature (t2 -t1) = 14700 / 42000 = 0.35oC.
23.10.2 Dropping lead shot
Drop a bag of lead shot is dropped several times and measure the temperature rise. Put one Kg of lead shot in a mailing tube, cardboard cylinder, invert 10 times and measure the rise in temperature rise is measured.
23.10.3 Hammer on lead
Hit a lead block with a heavy hammer and measure the temperature rise.
23.10.4 Heat by bending
Keep bending an iron wire and measure the rise in temperature.
23.10.5 Bow and stick, friction ignition, fire maker, drill and dowel
Make a fire with a bow and stick. Hold an electric drill with a hardwood dowel in the chuck against a wood block.
23.10.6 Flint and steel
Make sparks fly from flint rubbing against steel or a grindstone.
23.10.7 Mechanical equivalent of heat, J, by an electrical method
See diagram 32.2.64
The heat energy expended by a current of I amps flowing under a potential difference V volts for t seconds = VIt / J, where J = a constant called the mechanical equivalent of heat. If heat lost from the calorimeter to the surroundings is small, the heat energy supplied by the coil = heat energy received by the calorimeter + contents. Weigh the calorimeter + stirrer, m1. Weigh the calorimeter + stirrer + enough water to cover the heating coil, m2. Adjust the rheostat or power supply to a current of 3 amps. Open the switch, stir the water and note the initial temperature T1oC. Close the switch and record the time. Record the current I amps through the coil. Record the potential difference V volts across the coil. Allow the current to flow, still stirring, until the water temperature has risen 10oC. Open the switch and record the highest steady temperature, T2oC. Record the time of flow of the current, t seconds. The specific heat of water = 4.2 kg-1K-1 (or oC). The specific heat calorimeter and stirrer, usually copper = s. Calculate J using the following equation: Heat energy supplied = heat received by water + heat received by calorimeter and stirrer. VIt / J = ([m2 -m1]swater [T2 - T1]) + (m1 x s x [T2 -T1]).
23.4.6.2 Heating a flask with water
See diagram 23.4.6
Fill the flask of some cold water of height 1-2 cm. Seal the mouth of the flask with the 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 the temperature of 70oC to 80oC. During heating it tightly press the mouth of the flask with your hand to seal the air in the flask. After 2 minutes, suddenly leaving your hand off the mouth of the flask, a stream of water current spurts out of the upper end of the capillary. Place a wet coin on the upper end of the capillary. It will move up and down gently to produce some vibrancy sound. When you heat the air, its volume does not increase due to being sealed. So the air pressure increases. Thus a stream of water current spurts out of the upper end of the capillary when taking your hand off the mouth of the flask.
2.1.5 Compare the heat insulation properties of common materials
See diagram 4.1.5
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 Verify Newton's law of cooling, cups of coffee
See diagram 4.2.5
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
4.100 Angle of the sun's rays and the amount of heat and light received by the earth
Bend a piece of cardboard and make a square tube 2 cm x 2 cm X 32 cm. Use a piece of very stiff cardboard and cut from this a strip 23 cm long and 2 cm wide. Paste this to one side of the tube with 15 cm extending. Rest the end of the stiff cardboard on the table and incline the tube at an angle of about 25o. Hold a flashlight or lighted candle at the upper end of the tube and mark of f the area covered by the light through the tube on graph paper fixed to the bench. Repeat the experiment with the tube at an angle of 15o. Repeat the experiment with the tube vertical. Compare the areas of the three spots. Note whether the heat and light received per unit area from the sun are greater or less when the rays are slanting or direct.