Energy Transferred by Heating
Energy and Thermal Physics

Energy stored thermally

for 14-16

Experiments in this collection explore more subtle ideas: heating by friction, the nature of energy in hot stuff, and differences in the thermal capacity of different materials.

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Thermal conductivity: metal v. plastic

Energy Transferred by Conduction
Energy and Thermal Physics

Thermal conductivity: metal v. plastic

Practical Activity for 14-16

Demonstration

This demonstration shows, against intuition, that an ice cube melts more quickly when in contact with a metal block than a plastic block.

Apparatus and Materials

  • Metal and plastic blocks of identical dimensions
  • (approx 5 cm square by 1 cm thick)
  • Ice cubes at 0°C
  • Clock
  • 2 temperature probes with displays (optional)

Health & Safety and Technical Notes

Read our standard health & safety guidance


There are no safety problems with this demonstration.

A suitable ‘ice melting kit’ is available from the supplier: Timstar.

Procedure

  1. Pass the metal and plastic blocks around the class; ask your students what differences they observe. They are likely to comment that the metal block feels colder to the touch than the plastic one.
  2. Explain that you are going to place identical ice cubes on each block. Ask for predictions as to what will happen.
  3. Place one ice cubes on each block. Observe the ice melting over a few minutes. The film below shows how to carry out this demonstration, together with typical results.
  4. Thermal conductivity


  5. You could use a timer to determine the time for each cube to melt completely. Alternatively, attach a temperature probe to each block and observe how their temperatures change.

Teaching Notes

  • This demonstration can form the introduction to a structured development of ideas about energy transfers between objects at different temperatures. Ice cubes are placed on metal and plastic blocks; the cube placed on metal melts much more quickly than the cube placed on plastic. This is counterintuitive (for many students) because metals feel cold while plastics feel warm.
  • Energy is transferred to the ice cubes by conduction from the blocks on which they have been placed. A metal block is a better conductor and so energy is transferred more quickly to that ice cube.
  • Why isn’t this obvious? Metals feel cold to the touch. This is because, when you touch a piece of metal, energy conducts away from your fingers into the metal, lowering the temperature of your fingers. Plastics are good insulators so, even though the plastic is at a lower temperature than your fingers, little energy conducts to the plastic and it feels warm.
  • Hence it is best to start the demonstration by asking your students to feel the two blocks so that they may be misled by this experience. Then show that the ice on the metal block melts more quickly, and discuss the reasons.
  • You may then wish to take the discussion to a deeper level. Students may think that some materials (metals, water) are intrinsically cold, while others (plastic, wood) are intrinsically warm. (We talk about ‘warm clothing’). So you could use thermometers to test the temperatures of different objects and materials in the room.
  • Then repeat the demonstration with electronic thermometers monitoring the temperatures of the blocks as the ice cubes melt. Show that the two blocks are both at room temperature at the start, and observe the rapid drop in temperature of the metal block.
  • You could ask your students to explain why the temperature-time graphs for the two blocks are curved (they are roughly exponential). The reason for this is that the rate of transfer of energy from the block to the ice decreases as the temperature difference between them decreases.
  • Note that there is a complication to this analysis which we have avoided mentioning so far. The rate at which energy is transferred to the ice depends on both the conductivity of the block and its heat capacity. It might be that the ice on the plastic block melts very slowly because the temperature of the plastic block drops very rapidly to that of the ice. This would happen if plastic had a low specific heat capacity. This is shown not to be the case by when a temperature probe is used.
  • Some general notes on teaching about:

    conduction, convection and radiation


  • An experiment to compare the...

    thermal conductivities of different materials


Up next

Working against a band brake

Energy Transferred by Heating
Energy and Thermal Physics

Working against a band brake

Practical Activity for 14-16

Demonstration

Using a band or friction brake and wheel to show the transfer of work into energy stored thermally.

Apparatus and Materials

  • Demonstration forcemeters, 0-20N, 2
  • Wheel with band brake
  • Stopwatch
  • Rod and two bosses
  • Retort stands, 2

Health & Safety and Technical Notes

Read our standard health & safety guidance


You can improvise the wheel with band brake if you have a belt-driven table or disc. Slip off the belt and substitute a webbing belt or length of thick string. Alternatively, a bicycle ergometer could be used.

Procedure

  1. Secure the belt firmly at the ends of the two spring balances, which you have supported from above. Adjust the belt tension by raising or lowering the support so that both forcemeters read about half full scale.
  2. Turn the wheel by hand at a steady rate for at least 30 seconds and record the steady readings of the two forcemeters. Note the time taken to turn the wheel and count the number of turns taken.

Teaching Notes

  • As the wheel is turned, energy stored chemically (in food and oxygen) in the operator’s muscles is transferred to the band brake so warming it up and increasing the energy stored thermally.
  • If you want to calculate the energy transferred, the logic is quite tricky, but explained as follows.
  • Read the forces F1 and F2 from the spring balances while allowing the wheel to slip past the fixed belt, as in diagram I. This is equivalent to diagram II in which the spring balances are replaced by two loads suspended by pulleys with the tension in each side of the belt being F1 and F2 as before. Now the belt does not slip but rather the loads move. Finally this arrangement can be transformed into diagram III, in which one end of the belt is fixed to the wheel and the other carries a load equal to the difference between F1 and F2 . As the band brake is turned the belt does not slip but the load rises.
  • The energy transferred to the system, E= (F 1 F2 ) x distance moved.
  • So the energy transferred to band brake is E = (F 1 F2 ) x (circumference of wheel) x (number of turns)
  • This energy of the band brake stored thermally increases , and so its temperature rises.

This experiment was safety-tested in November 2005

Up next

Mixing hot and cold water

Energy Transferred by Heating
Energy and Thermal Physics

Mixing hot and cold water

Practical Activity for 14-16

Demonstration

Mixing two masses of water at different temperatures to discuss energy transfer.

Apparatus and Materials

  • Plastic buckets, 2
  • Thermometer (demonstration or digital display)
  • Domestic balance
  • Supply of hot water and supply of cold water

Health & Safety and Technical Notes

Read our standard health & safety guidance


The temperatures could be read with a mercury thermometer, but this would not allow the class to see the reading. Digital thermometers with large displays are now reasonably priced.

Procedure

  1. Weigh 3 kg of hot water into one of the plastic buckets.
  2. Weigh 2 kg of cold water into the other.
  3. Note the temperature of each.
  4. Pour the cold water into the hot water and stir. Take the final temperature.

Teaching Notes

  • Discuss with students what happens when hot water is mixed with cold water. Light containers are used so that the thermal capacity of the container itself can be ignored. When the waters are mixed the temperature ends up somewhere between the two initial temperatures. You might ask: "Has anything stayed the same during the mixing?"
  • Because the masses of water are different the temperature changes should not be equal. "What if we multiply the temperature change by the mass of water?"
  • This product does stay the same (approximately), and does so in many exchanges. It is directly proportional to the change in energy stored thermally.
  • The energy transfer between the two lots of water is not 100% because some energy comes from the bucket and some is transferred to the environment. But in this experiment the energy dissipated in these ways are minimized.
  • Therefore energy stored thermally in the warm water is transferred to the cold water, until they arrive at a common temperature.

This experiment was safety-tested in November 2005

Up next

Measuring thermal energy

Energy Transferred by Heating
Energy and Thermal Physics

Measuring energy stored thermally

Practical Activity for 14-16

Class practical

Quantitative measurement of changes to energy stored thermally as a result of heating from a range of sources.

Apparatus and Materials

For each student group

  • Immersion heater, 12 V 100 W (older, 60 W types will do)
  • Thermometer -10°C to 110°C
  • Aluminium container
  • Lever-arm or domestic balance (+/- 2g)
  • Stopwatch or stopclock
  • Low voltage power supply or transformer (to supply 8A)
  • The following apparatus is required if you wish to do the extension experiments...
  • Bunsen burner, with heatproof mat and tripod
  • Heatproof gloves
  • Small evaporating basin
  • Ethanol (methylated spirit)
  • Matches

Health & Safety and Technical Notes

Although the temperature rise should not be high, heat-proof gloves should be available for those members of the class who heat their containers up to 45 °C.

Take extreme care with using ethanol. All flames must be extinguished before ethanol stock is brought into the room. The teacher (or assistant) must dispense 1 ml into each evaporating basin (e.g. using teat pipette or pump dispenser).

Finally, matches are issued to the class. No one should repeat the experiment because of the danger of adding ethanol to a hot container.

Read our standard health & safety guidance


In procedure step 5, a convenient metal support for the container can be made from a strip of aluminium 20 cm x 7.5 cm bent to form both a wind-shield and a support.

Procedure

  1. Measure out approximately one kilogram of water and place it in the aluminium container. Measure the temperature of the water with the thermometer. Place the immersion heater in the water and connect it to the 12 V supply. Switch on and start the clock at the same moment. Stir the water constantly - this is essential for good results.
  2. After 5 minutes switch off the supply, continue to stir and note the highest temperature reached. REMOVE the immersion heater from the water and allow it to cool on the bench.
  3. Repeat the experiment using 1/2 kg of water.
  4. Empty the container and put another kilogram of water into it. Place a Bunsen burner underneath and heat the water for one minute. From the rise in temperature, calculate how much energy is transferred by the burner in one minute.
  5. Burn 1 ml of alcohol (methylated spirit) under another 1 kg of water. From the rise in temperature, calculate the energy transferred when the ethanol is burned.

Teaching Notes

  • Energy is transferred to the water by the electric current. The change of energy stored thermally in the water is calculated (see 4 below) from (mass of water) x (temperature rise). The temperature rise with half the mass of water should be about twice as much. Between experiments the apparatus should be cooled down to room temperature so that each experiment is carried out under the same conditions.
  • Students can be asked to measure the temperature of the water at regular intervals of time, of about 5 minutes, and then to plot a graph of temperature against time for the water. This will show that the temperature increases fairly uniformly with time as long as the temperature does not rise too much. If the temperature rise is too high the energy dissipated (stored thermally in the surroundings) increases because of the higher temperature difference between the container and its surroundings.
  • For experiment 4 the temperature rise of the water is noted and its mass measured. The change of energy stored thermally in the water is again calculated from (mass of water) x (temperature rise). Ignoring energy dissipated to the surroundings, this is the energy transferred from the Bunsen burner. A similar calculation in 5 gives the energy transferred from 1 cm3 of alcohol.
  • The units may cause concern to some teachers. They can be called kilocalories (if the mass is in kilograms, which they are), or thermal units. It is not necessary to introduce the concept of specific thermal capacity.
  • It is worth taking care to allow the heaters to cool in air, not water. If the heater has a crack in its seal, as it cools it will then draw in air not water. The problem with allowing water to enter is that when the heater is next used, the water boils. The heater then explodes with a bang, which is frightening if not very hazardous.

This experiment was safety-tested in March 2006 fe

Up next

Specific thermal capacity of aluminium

Specific Heat Capacity
Energy and Thermal Physics

Specific thermal capacity of aluminium

Practical Activity for 14-16

Class practical

Using an aluminium block and immersion heater to estimate the specific thermal capacity (also called the specific heat capacity) of aluminium.

Apparatus and Materials

For each group of students

  • Aluminium calorimeter with holes for heater and thermometer (see discussion below)
  • Thermometer -10°C to 110°C
  • Stopwatch or stopclock
  • Immersion heater, 12 V 100 W (older, 60 W types will do)
  • Low voltage power supply or transformer (to supply 8A)
  • Lever-arm or domestic balance (+/- 2g)
  • Insulation/cladding for the metal block OPTIONAL

Health & Safety and Technical Notes

The immersion heaters should have been allowed to cool in air after heating water, to eliminate the (small) risk that water has been drawn inside through a cracked seal.

Read our standard health & safety guidance


If bespoke insulation is not available, then scraps of material and or newspaper can be held on with string/elastic bands to provide a thick insulating jacket for the block.

If you drop some paraffin-oil into the thermometer hole it will ensure good thermal contact between the block and the thermometer. It is not necessary to use oil with the immersion heater. In fact, as there is a danger of cracking any oil which is left on the heater when it is removed from the block, it is wiser not to use it.

Procedure

  1. Find the mass of the aluminium block on the balance. Place a small drop of oil in the thermometer hole. (This will provide good thermal contact between the block and the thermometer bulb.) Insert the thermometer and immersion heater in the appropriate holes. Read the thermometer. Connect the heater to the 12 volt supply and switch it on for 5 minutes. Note the maximum temperature rise obtained after the supply has been switched off.
  2. Many suppliers can provide similar 1 kg blocks made of steel, copper, brass etc. If these are all set up at the same time they will show that different materials of the same mass will achieve different temperature rises when the same amount of energy is transferred to them.

Teaching Notes

  • Change in energy stored thermally (due to the temperature rise) = mass x specific thermal capacity x temperature rise
  • The temperature of I kilogram of aluminium rises about four times that of a kilogram of water. If the heater does not behave differently in aluminium compared to water there must be another factor which is peculiar to the aluminium. This is the specific thermal capacity (also called specific heat capacity) of the aluminium.
  • The specific thermal capacity of aluminium is 900 J/kg °C
  • The specific thermal capacity of water is 4200 J/kg °C
  • It takes more energy to raise the same temperature of water by each °C than it does to raise the temperature of the same mass of aluminium.
  • How Science Works extension: After collecting data, students calculate the specific thermal capacity of the aluminium (or other material) used. To assess the accuracy of their measured data, they can compare their value of specific thermal capacity with its accepted (true) value from data tables. You can also ask them to calculate the percentage difference between the two values, to show how the accuracy of measurements can be expressed quantitatively. Differences between the two values can also be used to prompt a discussion about errors and uncertainties in their measurements, identifying the main sources.
  • Energy dissipated so that it is stored thermally in the surroundings is something that students can investigate further, to obtain a more accurate value of the specific thermal capacity. The Guidance note:

    Cooling corrections


    suggests a procedure for controlling such transfers. A less sophisticated, but equally valid, approach is to repeat the experiment (the block needs time to cool}, using insulation around the block. Their second set of data will enable them to assess whether this gives a more accurate result for specific thermal capacity.
  • Before you make this comparison remember that power supplies may only give unidirectional potential differences and not fully smoothed values. The power measured is on DC meters as VI is only 0.8 of what it should be. See the guidance note...

    Explaining rms voltage and current


This experiment was safety-tested in December 2006

Up next

Specific thermal capacity of aluminium more accurately

Specific Heat Capacity
Energy and Thermal Physics

Specific thermal capacity of aluminium more accurately

Practical Activity for 14-16

Class practical

Measuring the specific thermal capacity (also called the specific heat capacity) of aluminium, including the use of a cooling correction.

Apparatus and Materials

For each group of students

  • Immersion heater, 12 V 100 W (older, 60 W types will do)
  • Aluminium calorimeter with holes for heater and thermometer (see discussion below)
  • Ammeter (0-5 amp)
  • Stopwatch or stopclock
  • Thermometer
  • Voltmeter, 0-15 volt (see discussion below)
  • Rheostat (10-15 ohms, rated at 5A or more)
  • Top pan balance
  • 12 volt supply, i.e. LV power supply with high current smoothing unit

Health & Safety and Technical Notes

Read our standard health & safety guidance


If you drop some paraffin-oil into the thermometer hole it will ensure good thermal contact between the block and the thermometer. It is not necessary to use oil with the immersion heater. In fact, as there is a danger of cracking any oil which is left on the heater when it is removed from the block, it is wiser not to use it.

Procedure

  1. Find the mass of the aluminium block using the top pan balance. Connect the immersion heater to the 12-volt supply in series with an ammeter and a rheostat. The immersion heaters are 12 volt, 60 or 100 watt, so adjust the rheostat to give a current of about 4 amps. Switch the heater off.
  2. Insert the immersion heater in the aluminium block and place the thermometer into its hole. Before switching on for the experimental run, wait for five minutes before taking the temperature of the block. Switch on the heater and start the clock.
  3. The easiest way to measure the temperature rise is to leave the heater switched on until a rise of about 10°C is achieved. Switch off the heater and continue to monitor the temperature until it begins to fall. Note the maximum temperature reached by the block.
  4. A more accurate method is to take temperature readings every half minute and to plot a graph of the results both whilst the heater is on and for approximately the same time after the heater is switched off. A cooling correction can be applied to the temperature rise measured, using a standard technique.

Teaching Notes

  • The specific thermal capacity can be determined from the relationship: mass x specific thermal capacity x rise in temperature/ time = current x p.d.
  • The ratio temperature rise / time can be obtained from the slope of a graph of temperature plotted against time.
  • The aluminium blocks can be lagged by enclosing them in foamed polystyrene.
  • You can attach the immersion heater to a joulemeter and so measure directly the energy transferred from the electrical supply to the material.
  • The choice of power supply makes a lot of difference in this experiment. You will get an accurate result with AC supplies and AC meters because the AC meters have been constructed to read correct values.
  • However, most school power supplies providing currents high enough to warm up immersion heaters are not smoothed at all and the DC terminals give voltages which are extremely bumpy. External smoothing units will help.
  • If you use moving coil meters, students will need to make a correction for the electrical power calculation.
  • A moving coil meter reads time-averaged values, which are (2/π) x peak value.
  • So actual power = 1.2 x power calculated from meter readings.
  • For further information, see the guidance note:

    Explaining rms voltage and current


This experiment was safety-tested in August 2007

Up next

Hammering lead to warm it up

Energy Transferred by Heating
Energy and Thermal Physics

Hammering lead to warm it up

Practical Activity for 14-16

Demonstration

Working mechanically to raise the temperature of different components.

Apparatus and Materials

  • Blunt drill bit
  • Electric drill
  • Brick and G-clamp
  • Piece of sheet lead
  • Hammer and hardwood anvil
  • Iron wire to hold piping
  • Bicycle pump

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Clamp the brick over a scrap of softwood to the bench.
  2. Bore a hole in the brick with the blunt drill, then pass the drill bit round so that it can be felt.
  3. Push the stiff iron wire through the lead piping and bend the end so as to hold the lead.
  4. Hammer the lead violently so that its temperature rises. A piece of lead sheet may be used instead of the piping, as shown in the diagram.
  5. Ask students to push in the piston of a bicycle pump quickly whilst holding a finger on the outlet so that they can feel the heating.

Teaching Notes

  • In all these demonstrations the components warm up. When the action stops, all the energy of the moving parts stored kinetically has been transferred to the components, so increasing the energy stored thermally.
  • The bicycle pump warms up because the speed of the air molecules inside the cylinder has increased. Momentum is transferred from the moving piston to the air molecules in the same way as hitting a ball with a moving bat transfers momentum. An increase in the speed indicates and increase in energy stored thermally. The temperature rises.
  • There are occasions when energy is transferred to a body but its temperature does not rise. If a beaker of crushed ice is melted with a Bunsen flame, the resulting slush remains at freezing point. In this case the heating increases potential energy in the force-fields of the molecular structure, as the molecules are pulled apart against the forces of mutual attraction that hold them in a solid crystal. The energy needed to do this is known as latent heat. (The term is too well established to think of calling it anything else - but beware of the word heat.)

This experiment was safety-tested in November 2005

Up next

The specific thermal capacity of lead

Energy Transferred by Heating
Energy and Thermal Physics

The specific thermal capacity of lead

Practical Activity for 14-16

Class practical

Transferring energy mechanically to lead shot and measuring its temperature rise.

Apparatus and Materials

For each group of students

  • Lever-arm or top pan balance (+/- 10g is sufficiently accurate)
  • Cardboard tube (approx 50 - 100 cm long)
  • Lead shot, 500 g
  • Plastic or cardboard cups
  • Thermometer
  • Metre rule
  • Corks or bungs to fit tube, 2

Health & Safety and Technical Notes

There is no need to handle the lead shot. However, if it is spilt and is collected by hand (for example), the hands must be washed thoroughly before eating.

Read our standard health & safety guidance


Procedure

  1. Measure out about 500 g of lead shot in one of the plastic or cardboard cups.
  2. Put a thermometer into the lead shot to find the temperature.
  3. Seal one end of the cardboard tube with a cork or bung. Put the lead shot into the tube and seal the open end.
  4. Measure the length of the tube, Δh.
  5. Turn the tube over 20, 40 or 50 times, counting the number. Quickly pour the shot into the cup and measure the maximum temperature again.

Teaching Notes

  • When the lead is falling take care that it falls vertically rather than sliding along the tube, when friction will come into play. Also a hand should not cushion the bottom of the tube when the shot hits the bottom, otherwise energy will be transferred into the hand.
  • Turning the tube over more times in order to achieve higher temperature rises is not advisable. The longer time and higher temperature differences will allow more thermal transfer to the surroundings.
  • The energy transferred is equal to the number of falls (n) x mgΔh and therefore n x mg x Δh = m x specific thermal capacity x temperature rise.
  • Note that there is no need to record the mass of the lead, m.
  • Lead is used because its specific thermal capacity is about 1/30 that of water. It is the thermal capacity per unit mass which is important. (Most metals have approximately the same thermal capacity per unit volume.) It is also an inelastic metal so that the energy of the shot stored gravitationally is then stored thermally. The temperature rises.
  • When Joule was investigating energy conservation he is said to have measured the temperature at the top and bottom of a waterfall on his honeymoon in Switzerland. This is a useful model of his experiment.

This experiment was safety-tested in January 2006

Up next

Calibrating a voltmeter

Energy Transferred by Heating
Energy and Thermal Physics

Calibrating a voltmeter

Practical Activity for 14-16

Class practical

Using the specific thermal capacity of water to check the reading of a voltmeter.

Apparatus and Materials

  • Stopwatch or stopclock
  • Thermometer
  • Immersion heater, 12 V
  • Measuring cylinder, 100 ml
  • DC ammeter (0-5 amp)
  • Plastic cup
  • Battery, 12 V
  • Retort stand and clamp
  • Glass rod stirrer
  • DC voltmeter (0 -15 volt)

Health & Safety and Technical Notes

Do not use a mains immersion heater which would involve unsafe mains connections.

Read our standard health & safety guidance


You can replace the battery by a 12 volt a.c. supply if appropriate a.c. meters are available.

Cheaper, cup-top immersion heaters are available. These remove the need for a separate support.

Procedure

  1. Place 200 ml (grams) of cold water in the plastic cup. Support the immersion heater in the cup so that it does not touch the base. Place the immersion heater in the water and connect it into the circuit shown. Record the temperature.
  2. Switch on the circuit and start the watch at the same instant. Stir the water and allow the current to flow for 2 minutes. Note the ammeter and voltmeter readings during this time.
  3. At the end of 2 minutes switch off the current, stir the water again, and note the maximum temperature. (A rise of about 7° C can be expected.)

Teaching Notes

  • This experiment makes use of the principle of conservation of energy in order to calibrate a voltmeter, rather than an experiment to measure the energy stored thermally by the water.
  • Knowing that all energy is measured in the same unit, joules, then the energy transferred electrically from the power supply can be equated to the gain in energy stored thermally by the water.
  • Energy transferred electrically, E = potential difference x current x time = VIt
  • Energy stored thermally, E = mass x specific thermal capacity x temperature rise
  • So, VIt = mass x specific thermal capacity x temperature rise
  • As all the values can be measured, you can compare the calculated value for V with the reading on the voltmeter. The specific thermal capacity of water is 4,200 J/kg °C.
  • If you are using d.c. meters, this experiment is best carried out using car batteries. The potential difference is ‘pure’ d.c. If rectified, unsmoothed d.c. is used from a power supply, then the calculated product of the readings on the voltmeter and ammeter will be 20% less than it should be. This is because the meters are measuring a time average not an r.m.s. average. If an a.c. supply and a.c. meters are used, r.m.s.values will be recorded, and the product will be accurate.
  • It may be helpful to remind students that the definition of potential difference is the energy supplied to each coulomb of charge flowing. Therefore the basic unit of the volt can be expressed as joules/coulomb.
  • In many textbooks, specific thermal capacity is also referred to as specific heat capacity.

This experiment was safety-tested in January 2006

Up next

Heat and temperature

Energy Transferred by Heating
Energy and Thermal Physics

Heat and temperature

Teaching Guidance for 14-16

One important aspect of students’ growing understanding of energy ideas involves sorting out the ideas of heat and temperature (hotness or coldness).

Kinetic theory describes the energy of an object as being due to the random motion of its molecules. If you give more energy to be shared out amongst the atoms and molecules of some piece of matter, it usually gets hotter. But ‘hotness’ is not energy. Something hot (like the surface of the Sun, or a flame in a gas cooker, rather easily gives up energy to cooler things (energy goes without help from hotter to cooler).

What counts is the average energy per particle, not the total energy stored. So hot objects have, as it were, very concentrated energy that easily spreads out and dilutes, warming other things. This is what lies behind talk about “heat is a form of energy”. It is best to refer, as soon as possible, to the sharing out of energy amongst the motion of all the particles.

Students will learn that all energy transfers involve some losses through energy dissipation. They deserve (and will understand) an explanation of how this happens, and not simply a dramatic conclusion about the Universe warming in some mysterious way.

In describing ways in which energy goes from one place to another, physicists distinguish between ‘heating’ and 'working’. Heating is the process whereby energy moves from one object to another, which is in contact with it, as a result of their temperature difference.

Compressing and expanding gases

If a gas is compressed by pushing a piston quickly into a cylinder, the gas grows hotter: all the energy transferred to the gas goes into energy of molecular motion. If the gas then cools back to the original temperature, it transfers energy to the surroundings until they reach the same temperature. This will make its pressure fall slightly too, but still the pressure will remain higher than it was before compression.

The compressed gas, back at room temperature, can still transfer energy to other things by pushing the piston out. But the energy which it now supplies will be taken from the gas by cooling it down below room temperature.

Up next

Helpful language for energy talk

Conservation of Energy
Energy and Thermal Physics

Helpful language for energy talk

Teaching Guidance for 14-16

Some ways of talking about energy are clearer and more helpful than others.

Energy stores

It is helpful to talk about energy stores. A spring, or a rubber band, can rather obviously store energy. You do work to stretch them (or to squash the spring), and you can get back pretty much the same amount of energy when they relax. These then are two of the best iconic examples for grasping what ‘potential energy’ is all about. It is energy in a mechanical store.

Many students find the term ‘potential’ confusing. They think ‘potential energy’ is somehow different from actual energy. Talking about energy stores offers a way of deferring the term ‘potential energy’ until later, for students who choose to continue studying physics.

You can similarly feel energy being stored when magnets are pushed together or pulled apart.

The example nearly all textbooks give of potential energy is perhaps the most difficult of all. It is the gravitational energy of a lifted mass. Now the energy is said to be ‘in’ the lifted object – as for a spring it is said to be ‘in’ the spring. If you have the courage, you could say that the energy is stored between the Earth and the lifted object (in the gravitational field). The trouble is of course that an external examiner might score that truthful answer as wrong because specialist understanding is not required at this level.

Another kind of energy store is a mixture of fuel and oxygen. In this case bonds between carbon and oxygen atoms can snap shut, releasing energy in a fire or explosion. It is common to talk about just the fuel – for example petrol – as the energy store, but do remember that for this chemical spring to snap shut, there must be oxygen too.

There are a limited number of energy stores:

  • chemical (e.g. fuel + oxygen)
  • kinetic (in a moving object)
  • gravitational (due to the position of an object in a gravitational field)
  • elastic (e.g. in a stretched or compressed spring)
  • thermal (in a warm object)
  • magnetic (in two separated magnets that are attracting, or repelling)
  • electrostatic (in two separated electric charges that are attracting, or repelling)
  • nuclear (released through radioactive decay, fission or fusion)

Energy carriers (or pathways) and energy transfers

It is often helpful to think of energy being carried from one place to another. For example, light carries energy from the Sun to the Earth. Light is not itself ‘energy’ – it is after all an electromagnetic wave, or a stream of photons (however you care to look at it). But energy does travel with the light. The same is true of radio waves. In a microwave oven microwaves carry energy from the microwave generator to the interior of the food. Other kinds of waves carry energy too, for example ocean waves.

Electric current in a circuit is another energy carrier. It is helpful to think about a power circuit as a way of moving energy from one place to another. The National Grid distributes energy from a number of power stations, via the wires and cables, to homes and factories.

It is often handy to think of moving matter as carrying energy, too. A strong wind delivers energy to a wind turbine. But, equally often, it is better to think of the moving mass as storing energy. A train has to be given energy to get it moving, and energy has to be taken from the train to stop it. This is what we call kinetic energy.

Energy carriers (or pathways, or transfers)

  • mechanically (when a force moves through a distance)
  • electrically (when a charge moves through a potential difference)
  • by heating (because of a temperature difference)
  • by radiation (e.g. light, microwaves, sound)

With all of these, we are interested in the rate at which energy is being transferred and not the amount stored anywhere.

You can use flow diagram representations to strengthen the distinction between energy stores and carriers, for example:

There are some very important scientific ideas in this way of looking at things. Among them are:

  • that energy tends, in most cases, to spread from a more concentrated store to more dispersed stores; and that this makes it less useful for doing anything more
  • that the energy often ends up warming the environment

Visit School Science Review for two useful papers: Richard Boohan Making sense of energy and Robin Millar 'Teaching about energy: from everyday to scientific understandings':

School Science Review


Up next

Cooling corrections

Newtons Law of Cooling
Energy and Thermal Physics

Cooling corrections

Teaching Guidance for 14-16

Experiments that involve changing the temperature of a material and measuring that change are necessarily subject to energy transfers between that material or materials and the surrounding environment. These transfers will often not be accounted for and can cause inaccuracies. If the temperatures used are within 10°C or so of the surroundings, the inaccuracy is unlikely to be significant compared to other school laboratory errors. However, if you really want to make the correction, a number of methods can be used, all based upon Newton's law of cooling.

1

In some cases it is possible to cool an object before starting the experiment. You can arrange this so that its temperature difference with the surroundings is equal (but opposite in sign) after heating. It is then reasonable to assume that any energy transfer away from the object when it is above the temperature of its surroundings is countered by a energy transfer into the object when its temperature is below. This technique can be employed when mixing liquids, or when measuring the specific thermal capacity of metal blocks.

2

The formal Newton's law method assumes that the rate of loss of heat to the surroundings is proportional to the temperature excess above the surroundings, i.e.

dQdt = k(T-Troom)

  • Where Q is the quantity of energy transferred in a time t,
  • T Troom are the temperatures of the cooling object and the surroundings respectively,
  • and k is a constant of proportionality.

Measure the temperature of the object (block, calorimeter, etc.) at the time of start of the heating, t0. Read the temperature at about 30-second intervals until the maximum temperature has been passed and for a significant time after. The longer this time, the more accurate the correction.

Plot the temperature against time on graph paper. On the graph (indicated in diagram below), select times t1 and t3, equal times either side of the maximum temperature at t2. The energy transfer between t2 and t3 is given by integrating the equation above between these values to give:

Q = kk(T-Troom)dt

The right-hand side of this equation is proportional to the area under the curve of k(T-Troom) versus t, denoted by A2 in the diagram below.

The left-hand side, Q, the energy transferred to the surrounding in the interval (t3-t2, is proportional to ΔT3, the drop in temperature during this time interval.

Remember that Q = mcΔθ, where m is the mass of the cooling body, c is its specific thermal capacity, and Δθ is the drop in temperature.

Therefore Δt3 = KA2, where K is another constant.

Similarly, the drop in temperature due to cooling in the time interval between t1 and t2, is given by Δt2 = KA1. (Note that, since the mechanism by which cooling takes place is the same for times between t1 and t2 and between t2 and t3, the constant of proportionality will be the same for both regions.)

So ΔT2ΔT3 = A1A2

If T2 is the temperature observed at time t2, the temperature which the object would have reached had there been no thermal transfer to the surroundings is:

T2 + ΔT2 = T2 + ΔT3 (A1A2)

A1 and A2 can be measured by counting squares on graph paper.

Image courtesy of www.upscale.utoronto.ca/IYearLab/heatcap.pdf

3

If you are using a heater, a simpler method is as follows (courtesy of Frank Grenfell on the CAPT email discussion list):

  • Observe, (there is no need to record) the temperature as it rises, starting a tt0. Turn off the heater and record the time t1. You need this anyway to find the energy transferred to the object.
  • Keep the clock running.
  • Observe the temperature as it continues to rise, and reaches its maximum value (temperature Tmax) at time t2. Keep the clock running.
  • Record the temperature ( T ) after another 0.5 t2 (i.e. half as long again as it took to reach the maximum temperature).
  • The cooling correction to be added is (Tmax-T).
  • Reasoning. The rate at which energy is transferred to the surrounding while the block is being heated is roughly half what it is at Tmax. So if you observe the temperature drop from Tmax in a time interval equal to half t2, that should be about right.

Up next

Fundamentals

Conservation of Energy
Energy and Thermal Physics

Fundamentals: energy

Practical Activity for 14-16

A discussion by Jon Ogborn, emeritus professor of science education at the Institute of Education, London.

An intrinsic problem of teaching about energy at secondary level is that school science is obliged to try to run before it can walk. School biology and chemistry need to use the idea of energy before its physical meaning or its measurement in terms of force multiplied by displacement can be taught.

Teachers want and need to talk about the role energy plays in changes, but the idea that energy is conserved (first law of thermodynamics) is simply not enough to do the job. What they need are some ideas from the second law of thermodynamics.

It is no real surprise that the world is richer and more complicated than science textbooks make it appear. And it is no surprise that it takes a lot of skill, knowledge and creativity to find good ways to explain things simply to young people.

In the resource downloadable below, I offer a rough guide to the fundamental physics, using these subtitles:

  • What is energy?
  • Energy is conserved
  • Energy amongst the molecules
  • Free energy
  • Is energy needed for a change to happen?

and concluding with

  • Is there a better way to teach energy?

Resource

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The law of conservation of energy

Conservation of Energy
Energy and Thermal Physics

The law of conservation of energy

Teaching Guidance for 14-16

Energy is conserved. What does this really mean, and why is it true?

Water in a reservoir is more or less conserved. So the amount of water can always be calculated from the amount that was there some time ago, plus the amount that has come in, minus the amount that has gone out (you may have to take account of evaporation as well as water drawn off).

Another way of saying the same thing is that water can’t be made or destroyed. For there to be more, it has to come in; for there to be less it has to go out.

Energy is similar. If you take any volume of space, then the total energy inside that volume at a given time is always the amount that was there earlier, plus the total amount that has come in through the surface, minus the total amount that has gone out through the surface.

Another way of saying the same thing is that energy can’t be made or destroyed. For there to be more, it must have come from somewhere; for there to be less it must have gone somewhere else. This also means that energy is a calculable quantity. The practical teaching implication here is that it is important to do sums about energy changes – how much in, how much out – and not just to talk generally about it.

The conservation laws, such as the conservation of energy, give physics its backbone. They are not really statements of knowledge but they contain implicit assumptions and definitions. They are however tied to the natural world, and they contain experimental knowledge.

The emergence of energy physics

By the early 19th century, steam engines were widely used. Both physicist and engineers sought to understand them by developing a ‘theory of steam engines’. Through the 1840s, as part of this process, several key people developed the concept of energy and its conservation : Mayer, Joule, Helmholtz and Thomson.

Julius Mayer, a German physicist, was the first person to state the law of the conservation of energy, in an 1842 scientific paper. Mayer experimentally determined the mechanical equivalent of heat from the heat evolved in the compression of a gas (without appreciating that heat could be explained in terms of kinetic theory).

In 1847 another German physicist, Hermann von Helmholtz, formulated the same principle in a book titled On the Conservation of Force. By contrast with Mayer, Helmholtz did view heat as matter in motion. The idea of conservation arose from his interest in animal (body) heat. He may not have known about Mayer’s prior work.

Between 1839 and 1850 the English brewer James Joule conducted a remarkable series of experiments, seeking to unify electrical, chemical and thermal phenomena by demonstrating their inter-convertibility and their quantitative equivalence. His numerical results and conclusion were published in the Philosophical Transactions of the Royal Society with the title On the mechanical equivalent of heat.

William Thomson (later Lord Kelvin) took the next step, considering the problem of irreversible thermal processes, until that time simply a contradiction between Carnot and Joule. Carnot, in his 1824 theory of heat engines, had argued that heat could be lost; more recently Joule argued that energy was convertible from one form to another but could be destroyed. In Thomson’s 1851 scientific paper The Dynamical Equivalent of Heat, he contended that energy was "lost to man irrecoverably; but not lost in the material world". Thomson was thus the first person to understand that all energy changes involve energy dissipation.

From energy to thermodynamics

In the second half of the 19th century Thomson and other scientists (including Clausius, Rankine, Maxwell and, later, Boltzmann) continued to develop these ideas. Kinetic theory and the science of thermodynamics gradually became established, with energy conservation as its First law and energy dissipation as its Second law.

Up next

Cannons, steam engines and ‘caloric’

Energy Transferred by Heating
Energy and Thermal Physics

Cannons, steam engines and ‘caloric’

Teaching Guidance for 14-16

The idea of 'heat' is an everyday phenomenon, familiar even before fire-making. Aristotle discussed it as one quality among others, such as colour or smell. Mediaeval scholars discussed ‘degrees of heat’ but only with the development of thermometers during the 17th century did it become possible to quantify the study of 'heat'. The Scottish professor Joseph Black (1728 – 99) was the first to distinguish between temperature and 'heat', or, as we would now say, energy stored thermally. 

By the 18th century it was generally thought that 'heat' was an invisible and weightless fluid, called ‘caloric’. In 1760 Black had conducted sufficient experiments to conclude that there was a different heat ‘capacity’ for each substance. In 1781 the Swedish scientist Johann Carl Wilcke independently came to the same conclusion. Black went on to measure water’s latent heats of fusion and of vaporisation.

The first person to seriously challenge the caloric idea was Benjamin Thompson, a founder the Royal Institution who in 1791 became Count Rumford. As director of the Munich arsenal, Rumford noticed that boring cannons produces a great heating effect, especially if the boring tool is dull. Rumford argued that the supply of 'heat' was limitless, showing that a boring drill would continue to boil water so long as the horses driving it kept moving. This is more easily explained by a mechanical theory of 'heat' than the caloric (fluid) theory.

But the fluid theory was still needed to explain 'heat' transfers, and so it prevailed for many decades. In France the publication of Joseph Fourier’s mathematical theory of heat conduction in 1822 did not rely on caloric theory yet Sadi Carnot’s 1824 theory of steam engines did. When explaining how heat engines did mechanical work, Carnot mistakenly assumed that caloric ('heat') is a conserved quantity.

Finally in the 1850s William Thomson (later Lord Kelvin) and Rudolf Clausius modified the Carnot theory and began to convince others that energy is conserved (not 'heat'). As kinetic theory became established, so caloric theory withered and died.

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