Efficiency
Energy and Thermal Physics

Measuring energy transfers

for 14-16

Experiments in this collection introduce the SI unit for energy measurement (the joule) and provide a variety of simple examples where energy transfers can be measured.

Up next

Defining the 'joule'

Efficiency
Energy and Thermal Physics

Defining the joule

Practical Activity for 14-16

Demonstration

Introducing the concept of conservation of energy and a definition of the joule.

Apparatus and Materials

    Steps 1,2 and 4:
  • Masses, 1kg, 2
  • Wooden lath, 1 m
  • Shelves, 3, equally-spaced, e.g. on the lab wall
  • Motor/generator unit
  • Line shaft unit and string
  • Low voltage power supply, set at 6 V
  • G-clamps, 5cm, 2
  • Step 3:
  • Bricks, 2
  • Strong cardboard box
  • Retort stand
  • Single pulley on clamp
  • G-clamp, 10cm
  • Length of strong cord
  • Metre rule
  • Step 5:
  • Retort stands and bosses, 2
  • Nail, 15cm, 2
  • S-hook
  • Compression spring
  • G-clamps,10cm, 2
  • Single pulley on clamp (If it is difficult to clamp the stands on the bench, a large board can be placed on the bench to carry everything).
  • Slotted masses, 6 x 100 g

Health & Safety and Technical Notes

The hazard presented by these activities is that of working at heights. No one must stand on a stool or bench to set up the apparatus on a high shelf. If apparatus (e.g. motor and line shaft unit) can be clamped onto the shelf at bench level, it can be lifted into place by two tall persons standing on the floor. The shelf supports must be rigid. Otherwise, the demonstration(s) must be done from the floor level.

Read our standard health & safety guidance


The 1-m wooden lath should be marked in centimetres, like a ruler. A metre rule with very clearly marked centimetre lines is an alternative.

For step 4 you should fit the three shelves approximately 1/3 metre apart, so that the top shelf is at the same height (about 1 metre) as in step 1.

Procedure

  1. Fix one shelf approximately 1 metre above the bench top. Lift the 1kg load from the bench to the 1m shelf. Refer to the teaching notes below for a possible script.
  2. Clamp the dynamo unit to the shelf, with the line shaft unit clamped beside it. Secure one end of a length of cord to the axle of the line shaft. Attach the other end to the 1kg load on the bench-top. When you connect the motor to the supply, it will wind up the 1-kg to the shelf height.
  3. You can use a brick or a block of wood to represent a lift. Alternatively, a more realistic model can be made by using a cardboard box strong enough to take a brick, or two bricks on end, side by side. The retort stand base should be fixed to the bench with a G-clamp. Fix the pulley to the top of the stand, pass the cord over the pulley, and tie it around the cardboard box to form the lift. Raise the load from the bench top by pulling on the cord and raising the model lift.
  4. Lift the 1kg from one shelf to the next, reaching 1 metre high, but in three equal steps. (See the teaching notes on adding energies.) NB Clamp the stands to the bench.
  5. Use the G-clamps to clamp two retort stands about 50 cm apart on the edge of the bench. Use a boss to anchor one end of the compression spring to one of the retort stands. Use a second boss to attach the nail to the other retort stand as an anchoring pin.
  6. Clamp a pulley to the end of the bench. Pass the string over the pulley, tying one end to the brick resting on the floor, and the other to the S-hook attached to the end of the spring held by the nail. Stretch the spring horizontally and anchor the free end to the nail.
  7. Connect the spring to the string, using the S-hook. When you release the spring, the load will be pulled up by some distance. The spring and load must be such that the tension produced when the spring is stretched is sufficient to lift the load.

Teaching Notes

  • Teachers and students often take it for granted that energies can be added together like masses. It is a basic property at the root of all ideas of conservation of energy. These demonstrations reinforce this principle.
  • Step 1 is the starting point. This is defining the job we want to get done (lifting the load).
  • Step 2 emphasizes the need for a fuel of some sort by using an electric motor to do the same job.
  • In step 2 the electric motor transfers the same amount of energy as in step 1 when it winds the kilogram up to the shelf. (The speed might drop as the layers of string increase the effective winch diameter). The energy is stored gravitationally in the load.
  • Instead of lifting the load by hand you could use an electric motor for the job. You would then have to pay for the fuel that the power station uses. If a person is used to raise the bricks, then they will need to be given extra food in order to do the job.
  • In step 3 students may be distracted by the very obvious manual method of step 1. Emphasize that whatever way we raise the load, fuel is needed from somewhere. If by hand, fuel comes from the food we eat.
  • "When I haul up this model of a lift, do I use fuel? I certainly don't take in petrol or coal but I do eat food. If I had to do a lot of hauling I should get very hungry and have to eat more."
  • "As you are learning in biology, the food you eat goes to provide many things that you need: keeping you warm, mending damaged tissue, producing growth and providing energy for movement. Some chemicals in food provide fuel to run your muscles like an engine. When you haul up a load, your muscles burn some of those chemicals hauling up the load and heating your body. When your muscles work you are drawing on fuel, (chemicals), which came from your food."
  • In step 4 introduce the concept of adding energies. Show that the same job is done whether it is achieved in one step, or broken down into stages. This is the point at which to introduce the term joule.
  • "Suppose I now lift one kilogram up a 1/3 metre step, then a second 1/3 metre step and finally a third 1/3 metre step. How will this compare with the amount of fuel needed to raise the one kilogram through 1 metre in one go? The same amount of food would be needed for both jobs."
  • In step 5, show that the energy can be stored in a spring, just as it is stored in the food we eat. The spring does not pull all the way back to its original unstretched length because the load is applying a force to the spring. Some of the energy ends up stored elastically in the stretched spring and some stored gravitationally in the raised load.
  • Introducing the joule: "At the Earth's surface one kilogram has a force on it of about 10 N. When it is raised one metre we say that 10 J ( 10 joules) of energy have been transferred, or shifted, so that it is stored gravitationally. Two kilograms raised through one metre means that 20 J of energy is stored gravitationally. Two kilograms raised three metres will store 60 J gravitationally."

This experiment was safety-tested in November 2005

Up next

Shift a joule

Efficiency
Energy and Thermal Physics

Shift a joule

Practical Activity for 14-16

Demonstration

Students ‘experience’ forces and reinforce their understanding of force and energy units.

Apparatus and Materials

Health & Safety and Technical Notes

Read our standard health & safety guidance


If you do not have a forces demonstration box, simply use a 100 g bag of beans (weight about 1 N) on a string over a pulley. Students pull the string out by 1 m to experience 1 joule of work.

Procedure

  1. Let students pull each of the masses in turn and ‘feel’ the pull of the Earth on masses of one pound, one kilogram and 102 grams. (1 lb-wt, 1 kg -wt and 1 newton.)
  2. If you leave the box available in the lab over a period of weeks, students can return to it to reinforce their knowledge. It also avoids a queue, which would be wasteful if all the class had to try the forces in one session.

Teaching Notes

  • This piece of equipment is very useful to have around the laboratory so that students get a feel for force and energy units. The Imperial units are included as a few students may be more familiar with a pound mass, but you can omit if it is more likely to confuse.
  • The pull of the Earth on any body is a force. This is known as the weight of that body. The pull of the Earth on a mass of 102 g is 1 newton and on a mass of 1 kg is about 10 N (9.81 N). The weight of an apple is about 1 N.
  • The joule is a secondary unit. It depends on the units of force and distance, and so it is a difficult concept for beginners to grasp. Joulemeters, which read in joules directly, have been developed for measuring the transfer of energy from an electrical supply to a heater, just like the electricity meters in the home. But there is nothing so convenient for measuring transfers from mechanical work.

This experiment was safety-tested in November 2005.

Up next

Increasing a gravitational store

Efficiency
Energy and Thermal Physics

Increasing energy stored gravitationally

Practical Activity for 14-16

Demonstration

Using a dynamics trolley on a steep ramp, where the energy transfer is not easily measured.

Apparatus and Materials

  • Dynamics trolley
  • Pulley, single, on clamp
  • G-clamps, 4
  • Cord
  • Length of angle iron, 2
  • Hardboard sheet, approx 3 m x 300 mm
  • Mass, 1 kg

Health & Safety and Technical Notes

It is important to have the board supports very stable so that the system cannot collapse as students gather round it to watch. A trolley catcher might also be required.

Read our standard health & safety guidance


Clamp one end of the strip of hardboard to the bench-top. Raise the other end about 0.75 cm and rest it on two 1.25 lengths of angle iron (Handy Angle or Dexion, used in rack storage systems). Clamp the board to the bench again about halfway along its length as in the diagram. This arrangement needs to be very secure.

Cut a vertical slit, not more than 1 cm wide, in the middle of the board. Pass a cord through the slit without touching the hardboard and, keeping it parallel to the bench-top, pass it over a pulley secured to the edge of the bench. Tie a loop (about 1/2 m long) in the end of the cord that goes through the slit. Pass the other end over the pulley and fasten it to a 1 kg mass. Hang the loop loosely over two bent posts as shown. The part of the loop that is not suspended between the posts should lie flat on the board (so that the trolley can run over it).

A dynamics trolley with a single peg in the top is released from the top of the ramp, with the single wheel end leading, and the single peg at the rear. The peg engages the loop after the trolley has run over those parts of the loop that are on the board. The trolley is brought to rest, raising the 1 kg mass.

Before you release the trolley, check that its leading end will pass under the raised part of the loop, so that the loop may be engaged by the peg.

Have the minimum of slack string between the slit and the mass, so that the mass starts to rise as soon as the loop is engaged.

Procedure

  1. Hold the trolley at the top of the slope and let it run down the board. The peg should catch the loop of cord so that the trolley is brought to a halt by the tension in the cord connected to the 1 kg mass.

Teaching Notes

The energy of the trolley stored kinetically is transferred to the the rising mass, increasing the energy stored gravitationallly. Use E=mgΔh to calculate the energy stored gravitationallly by the trolley at the start of its fall and compare it with the energy stored gravitationallly that was transferred to the mass. Typically, only 50% of the energy of the trolley stored kinetically will transfer to the mass. Point out to students that energy must have been dissipated (stored thermally in the surroundings) because of conservation of energy.

This experiment was safety-tested in January 2006

Up next

Trolley and falling mass

Efficiency
Energy and Thermal Physics

Trolley and falling mass

Practical Activity for 14-16

Class practical

Measuring the energy stored gravitationally transferred so as to be stored kinetically in a dynamics trolley.

Apparatus and Materials

  • Ticker-tape
  • Pulley, single, on clamp
  • Dynamics trolley
  • Runway
  • Ticker-timer
  • Mass hanger and slotted masses (100 g)
  • Balance, 5 kg
  • Thread
  • Knitting needle or length of glass tube

Health & Safety and Technical Notes

Long runways or heavy shorter ones should be handled by two persons. Ensure that a buffer is tied across the bottom of the runway, to prevent the trolley falling onto anyone.

Read our standard health & safety guidance


Procedure

  1. Clamp the pulley to the end of the runway. Compensate it for friction in the normal way. Do this by raising one end of the board so that the trolley, once started, will continue at constant speed as judged by the equal spacing between ticker-tape dots. See the experiment:

    Compensating for friction


  2. Attach a length of thread to the trolley. Thread it over the pulley and tie it to the mass hanger. The length of thread must be long enough for the mass hanger to hit the ground well before the trolley reaches the end of the runway.
  3. Attach a length of ticker-tape to the trolley. Pass the other end through the ticker-timer. See also the experiment:

    Using the ticker-timer to measure time


  4. Release the trolley, so that the falling mass accelerates it until the mass hits the ground. After this, the trolley will move with constant velocity v.
  5. Estimate the value of v from the ticker-tape. Measure the mass of the trolley on the balance.
  6. Calculate 1/2 mv2.
  7. Compare this with the change in energy of the load stored gravitationally, Δ E = m × g{Δ{h}

Teaching Notes

  • The energy stored gravitationally in the load end up being stored kinetically in the trolley. Students should consider the start point of the load at its lowest point and end point of the load at its highest point. At the end point the load itself will be moving, so there will be some energy stored kinetically in the load and in the trolley. However, if the mass of the load is very small compared to the mass of the trolley then the energy stored kinetically will be (almost) negligble.
  • Students are likely to be disappointed when they find that the values for 1/2 mv2 and Δ E = m × g{Δ{h} do not agree. You will need to discuss the results. How reliable is the experiment? Where do students think that the energy might have been transferred to? Some energy will be stored thermally s, e.g. warming the pulley, and the wheel bearings, the air.
  • It is impossible to demonstrate the principle of conservation of energy for thermodynamic reasons. As a result of friction, energy will always be stored thermally in the surroundings. However, if the demonstration is carried out slowly, and as many energy losses as possible are accounted for, then the two values should be close enough to satisfy the students.
  • The experiment can be repeated but in reverse, using the trolley to raise the load.
  • Compensate the runway for friction the opposite way round. The thread should be attached to the trolley and carry a 100 g weight hanger as before. This time start the trolley at the end of the trolley board nearest the pulley, with the thread slack. Because the thread is slack it will not stay in a pulley groove, and so a length of glass tube or knitting needle should be used as a roller. The ticker-tape is also fixed to the reverse end of the trolley so that it runs out behind the trolley and passes through the ticker-timer.
  • This time when the trolley is given a push, it travels with constant velocity v down the compensated runway until halfway down. Then the thread goes taut and the load is raised a distance d as the trolley comes to rest. The decrease in the energy stored kinetically is compared to energy stored gravitationally.
  • This experiment could be extended into a series of readings for different loads and different distances of fall. This would provide different values of v in 1/2 mv2.
  • The mass of the trolley, m , could also be changed. Students could plot graphs to show relationships between d and v 2, and graphs for different masses.

This experiment was safety-tested in August 2007

Up next

Stretched elastic band: an elastic store of energy

Elastic Potential Energy
Energy and Thermal Physics

Stretched elastic band: energy stored elastically

Practical Activity for 14-16

Class practical

Comparing the energy stored in a stretched elastic band with the energy stored kinetically in a dynamics trolley.

Apparatus and Materials

  • Dynamics trolley
  • Runway
  • Ticker-tape
  • Ticker-timer
  • Elastic band
  • Forcemeter

Health & Safety and Technical Notes

Long runways or heavy shorter ones should be handled by two persons. Ensure that a buffer is tied across the bottom of the runway, to prevent the trolley falling into anyone.

Read our standard health & safety guidance


The runway must be adapted, as described in the experiment:

Energy stored by a moving trolley


...so that there is a catapult at one end. This is made with an elastic band stretched between dowel rods.

Procedure

  1. The runway should be compensated for friction. See the experiment:

    Compensating for friction


  2. Set up the catapult towards the upper end of the runway. Do this by stretching a 10 cm elastic band taut between two dowel rods. This should be at a height that will engage the vertical rod on the trolley firmly.
  3. Pull the trolley back so that the rubber band stretches. Measure the distance that the trolley has been pulled back from its initial point in increments of 1.0 cm. Energy will be stored elastically in the catapult. Release the trolley and obtain a ticker-tape record of its constant velocity. Calculate the energy stored kinetically = 1/2 mv2.
  4. Repeat the experiment, obtaining ticker-tape records for the trolley after it has been pulled back through various known distances. See also the experiment:

    Using the ticker-timer to measure time


  5. Pull the trolley back from the initial mark with the forcemeter. Note the forcemeter reading at 1 cm intervals, for a range of distances covering the distances used to obtain the ticker-tape records.
  6. Plot a graph of ‘force’ against ‘distance pulled back’ as shown in the diagram.

Teaching Notes

  • This experiment is not easy. Students should not expect more than general agreement between the energy stored elastically and energy stored kinetically.
  • Stopwatches and metre rules, or light gates, could be used instead of tape and timers.
  • On the graph of force against distance pulled back, a small part of the distance pulled back is selected and vertical lines drawn up to meet the curve. The area of that small section gives the force x distance pulled back. This is the energy stored chemically (fuel + oxygen) in muscles that is transferred to the elastic band, in stretching the band that small distance.
  • Count the squares to work out the total area under the graph from the beginning of the loading process, when the forcemeter begins to extend the rubber band, to the total distance pulled back. This gives the energy stored elastically in the rubber band for that particular distance pulled back. When the elastic band is extended by the trolley pushing into it and then the trolley is released, this energy stored elastically in the elastic band will be stored kinetically in the trolley.
  • If a spring were used instead of a rubber band, the shape of the graph would be a straight line. Instead of working out the area under the graph by counting squares, it could be calculated as 1/2 x force x distance pulled back because the area under the graph would be a triangle.
  • Compare the values for the energy stored elastically and energy stored kinetically. Discuss why they might not be equal (e.g. energy is stored thermally as the rubber band heats up).

This experiment was safety-tested in November 2005

Up next

A trolley started and stopped by catapults

Efficiency
Energy and Thermal Physics

A trolley started and stopped by catapults

Practical Activity for 14-16

Class practical

Comparing the energy stored by two rubber bands.

Apparatus and Materials

  • Dynamics trolley
  • Runway
  • Forcemeter
  • Rubber bands
  • Light gates and electronic timer (optional extension)
  • Balance (optional - to find mass of trolley)

Health & Safety and Technical Notes

Long runways or heavy shorter ones should be handled by two persons. Ensure that a buffer is tied across the ends of the runway, to prevent the trolley falling onto anyone (if necessary).

Read our standard health & safety guidance


The runway must be adapted, as described in the experiment...

Energy stored by a moving trolley


...using a runway with a catapult at each end.

Procedure

  1. The runway should be compensated for friction. See the experiment:

    Compensating for Friction


  2. Pull one of the catapults back from its rest position with the forcemeter. Note the forcemeter reading at 1 cm intervals for the range of distances that will be used in catapulting the trolley.
  3. Repeat this calibration for the second catapult.
  4. Project a trolley from the one catapult to the other. Note exactly how far the trolley is pulled back before release. Note how far the second catapult is pushed back to stop the trolley. Compare the energies stored elastically in each catapult.
  5. An extension experiment is to calculate the energy stored kinetically by the trolley, 1/2 mv2
  6. Do this by measuring the trolley's velocity (using a stop watch, light gates or ticker-timer) and mass, and comparing this with the energies stored elastically.

Teaching Notes

  • When a catapult is pulled back by the trolley and released, the energy stored elastically in the rubber band is then stored kinetically in the moving trolley. When the trolley stretches the opposite band, the energy stored kinetically is then stored elastically in the second band, and the trolley comes to a stop briefly. If both rubber bands are similar then the two ‘distances pulled back’ will be the same, showing that all the energy stored elastically in the first rubber band is now stored elastically the second.
  • If the rubber bands are not identical, the energy stored elastically in the bands will have to be calculated from the area under a force / ‘distance pulled back’ graph as in the experiment:

    Stretched elastic band: energy stored elastically


This experiment was safety-tested in November 2005

Up next

Moving an object across the table

Efficiency
Energy and Thermal Physics

Moving an object across the table

Practical Activity for 14-16

Demonstration

To move along a horizontal plane there is no net change to the way energy is stored.

Apparatus and Materials

  • Runway
  • Dynamics trolley
  • Pulley, single, on clamp
  • Bosses, 8
  • Retort rods, 3
  • Retort stands, 2
  • Hanger, 10 g mass
  • Platform, wooden, approx 5 cm x 25 cm
  • G-clamp
  • Thread

Health & Safety and Technical Notes

Long runways or heavy shorter ones should be handled by two persons. Ensure that a string is tied across the bottom of the runway, to prevent the trolley falling onto anyone. At least one retort stand should be clamped to the bench.

Read our standard health & safety guidance


Procedure

  1. Compensate the runway for friction. See the experiment:

    Compensating for friction


  2. Half-way along the runway, place a retort stand (preferably 100 cm high) on each side. Connect a single rod between the tops of the retort stands. Suspend a pulley on a clamp at the centre, so that the pulley runs freely, with the plane of the pulley parallel to the runway. Fix a simple wooden platform between the retort stands, about 30 cm below the pulley.
  3. Lower down the retort stands, fix two rods parallel to each other and close together across the runway as illustrated. These must be at such a height that a trolley moving along the runway will just clear them. At least one of the retort stands should be clamped firmly to the bench with a G-clamp.
  4. Join a length of thread to the 10 g mass hanger on the wooden platform and over the pulley, down between the double rods, and fasten it to the trolley. The thread should be just long enough for the trolley to be about 30 cm from the parallel rods.
  5. Pull the trolley back so that the weight hanger rises to the pulley. Release the trolley. It is pulled by the descending mass for the first 30 cm of its travel and then proceeds at constant velocity. Towards the end of its run, the thread tightens and the mass is hauled up again. Ideally, it should rise to its original position.

Teaching Notes

  • It is essential to arrange this so that energy dissipated is reduced to a minimum. The mass of the load should be quite small by comparison with the mass of the trolley, so that the energy dissipated when the load hits the platform is small.
  • Living in a world where there is plenty of friction, students are likely to think that work must always be done to move an object from one place to another at the same horizontal level. A force is needed to keep an object moving with a steady speed to overcome the frictional force. Demonstrations with CO2 pucks on a glass plate refute that, as the contact is almost friction-free.
  • Other experiments should support the story of no work being needed to move across a table. Students can accept that the energy of a brick stored gravitationally at one end of the table is the same as its energy of a brick stored gravitationally near the other end. They will agree that, if the brick is at rest in the first position and again at rest in the second position there is no energy in the stored kinetically, and that the energy stored gravitationally has not changed. Yet they will feel uneasy if you say that there has been no change to the way or ways that energy is stored due to the journey from one position to the other.
  • In fact, unless you are prepared to allow infinite time for it, the journey does require the shifting of some energy, temporarily. To get across, in reasonable time, the brick must move quite fast and energy must be stored kinetically in the brick. So to transport it so energy has been shifted from somewhere; but at the end of the trip that energy can be shifted back.
  • Ideally the load would be hauled up just as far at the end as it fell at the beginning. This would demonstrate that the same initial energy stored gravitationally is transferred to be stored kinetically, and then is stored gravitationally at the end. Unfortunately there is not only friction but an unavoidable inelastic collision when the thread pulls taut. Also, unless the mass of the falling load is a very small fraction of the mass of the trolley, energy is stored kinetically in the load itself, which will be stored thermally in the platform when it hits it. The platform heats up. Altogether there will be a much smaller rise than the original fall of the load.
  • If the load rises to a height that is as low as 60 per cent of the original height, the experiment is not worth doing.

This experiment was safety-tested in November 2005

Up next

Using an electric motor to raise a load

Efficiency
Energy and Thermal Physics

Using an electric motor to raise a load

Practical Activity for 14-16

Demonstration

An electric motor lifts a load.

Apparatus and Materials

  • Switch unit (very useful to break circuit quickly)
  • Line shaft unit
  • Motor unit
  • Demonstration meter, 0 - 5 amp DC
  • Rubber band or driving belt
  • Cord
  • Mass, 1 kg
  • Power supply, 0–12 V

Health & Safety and Technical Notes

Read our standard health & safety guidance


The mass you select as the load must be suitable for the size of motor you have available.

Procedure

  1. Clamp the motor unit next to the line shaft unit and connect their pulleys with a rubber band or driving belt.
  2. Secure a length of cord to the axle of the line shaft and attach the other end to the chosen mass.
  3. Connect the motor to the power supply in series with the demonstration meter.
  4. Read the ammeter when the load is being lifted and compare this with the reading obtained when the motor is running light (that is, when disconnected from the line shaft}.

Teaching Notes

  • In this demonstration the current flowing in the motor produces a force that lifts the load.
  • When analysing the situation in terms of energy it is helpful to be clear about start and end points.
  • Before the motor is turned on, there is more energy stored chemically in the battery or the fuel (and oxygen) in the power station.
  • When the load has been lifted and is stationary, there is more energy stored gravitationally in the load, and a small amount is stored thermally in the surroundings due to heating in the wires, heating of the air, heating due to the effects of friction.
  • At a point, say halfway, when the load is moving at a steady speed, then there is energy is stored kinetically and gravitationally in the load, stored kinetically in the motor, and stored thermally in the surroundings.
  • It is important to point out that these changes are happening concurrently and not consecutively.
  • The energy stored kinetically only increases or decreases when there is a change of speed.
  • The current increases as the load increases showing that a bigger force needs to be used to raise greater loads. More work is done. More energy is stored gravitationally.
  • Even when the motor is running light with no load connected to it, a current flows and the motor turns. The energy stored chemically in the battery or fuel (and oxygen) is decreasing. You might ask students: "Where does this energy get transferred to?" The answer is that it warms up the motor, and the surroundings. Energy is now stored thermally.
  • You can analyse the energy transferred using the following equations:
  • Energy transferred by the electric current, E = I x V x t
  • Change in energy stored gravitationally, E = m x g x change in h
  • If you measure these, it is very unlikely that the two will be equal enough to satisfy students because of the energy losses (dissipated) in the system, but they could be used to measure the efficiency of the energy transfer.
  • Efficiency = (m x g x change in h /I x V x t) x 100%

This experiment was safety-tested in August 2007

Up next

Trolley collisions

Efficiency
Energy and Thermal Physics

Trolley collisions

Practical Activity for 14-16

Demonstration

Collisions between trolleys that result in energy being dissipated to the surroundings.

Apparatus and Materials

  • Dynamics trolleys, 2
  • Elastic cords, 2
  • Large pin and cork

Health & Safety and Technical Notes

In place of the elastic cords, a weak spiral spring of good steel wire can be used.

Read our standard health & safety guidance


Procedure

  1. Place the two trolleys on the bench with one or two elastic cords held between them, secured over a wooden dowel post on each of the trolleys. Start with the trolleys close together and the elastic slack. With a hand on each trolley, give them outward motions and let go so that they move apart. The elastic will stretch and bring them to rest for an instant. At this point, hold the trolleys in that position and ask where the energy is stored. Release the trolleys so they move towards each other and collide.
  2. Now start with the trolleys well apart and the elastic stretched. Release them so that the trolleys meet with a bang. Again ask where the energy is stored.
  3. Repeat with a large pin sticking out of the end of one trolley and a cork attached to the other so that the trolleys stick together on collision. (To fix the cork, it may be easier to fix a pin on each trolley and then fix a cork on one of the pins beforehand.}
  4. Repeat 3 using the trolleys with the sprung buffer-rods protruding from them. When the trolleys collide, they will now rebound apart, be stopped by the elastic, return and collide again. This process will be repeated several times before they finally come to rest. Again, discuss where the energy is stored.

Teaching Notes

  • When the trolleys are moved apart energy stored kinetically is transferred to the cords connecting them, storing energy elastically. Releasing the trolleys, the energy in the stretched cord is transferred to the trolleys, storing energy kinetically.
  • When the two trolleys collide they come together with a bang; energy stored kinetically is now stored thermally in the surroundings. The energy stored kinetically is not conserved. Collisions of this type are called inelastic. The energy has been transferred by sound waves and dissipated by warming up, and maybe deforming, the colliding trolleys.
  • Spring buffers between the trolleys: As the trolleys collide energy stored kinetically is transferred to the springs as the trolleys briefly come to rest, and energy is stored elastically. The process reverses and the energy stored elastically in the compressed spring is transferred to the trolleys, storing energy kinetically. The trolleys will oscillate backwards and forwards a few times. Ultimately, the trolleys will come to rest as all the energy stored kinetically is transferred to the environment, storing energy thermally so as to warm it up.
  • In some collisions, the energy stored kinetically before and after is exactly the same. These are called elastic collisions. Collisions between molecules in air are elastic, for example.

This experiment was safety-tested in November 2005

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Human energy - food and exercise

Efficiency
Energy and Thermal Physics

Human energy, food and exercise

Practical Activity for 14-16

Class practical

Considering the energy stored in foodstuffs and the energy demanded by human activity.

Apparatus and Materials

Data in the tables below.

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. You should display or provide the data from table A: energy stored in food. Information given on the packet tells you the energy stored in different foods. Students can be asked to compare the energy stored in different foodstuffs.
  2. Display or provide the data from the next two tables, Table B (human energy demands) and Table C (data for a coal miner). The miner was 32 years old, 1.75 m tall and had a mass of 67 kg.

Table A: Energy stored in food

FoodEnergy value (kcal /100g)Energy value (kJ /100g)
butter4992,087
sugar3891,627
white bread2661,112
margarine6202,590
potato, baked89372
MacDonald's hash browns2571,075
hamburger (no cheese)2751,150
fried fish221924
oranges, raw47196
lentils, boiled116485
carrots, raw41171
eggs, fried201840
cheese pizza 14"2571,075
hocolate chip cookies, low fat4531,895
cola carbonated drink37154
corn flakes, breakfast cereal3601,506

Table B: Human energy demands

PersonEnergy required (kJ/day)
Child (either sex)
0 to 1 yr4,185
2 to 6 yr6,278
7 to 10 yr8,370
TeenagerMalesFemales
11 to 14 yr11,50011,500
15 to 19 yr14,65010,460
Adult (20 yrs and over)
lying in bed7,3246,278
light work11,5009,420
heavy work14,65012,550
extremely heavy work20,925

Table B: Data for a coal miner

ActivityEnergy needed (kJ/minute)
resting in bed3.9
washing, shaving, dressing13.8
walking20.5
standing7.5
cycling27.6
digging coal28.0
shovelling coal26.9
walking (in coal mine)28.0

Teaching Notes

  • From Table A, you might ask students to calculate the energy stored in a recent day's food. They will need to know the approximate mass of a normal serving.
  • From Table B you might ask students how much energy they need each 24 hours. The answer depends very much on the sort of person, particularly age and occupation. Table C gives some data for a very physical job.
  • The data in these tables could be displayed by a data projector, issued as worksheets, or prepared as wall charts to be left in the classroom or laboratory.

This experiment was safety-tested in January 2006

Resources

Download the PDF of the tables.

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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

Measuring energy transfers

Conservation of Energy
Energy and Thermal Physics

Measuring energy transfers

Teaching Guidance for 14-16

In physics, there is a standard way to work out how much energy has been transferred. It is to calculate the work done.

Work is done when an applied force causes something to move in the direction of the force.

ΔE = work done = force x distance moved in the direction of the force.

Notice that no energy is shifted in the two situations below:

  • when an object rests on a shelf – although the object has weight, there is no movement.
  • if the force is perpendicular to the direction of movement - e.g. a satellite in orbit around the Earth.

This equation leads to the definition of the SI unit for energy, the joule: 1 joule is the work done when a 1 N force moves through a distance of 1 m.

For example, a motor or a human arm might raise kilogram masses onto different height shelves. The change in energy stored gravitationally can be calculated using the formula,

ΔE = weight x Δh =mgΔh, where Δh is the vertical distance a mass m has been raised, and g is the gravitational field strength.

Energy and the human body

However, there is more than this to working out how much energy has been transferred. When you lift bricks your body also gets warmer, due to the energy from digested food. It does not look as if there is any “force x distance” here. But the energy that is transferred by heating to make it warmer can be calculated in this way, and can be measured in the same unit, joules. (See food packets, labelling portions in kJ.)

Human beings are only about 25% efficient for doing mechanical jobs. For every 1,000 joules of energy which are transferred from fuel stored in muscles, only 250 joules are transferred to raising a load or doing some other kind of job. 750 joules are stored thermally (the body warms up). Thermodynamics shows that muscles could be more than 70% efficient in transferring their energy to do useful jobs, but only if the action was conducted infinitely slowly. So when estimating the useful energy transferred from energy stored in food to muscles in order to climb the stairs, for an eight hour day, then the answer needs to be multiplied by four to find the demand on food.

When a 1kg mass is raised by a height of 1 metre, then 10 J of energy is now stored gravitationally . This can be obtained from four grains of sugar, a mini-snack. One grain of sugar is for doing work to raise the load, and three grains are for heating the room. If you raise 1 kg through a height of 1 m every second requiring 1 mini-snack per second then this is about 10 grams of sugar per hour. Not enough to allow you to eat a cream-cake or a bar of chocolate without putting on weight (i.e. mass)!

Transferring energy electrically

Energy transferred electrically is calculated using the equation ΔE = IVt , where I is the current, V is the potential difference and t is time.

Heating with friction

In frictional rubbing, a force moves over a surface, but just makes it hot. You measure the rise in temperature of the material, and how much of it is warmed up. Then, next time something gets warmer, you know what amount of “force x distance” or work would have been needed if the warming up had been done in this way.

Sooner or later you’ll need to tell a story about what “getting hotter” means, in energy terms. It just means that the invisible atoms or molecules are moving about faster. Energy is stored kinetically by a large number of molecules. And it isn’t easy to claim it back again, because they have shared it out randomly amongst a huge number of particles.

There are plenty of practical examples of friction making something hotter. Car (or bicycle) brakes are a case where we want to transfer the energy of a moving car stored kinetically as speedily as possible. Exercise bicycles let students feel how what seems a large amount of mechanical work done produces only what seems like a modest heating effect.

A key teaching point is not to let ‘friction’ become a kind of excuse for things not working properly. It’s the way that the work done by forces ‘gets inside’ matter.

Up next

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.

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Doing energy sums

Efficiency
Energy and Thermal Physics

Doing energy sums

Teaching Guidance for 14-16

Including simple sums about energy and power is very important. It introduces the units that are in practical use, without much formality. It introduces both energy and power (rate of energy supply or use; a bit of trouble taken early over amount and rate of change will be repaid later).

  • Nearly all foods are now labelled with their ‘energy content’ (how much energy is liberated when they are digested). Valuable energy lessons can be taught based on diet energy calculations.

An active grown man needs around 2,000 kilocalories per day (about 8400 kJ per day). Women generally need a bit less. The energy has to come from ‘burning’ food in the body. Most of this energy is ‘wasted’ through cooling (humans run at about 100 W). Only a relatively small fraction is expended in physical activity. (Note the dietary Calorie is a kilocalorie.)

  • Heating water makes a useful start on measuring amounts of energy. An electric kettle is marked with the rate at which it delivers energy – its power. This is in watts, and is often about 2 kW. Multiply by the number of seconds it is switched on for, and you have the number of joules delivered. [Avoid calculating energy exchanges from electrical equations at an early stage.]

Heating a kettle of water to boiling point takes about 0.5 MJ, for example. Leaving a 100 W lamp on for 3 hours uses a bit more than 1 MJ. It’s worth comparing this with the amount of energy provided by a single meal.

  • Collect from the class examples of household fuel bills: gas, electricity, oil. They can show how much energy is transferred to the home, and give pointers to where savings might be made.

The fuel bill for gas tells you how many cubic metres of gas you have burned. The bill for oil tells you how many litres of heating oil have been put in your tank. The electricity bill tells you how many kilowatt hours you have used. But all of them also convert these amounts to a common unit: say megajoules. [Note that 1 kW hour is 3.6 MJ]

The fact that all fuel uses can be expressed in a common unit reflects the deeper fact that fuel sources are interchangeable as far as energy is concerned. Heating a bath full of water by burning oil or by using electricity uses the same amount of energy for the water, even though the two methods may waste different amounts by letting energy leak elsewhere.

The teaching trick is to use the units for electricity supplies to give the units for energy and power:

Power = rate of supply of energy

1 watt = 1 joule per second

1 kW = 1000 J per second (1 kJ per second)

1 MW = 1 MJ per second = 1000 kJ per second

This calls for some work with the labels on a variety of electrical appliances. Each has its power on the label (even your computer). One can compare kettles, electric irons, refrigerators, washing machines, ovens, hair driers etc.

  • Use Sankey diagrams to represent processes in energy terms.

This representation is useful in conveying the idea that the total amount of energy is the same at the beginning and end of a process, without having to state this explicitly.

Working out money costs is important in both making it seem real, and in keeping the ideas relevant. A good aim is to send students home with information their families will find interesting or surprising.

Most important, activities such as these make it clear that energy changes are the kind of thing you have to calculate , not just look at or chat about. At the same time, doing sums like this gives students a feeling of definiteness and practical use of the ideas. That will probably work better than logical definitions to make them feel secure.

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The automatically straight-line graph

Acceleration
Energy and Thermal Physics

The automatically straight-line graph

Teaching Guidance for 14-16

Examples of using a straight line graph to find a formula.

Example 1: To show that πR 2 gives the area of a circle.

For any circle π is the number 3.14 in the equation:

circumference = 2π x radius or π x diameter

So π is circumferencediameter

Starting from that (as a definition of π) we can show that the area of a circle is πR 2.

Draw a large circle with centre 0 and radius R. Plot a graph of 2πr upwards against r along.

Then the graph must be a straight line and its slope will be 2π.

The end-point A, of the graph belongs to a big circle of radius R. Each other point of the graph: line 0A belongs to a smaller circle, of radius r.

Sketch III shows two small circles close together with radii (r) and (r + tiny bit of radius).

What is the area of the shaded ring between them? The ring has width (tiny bit of radius) and lengthr (its circumference). Its area is 2πr x (tiny bit of radius).

On the Graph IV the shaded pillar shows just that same area, 2πr x (tiny bit of radius).

Now ask about all such rings from the centre 0 out to radius R. Their total area is the same as the area of all the pillars in Graph V. That is the triangle of height2πR and base R.

AREA = ½2πR x R = πR 2.

Therefore area of circle is πR 2.

Example 2: To show that s = ½at 2 for constant acceleration from rest.

Plot a graph of at upwards against t along. Then with a constant the graph must be a straight line; and its slope will be a (Graph VI).

Choose a tiny bit of time on the t-axis and draw a pillar up to the line (Graph VII). The area of the pillar is: height x width,

(at) x (tiny bit of time)

and that is (v) x (tiny bit of time), since acceleration x time is speed.

And that is (tiny bit of time travelled).

Then total distance travelled, s, is given by the total area of all such pillars (Graph VIII).

s = area of triangle OAB = ½at x t = ½ at 2.

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Power and energy

Power
Energy and Thermal Physics

Power and energy

Teaching Guidance for 14-16

There are many occasions when you might want to know how fast energy is being transferred:

  • an electric motor driving a sewing machine or a lathe
  • an immersion heater in a water tank warming up the bath water
  • sunlight concentrated by mirrors on a boiler of water to produce steam
  • a loudspeaker emitting sound waves
  • your own body lifting itself, or a weight.

You may want to know how much energy is transferred in a day so that you know how much fuel has been used, and so calculate the size of a fuel bill.

The rate that energy is being transferred is called power.

Efficiency

The efficiency of a machine is a measure of how much energy is transferred to the machine (from, for example, energy stored chemically in fuel and oxygen) and how much is then transferred to do a useful job (to, for example, energy stored gravitationally when a lift full of people is lifted up).

Efficiency = useful energy transferred from the machineenergy transferred to the machine x100%

Machines are not 100% efficient because energy is dissipated to the surroundings; warming it up. These energy ‘losses’ can be reduced but never eliminated.

‘Wasted’ energy

Cars and power stations need cooling systems; the energy dissipated needs to go somewhere. There is a tendency for energy transfers to be lopsided. Energy stored thermally in a high temperature furnace can be used to do work. Energy stored thermally in the surroundings (at a lower temperature) cannot. A kettle of boiling water can run a model steam engine; but emptied into a bath of cold water it will only provide a tepid bath which could not run a steam engine. The same amount of energy is there but it is less available, less useful.

Power range of an electric motor

Machines have a maximum power at which they operate, which is a trade-off between the load and the time they take to do the job. If a motor is spinning without any load being raised then the useful output power is zero; all the input power is being used to fan the air and warm it up a little. If the motor is stalled, by too heavy a load, its useful power is again zero. Between these two extremes the motor has a wide range of adjustable power transfer behaviour.

The watt and its origins

The SI unit of power is the watt. A watt is not just an electrical unit even though we come across it most frequently applied to electrical devices. Car engines can be rated in watts too.

Before the age of steam engines, machinery used to pump water from mines was driven by horses. The business partnership between Matthew Boulton and James Watt, in the late 18th century, has been described as follows:

“Boulton’s idea was that he would sell something that no one had ever sold before – power. He actually used those words; he wrote to Empress Catherine of Russia saying, ‘I am selling what the whole world wants: power’. And this is how he did it. He sent his people down to Cornwall to say: ‘We are offering engines on these terms. Our firm, Boulton & Watt, will set up the engines, free, gratis and for nothing, at your mine. We will service them for the first five years and all we are asking in return is one-third of the difference between the cost of coals and the cost of hay for the horses that would have to do the same amount of work.’ Well, the mine owners thought he was obviously crazy but they accepted the offer.”

“Now of course came the disputed question of how much work a horse could do. …Watt measured the amount of work a horse could do by making a horse pull something lifted over a pulley. He conceived of the idea of work being the product of force and distance and of power being the rate of doing work.” [J D Bernal (1973) The Extension of Man: A history of physics before 1900 . Paladin pp 270, 271]

In modern values, 1 horsepower = 746 watts. To give a ‘feeling’ for the size of a watt, it is about the amount of energy transferred per second by a rat. So a watt is about 1 rat-power.

The kilowatt hour

A common energy unit is used by power companies to measure the amount of energy transferred by the electrical devices that consumers use. This unit is the kilowatt hour. This means that energy is being transferred at a rate of one kilowatt for an hour. (The power unit is multiplied by time to give an energy unit.)

1 kWhour = 1,000 x 60 x 60 = 3,600,000 joules.

Humans can work steadily at a rate of about 100 W. We pay about 8p for a kilowatt hour of energy transferred to us by electrical companies. If we were paid the same amount for labouring, that would be only 0.8p for an hour.

You could not live on a wage like that in countries where push-button controlled motors are in abundance. But in the developing world, where subsistence farming depends on manual labour, then this represents a real ‘currency exchange rate’. The industrialized world has created ‘power stations’ which act like slaves working for each of its citizens. A 1GW power station provides the power of 10 million slaves working at a rate of 100 W.

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Work done by a force

Work done (energy transferred by mechanical working)
Energy and Thermal Physics

Work done by a force

Teaching Guidance for 14-16

Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.

Energy transferred = work done = force x distance moved in the direction of the force

When energy is transferred from energy stored chemically in muscles to energy in a raised load, or to energy stored elastically in a stretched spring, the energy transferred is a measure of how much work has been done.

Energy transferred = mgΔh

This second equation is illustrated by raising kilograms onto different height shelves. You can show that the equation is a good summary of what happens. It takes account of the mass, the height raised and whether the kilogram is raised on the Earth or the Moon.

The useful thing which you get from fuels by burning them is a transfer of energy, so that a load can be raised, or an object accelerated.

However, not all the energy available does a useful job. If you lift a lot of bricks, you can get too hot. As well as transferring energy to the raised bricks, some of the energy in your muscles warms you up. The transfer of energy is not 100% efficient and not all the energy transferred is represented by mgh. Nor do you know how much total energy is stored gravitationally. You can only calculate energy that is transferred.

Concepts develop with steam engines

Humans first domesticated animals to do useful work and later found other ways of exploiting energy from natural sources, such as falling water and wind. But the abstract idea of an ‘engine’ really developed with steam engines.

By the 1820s the concept of ‘work’ as mechanical effect had been introduced into discussions about what are now called power technologies. Early on, a major use of steam engines was pumping water out of mines. Manufacturers such as Boulton & Watt persuaded mine owners in Cornwall to buy a steam engine in place of their pit ponies, by comparing the amount of work each could do.

Watt went even further, developing the concept of rate of working, or power, with his steam engines described in ‘horsepower’. Steam engines enabled the output of many Cornish mines to quadruple.

An analogy to use when teaching about energy transfers

Consider two bank accounts. If I transfer a £1 cheque from my account to yours then my account goes down by £1 and yours will go up by £1. But a cheque is not cash of any kind. It is an instruction to my bank to pay out £1 into your account. We have to pay the banks for doing the job for us and so although my account falls by £1 yours may only gain 95p because you have to pay bank charges. It is also impossible in this transaction to know how much is stored in each account.

Pushing this analogy to its limits helps to show that whilst you can store real cash in the bank (the energy stored, for example, in a fuel + oxygen mixture), the cheque which passes between accounts is something different. The cheque is a means of transferring the cash value (the work done for example when a brick is raised). Work is energy being transferred.

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.

Up next

James Prescott, Joule and energy conservation

Conservation of Energy
Energy and Thermal Physics

James Prescott Joule and energy conservation

Teaching Guidance for 14-16

As the son of a Manchester brewer, privately tutored for several years by the chemist John Dalton, James Joule took an early interest in all the technical equipment associated with brewing. In 1840, at the age of 22, he experimentally discovered that the heat generated in a coil of wire is proportional to the square of the current through it. This effect is now called ‘Joule heating’.

In the following decade, Joule sought to unify electrical, chemical and thermal phenomena by conducting dozens of different experiments to demonstrate their inter-convertibility and quantitative equivalence. He gave particular attention to the conversion of heat into mechanical work, regarding this as fundamental to the theory of steam engines.

Churning fluids

Joules’ best-known experiment involved a paddle wheel which rotated so that it churned water in a large cylinder. The wheel itself was driven by falling weights so that he could determine the work done. The same experiment was repeated using whale oil and then mercury. Joule worked meticulously, constantly improving the accurately of his results. He took great care to minimise heat losses to the surroundings and introduced appropriate correction factors.

With the help of scientific instrument-maker John Dancer, Joule was also able to use very sensitive thermometers. Some contemporaries doubted the claim that he could measure temperatures to within 1/200 of a degree Fahrenheit.

Honeymoon

Famously, Joule packed thermometers for his honeymoon in the Swiss Alps, so that he could compare the temperatures of water at the top and bottom of a waterfall near Chamonix. In fact this particular experiment failed, because the water produced too much spray at the bottom of its fall.

SI unit of energy

In recognition of Joules’ importance in demonstrating energy conservation, the SI unit of energy is named after him.

Resources

Some diagrams and a chronology of increasingly accurate experiments to determine the energy needed to increase the temperature of 1 kilogram of water by 1 °C, carried out by Joule and others during the period 1842 – 1939. This is a six-page extract from a Nuffield Physics pupil textbook.

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