Conservation of Energy and Energy Diagrams

If energy is never "used up", where does it all end up? A lamp gives out light, yet it also grows warm; a car burns petrol, yet much of that energy heats the engine and the road. The answer is one of the deepest ideas in physics: the principle of conservation of energy. Energy cannot be created or destroyed — it can only be transferred from one store to another. This lesson, part of Topic P5 (Energy) of OCR Gateway Combined Science A, states the conservation principle, explains how energy is dissipated into less useful stores, and shows how a Sankey diagram lets you see at a glance how much of the energy supplied to a device does something useful and how much is wasted.

By the end of this lesson you should be able to state the principle of conservation of energy, explain dissipation as energy spreading to less useful stores, describe what is meant by useful and wasted energy, and draw and interpret a Sankey diagram.

This lesson develops AO1 (stating conservation and defining useful/wasted energy) and AO3 (drawing, reading and evaluating Sankey diagrams to interpret where energy goes).

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The Principle of Conservation of Energy

The principle of conservation of energy states:

Energy cannot be created or destroyed; it can only be transferred from one store to another, or dissipated, but the total amount of energy always stays the same.

This holds in every situation ever tested, with no exception found. In a closed system — one that lets no energy in or out — the total energy never changes; energy is simply shuffled between the stores inside the system. When a ball bounces, a kettle boils or a phone charges, the energy at the end is exactly equal to the energy at the start. None has vanished; it has only been redistributed.

The reason energy can appear to disappear is that some of it always finishes in stores that are spread out and no longer useful — usually the thermal store of the surroundings. That energy is still present, but it is so thinly spread that we can no longer put it to work.

Exam Tip: The precise wording matters. Write that energy is "transferred from one store to another" and that "energy cannot be created or destroyed". Avoid saying energy is "lost" — say it is dissipated to the surroundings. The total energy of a closed system is always conserved.

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Useful and Wasted Energy

Every device is designed to make one useful energy transfer — a kettle to heat water, a lamp to give light, a motor to make movement. But no device transfers all the energy supplied to it in the way we want. Some energy always ends up in stores we do not want, and this is the wasted energy.

• Useful energy is the energy transferred to the store the device is meant to fill (light from a lamp, kinetic energy from a motor).
• Wasted energy is the energy transferred to other stores, usually the thermal store of the surroundings, often because of friction, air resistance or electrical resistance.

For instance, in an old filament light bulb only a small share of the electrical energy becomes light; most is transferred to the thermal store (the bulb gets hot) and is wasted. The total energy supplied equals the useful energy plus the wasted energy:

$\text{total energy in} = \text{useful energy out} + \text{wasted energy}$total energy in=useful energy out+wasted energy

Both the useful and the wasted energy are real energy that still exists — "wasted" simply means it has ended up somewhere we cannot use.

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Dissipation: Energy Spreading Out

Dissipation is the spreading of energy into less useful stores — almost always the thermal store of the surroundings. Wherever there is friction between surfaces, or air resistance as something moves through air, energy is transferred to the thermal store and the surroundings warm very slightly. This energy becomes shared out among an enormous number of particles in the air and nearby objects, so it is far too thinly spread to gather back and reuse.

Picture a swinging pendulum. On every swing, a little of its energy is transferred by air resistance to the thermal store of the air. The pendulum swings a touch lower each time until it eventually stops — not because energy was destroyed, but because it has all been dissipated to the surroundings as thermal energy. The total energy is unchanged; it has just spread into a form we cannot recover.

Exam Tip: Dissipated energy is not destroyed — it is transferred to the thermal store of the surroundings and spread out so thinly that it can no longer be used. The usual causes to name are friction and air resistance.

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Reducing Wasted Energy

Because wasted energy makes devices less effective and wastes fuel, engineers work hard to cut it down. The main ways to reduce unwanted transfers are:

• Lubrication — oil or grease between moving surfaces reduces friction, so less energy is dissipated as heat.
• Streamlining — a smooth, tapered shape reduces air resistance (or water resistance), so less energy is wasted pushing through the fluid.
• Insulation — wrapping a hot object in an insulating material slows the rate at which energy is transferred by heating to the surroundings.

None of these methods break conservation of energy — they simply make sure a larger fraction of the energy is transferred usefully and a smaller fraction is wasted. You will put a number on this idea as efficiency in a later lesson.

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Sankey Diagrams

A Sankey diagram is a clear way of showing how the energy supplied to a device splits between useful and wasted transfers. It is drawn as a set of arrows:

• the width of each arrow is proportional to the amount of energy it stands for;
• the total energy in enters from the left as one wide arrow;
• useful energy carries straight on to the right;
• wasted energy branches off (usually downwards) as a separate arrow.

Because energy is conserved, the width of the input arrow equals the combined width of all the output arrows — what goes in must come out.

The diagram below is a Sankey diagram for a filament lamp supplied with $100 \text{ J}$100 J of electrical energy, of which only $10 \text{ J}$10 J is transferred usefully to light and $90 \text{ J}$90 J is wasted as thermal energy.

To read a Sankey diagram, compare the widths: a wide useful arrow and a thin wasted arrow mean an efficient device; a thin useful arrow and a wide wasted arrow (as for the filament lamp above) mean an inefficient one. The numbers on the arrows must always add up: here $10 \text{ J} + 90 \text{ J} = 100 \text{ J}$10 J+90 J=100 J, which satisfies conservation of energy.

Worked Example — Reading a Sankey diagram

An electric motor is supplied with $500 \text{ J}$500 J of energy. The Sankey diagram shows $350 \text{ J}$350 J transferred usefully to the kinetic store. How much energy is wasted, and to which store?

Step 1 — apply conservation of energy: total in = useful out + wasted.

Step 2 — rearrange: wasted = total in − useful = $500 - 350$500−350.

Step 3 — calculate: wasted $= 150 \text{ J}$=150 J.

Answer: $150 \text{ J}$150 J is wasted, transferred to the thermal store of the surroundings (the motor warms up because of friction and electrical resistance).

Exam Tip: On a Sankey diagram the arrow widths are proportional to the energy, and the input width always equals the total output width. To find a missing value, use energy in = useful + wasted. The widest output arrow shows where most of the energy goes.

Worked Example — Drawing a Sankey diagram

A kettle is supplied with $200\,\text{kJ}$200kJ of electrical energy. Of this, $180\,\text{kJ}$180kJ is transferred usefully to the thermal store of the water and the rest is wasted heating the kettle body and the surrounding air. Describe how you would draw the Sankey diagram, and state the width relationship between the arrows.