Conservation of Energy and Energy Diagrams

If energy is never "used up", where does it all go? A light bulb gives out light, but it also gets warm; a car burns petrol, but a lot of the energy ends up heating the engine and the road. The answer is one of the most important ideas in all of 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 P7 (Energy) of OCR Gateway Science A, sets out the conservation principle, explains how energy is dissipated to less useful stores, and shows how a Sankey diagram lets you see at a glance how much of the energy supplied to a device ends up doing 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 in terms of energy spreading to less useful stores, describe what is meant by useful and wasted energy, and draw and interpret a Sankey diagram.

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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 is true in every situation, with no exceptions ever found. In a closed system — one where no energy can enter or leave — the total energy never changes; energy is simply moved around 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 been lost; it has only been redistributed.

The reason it can look as though energy disappears is that some of it always ends up in stores that are spread out and no longer useful — usually the thermal store of the surroundings. That energy is still there, but it is so thinly spread that we can no longer do anything useful with it.

Exam Tip: The exact 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 built to make a 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 is always transferred to stores we do not want — this is the wasted energy.

• Useful energy is the energy transferred to the store the device is designed 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 example, in an old filament light bulb, only a small fraction of the electrical energy is transferred usefully to light; most is transferred to the thermal store (the bulb gets hot) and is wasted. The total energy in 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 ended up somewhere we cannot make use of.

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Dissipation: Energy Spreading Out

Dissipation is the spreading out of energy to less useful stores — almost always the thermal store of the surroundings. Whenever there is friction between surfaces, or air resistance as something moves through air, energy is transferred to the thermal store and the surroundings warm up very slightly. This energy becomes spread out over a huge number of particles in the air and surrounding objects, so it is far too thinly distributed to be gathered back and used.

Picture a swinging pendulum. Each swing, a little of its energy is transferred by air resistance to the thermal store of the air. The pendulum swings a tiny bit lower each time until it finally stops — not because the 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 out 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 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 reduce it. The main ways to cut unwanted energy 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 reduces the rate at which energy is transferred by heating to the surroundings.

These methods do not break the conservation of energy — they simply ensure a larger fraction of the energy is transferred usefully and a smaller fraction is wasted. You will quantify 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 is split 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 represents;
• the total energy in enters from the left as one wide arrow;
• useful energy continues straight across 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.