Conservation of Energy

The principle of conservation of energy states that:

Energy cannot be created or destroyed, it can only be transferred from one store to another

This means that for a closed system, the total amount of energy is constant
The total amount of energy transferred into the system must be equal to the total amount of energy transferred away from the system

Therefore, energy cannot be ‘lost’, but it can be transferred to the surroundings
- Energy can be dissipated (spread out) to the surroundings by heating and radiation
- Dissipated energy transfers are often not useful, in which case they can be described as wasted energy

Energy Flow Diagrams

Energy stores and transfers can be represented using a flow diagram
- This shows both the stores and the transfers taking place within a system

Energy Transfers in a Nuclear Power Plant

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Energy flow diagram showing energy stores and transfers in a nuclear power plant. Note the colour difference of the labels (stores) and the arrows (transfer pathways)

Worked example

The diagram shows a rollercoaster going down a track.

The rollercoaster takes the path A → B → C → D.

WE - Energy transfers question image, downloadable AS & A Level Physics revision notes

Which statement is true about the energy changes that occur for the rollercoaster down this track?

A. E_K → ΔE_P → ΔE_P → E_K

B. E_K → ΔE_P → E_K → ΔE_P

C. ΔE_P → E_K → E_K → ΔE_P

D. ΔE_P → E_K → ΔE_P → E_K

ANSWER: D

At point A:
- The rollercoaster is raised above the ground, therefore it has energy in its gravitational potential store
- As it travels down the track, energy is transferred mechanically to its kinetic store

At point B:
- Energy is transferred mechanically from the kinetic store to the gravitational potential store
- As the kinetic energy store empties, the gravitational potential energy store fills
At point C:
- Energy is transferred mechanically from the gravitational potential store to the kinetic store

At point D:
- The flat terrain means there is no change in the amount of energy in its gravitational potential store, the rollercoaster only has energy in its kinetic store
- The kinetic energy store is full
In reality, some energy will also be transferred to the thermal energy store of the tracks due to friction, and to the thermal energy store of the surroundings due to sound

We say this energy is dissipated to the surroundings
- The total amount of energy in the system will be constant
- Total energy in = total energy out

Exam Tip

It is helpful to think of energy stores as beakers and the total energy in the system as water. The water can be poured from one beaker into another back and forth as energy is transferred between stores.

You may not always be given the energy transfers happening in the system in exam questions. By familiarising yourself with the energy stores and transfer pathways, you will be able to relate these to the situation in the question. For example, a ball rolling down a hill is transferring energy from the ball's gravitational potential energy store to its kinetic energy store mechanically, whilst a spring transfers energy from its elastic potential energy store to its kinetic energy store mechanically.

Sankey Diagrams

Sankey diagrams can be used to represent energy transfers
- Sankey diagrams are characterised by the splitting arrows that show the proportions of the energy transfers taking place
The different parts of the arrow in a Sankey diagram represent the different energy transfers:
- The left-hand side of the arrow (the flat end) represents the energy transferred into the system
- The straight arrow pointing to the right represents the energy that ends up in the desired store; this is the useful energy output
- The arrows that bend away represent the wasted energy
Sankey Diagram of Energy In and Energy Out

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Total energy in, wasted energy and useful energy out shown on a Sankey diagram

The width of each arrow is proportional to the amount of energy being transferred
As a result of the conversation of energy:

Total energy in = Useful energy out + Wasted energy

A Sankey diagram for a modern efficient light bulb will look very different from that for an old filament light bulb
A more efficient light bulb has less wasted energy
- This is shown by the smaller arrow downwards representing the heat energy
Sankey Diagrams showing Different Efficiencies

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Sankey diagram for modern vs. old filament light bulb

Worked example

An electric motor is used to lift a weight. The diagram represents the energy transfers in the system.

WE Sankey Question image, downloadable IGCSE & GCSE Physics revision notes Calculate the amount of wasted energy.

Answer:

Step 1: State the conservation of energy

Energy cannot be created or destroyed, it can only be transferred from one store to another
This means that:

Total energy in = Useful energy out + Wasted energy

Step 2: Rearrange the equation for the wasted energy

Wasted energy = Total energy in – Useful energy out

Step 3: Substitute the values from the diagram

500 – 120 = 380 J

Conservation of Energy (Cambridge O Level Physics)

Revision Note