1.2.4Electricity, Energy and Waves
Sankey Diagrams and Efficiency — WJEC GCSE Science (Double Award) - Physics Revision Notes & Topical Questions
5 min read 7 parts Lesson 14 of 36
Section 1 of 7What efficiency tells you
Definition
- Definition Efficiency compares the useful energy or power coming out of a system with the total energy or power going in.
- A high efficiency means most of the input is useful, and a low efficiency means most is wasted.
Conservation of energy
- Conservation of energy Energy is never created or destroyed, so total energy input = useful energy output + wasted energy output.
- The wasted energy is usually spread to the surroundings as heat.
Typical value
- Typical value A thermal power station is only about 30% efficient overall, so around 70% of the fuel energy is wasted.
Section 2 of 7Reading a Sankey diagram
Sankey diagram
Arrow width
- Arrow width The width of each arrow is drawn to scale and shows the amount of energy it carries.
Input
- Input The wide, flat starting end of the diagram represents the total energy supplied.
Useful output
- Useful output The arrow that carries on straight ahead shows the useful energy transferred.
Wasted output
- Wasted output Arrows branching downwards show energy wasted to the surroundings.
- The widths of the output arrows must add up to the width of the input.
Section 3 of 7Efficiency equations
| Equation | Meaning |
|---|---|
| efficiency (%) = (useful energy output ÷ total energy input) × 100 | Gives a percentage |
| efficiency (%) = (useful power output ÷ total power input) × 100 | Power version of the same ratio |
| P = E ÷ t | Power is energy transferred per second |
| wasted energy = total energy in − useful energy out | Rearranged conservation of energy |
Section 4 of 7Worked example: wasted energy
1
Question: an electric motor takes in 500 J while lifting a weight and gives 120 J of useful energy. Find the wasted energy.
2
Write the conservation equation: total energy in = useful energy out + wasted energy.
3
Rearrange: wasted energy = total energy in − useful energy out.
4
Substitute: wasted energy = 500 J − 120 J = 380 J.
Section 5 of 7Worked example: efficiency
1
Question: a gas-fired power station takes in 20 000 kJ and gives 6500 kJ of electrical energy, the rest being heat. Find its efficiency.
2
The useful output is the electrical energy, 6500 kJ, and the total input is 20 000 kJ.
3
Efficiency = (6500 ÷ 20 000) × 100.
4
Efficiency = 32.5%. The heat figure is not needed.
5
Because the units cancel in a ratio, there is no need to convert kJ to J.
Section 6 of 7Key terms
| Term | Meaning |
|---|---|
| Efficiency | The fraction of the total energy or power input that is usefully transferred, often given as a percentage. |
| Useful energy | Energy transferred to where and in the form it is wanted. |
| Wasted energy | Energy transferred in a way that is not useful, usually as heat to the surroundings. |
| Sankey diagram | A diagram whose arrow widths show how much energy goes to each output. |
| Dissipated | Spread out into the surroundings and not easily recovered. |
Section 7 of 7Exam technique
1
Quoting efficiency greater than 100%, which is impossible because energy cannot be created.
2
Dividing by the useful output instead of the total input.
3
Forgetting to multiply by 100 when a percentage is asked for.
4
Using the wasted energy value as the useful energy in the efficiency equation.
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