Sankey Diagrams & Efficiency (WJEC GCSE Science (Double Award)): Revision Note

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

Calculate the amount of wasted energy. 

Answer:

Step 1: State the conservation of energy equation

total energy input = useful energy output + wasted energy output 

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

wasted energy = 500 – 120

wasted energy = 380 J

Some energy values for a gas-fired thermal power station are listed below.

Input energy = 20 000 kJ

Heat energy = 13 500 kJ

Electrical energy = 6500 kJ

Use this information and the equation below to calculate the % efficiency of the power station.

Answer:

Step 1: State the known quantities

• Useful energy transferred = electrical energy = 6500 kJ

• Total energy supplied = input energy = 20 000 kJ

• The heat energy is the wasted energy, but this is not required for the calculation 

Step 2: Write out the equation

Step 3: Substitute the known values

Usually in a calculation, you would convert the kJ to J before you input any numbers. However, in a ratio calculation like this, the units cancel out, so you don't need to do it. If you did convert the units to joules, you would still get the same answer, and therefore you would still gain full marks. It would just take you slightly longer to complete the calculation, so this is a good short cut if you feel confident with your maths skills. You will never lose marks for doing conversions (correctly!) when you don't need to, but you will lose marks if need to do a conversion and you don't do it. So if in doubt, always do the conversion.