Efficiency

As mentioned in the article about conservation of energy, energy cannot be created or destroyed.

But it can be transferred from one form to another: and sometimes, we don’t want that energy form.

For example, in a computer CPU, we want the energy to be transferred as efficiently as possible so that as little heat is produced as possible.

Calculating efficiency as a decimal

The formula for calculating efficiency as a decimal is:

\text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}}

Or, if we’re instead measuring the power used and produced, we can use:

\text{Efficiency} = \frac{\text{Useful power output}}{\text{Total power input}}

Calculating efficiency as a percentage

The formula for calculating efficiency as a percentage is:

\text{Efficiency} = \left( \frac{\text{Useful energy output}}{\text{Total energy input}} \right) \times 100\%

If we’re instead measuring the power used and produced, we can use:

\text{Efficiency} = \left( \frac{\text{Useful power output}}{\text{Total power input}} \right) \times 100\%

100% efficiency

Almost nothing can be 100% efficient, because there are always some energy losses in the system.

For example, in a car engine, some of the energy from the fuel is lost as heat and sound, so the efficiency isn’t anywhere close to 100%.

However: all energy transfers usually will end up as heat in the end. In a way, heating machines (e.g. electric radiators) are 100% efficient, in that they transfer all the energy they use into heat energy - which is what we want them to do!

Examples

A machine uses 1000 J of energy to produce 800 J of useful energy. What is the efficiency of the machine?

• \text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}}
• \text{Efficiency} = \frac{800\,J}{1000\,J}
• \text{Efficiency} = 0.8 (or 80%)

A machine uses 2000 J of energy to produce 1500 J of useful energy. What is the efficiency of the machine?

• \text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}}
• \text{Efficiency} = \frac{1500\,J}{2000\,J}
• \text{Efficiency} = 0.75 (or 75%)

A machine has an efficiency of 90% and produces 900 J of useful energy. How much energy does it use in total?

• \text{Efficiency} = \left( \frac{\text{Useful energy output}}{\text{Total energy input}} \right) \times 100\%
• 0.9 = \frac{900\,J}{\text{Total energy input}}
• \text{Total energy input} = \frac{900\,J}{0.9}
• \text{Total energy input} = 1000\,J

A person charges a power bank. The total input energy was 800 kJ. The charging has an efficiency of 80%. They then charge their phone using the power bank, and the phone charging has an efficiency of 90%. How much energy is transferred to the phone in the end?

• \text{Energy transferred to power bank} = \text{Total energy input} \times \text{Efficiency of charging power bank}
• \text{Energy transferred to power bank} = 800\,kJ \times 0.8
• \text{Energy transferred to power bank} = 640\,kJ
• \text{Energy transferred to phone} = \text{Energy transferred to power bank} \times \text{Efficiency of charging phone}
• \text{Energy transferred to phone} = 640\,kJ \times 0.9
• \text{Energy transferred to phone} = 576\,kJ

A machine has an efficiency of 70% and produces 700 J of useful energy. How much energy does it use in total?

• \text{Efficiency} = \left( \frac{\text{Useful energy output}}{\text{Total energy input}} \right) \times 100\%
• 0.7 = \frac{700\,J}{\text{Total energy input}}
• \text{Total energy input} = \frac{700\,J}{0.7}
• \text{Total energy input} = 1000\,J

A machine with an efficiency of 0.8 uses 500 J of energy. How much useful energy does it produce?

• \text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}}
• 0.8 = \frac{\text{Useful energy output}}{500\,J}
• \text{Useful energy output} = 0.8 \times 500\,J
• \text{Useful energy output} = 400\,J

flashcards