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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.

The formula for calculating efficiency as a decimal is:

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

The formula for calculating efficiency as a percentage is:

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

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 efficience 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!

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

Section titled “A machine uses 1000 J of energy to produce 800 J of useful energy. What is the efficiency of the machine?”
  • (or 80%)

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

Section titled “A machine uses 2000 J of energy to produce 1500 J of useful energy. What is the efficiency of the machine?”
  • (or 75%)

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

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

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?

Section titled “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?”

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

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

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

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