# Doing energy sums

Including simple sums about energy and power is very important. It introduces the units that are in practical use, without much formality. It introduces both energy and power (rate of energy supply or use - a bit of trouble taken early over amount and rate of change will be repaid later).

- Nearly all foods are now labelled with their ‘energy content’ (how much energy is liberated when they are digested). Valuable energy lessons can be taught based on diet energy calculations.

An active grown man needs around 2,000 kilocalories per day (about 8400 kJ per day). Women generally need a bit less. The energy has to come from ‘burning’ food in the body. Most of this energy is ‘wasted’ through cooling (humans run at about 100 W). Only a relatively small fraction is expended in physical activity. (Note the dietary Calorie is a kilocalorie.)

- Heating water makes a useful start on measuring amounts of energy. An electric kettle is marked with the rate at which it delivers energy – its power. This is in watts, and is often about 2 kW. Multiply by the number of seconds it is switched on for, and you have the number of joules delivered. [Avoid calculating energy exchanges from electrical equations at an early stage.]

Heating a kettle of water to boiling point takes about 0.5 MJ, for example. Leaving a 100 W lamp on for 3 hours uses a bit more than 1 MJ. It’s worth comparing this with the amount of energy provided by a single meal.

- Collect from the class examples of household fuel bills: gas, electricity, oil. They can show how much energy is transferred to the home, and give pointers to where savings might be made.

The fuel bill for gas tells you how many cubic metres of gas you have burned. The bill for oil tells you how many litres of heating oil have been put in your tank. The electricity bill tells you how many kilowatt hours you have used. But all of them also convert these amounts to a common unit: say megajoules. [Note that 1 kW hour is 3.6 MJ]

The fact that all fuel uses can be expressed in a common unit reflects the deeper fact that fuel sources are interchangeable as far as energy is concerned. Heating a bath full of water by burning oil or by using electricity uses the same amount of energy for the water, even though the two methods may waste different amounts by letting energy leak elsewhere.

The teaching trick is to use the units for electricity supplies to give the units for energy and power:

Power = rate of supply of energy

1 watt = 1 joule per second

1 kW = 1000 J per second (1 kJ per second)

1 MW = 1 MJ per second = 1000 kJ per second

This calls for some work with the labels on a variety of electrical appliances. Each has its power on the label (even your computer). One can compare kettles, electric irons, refrigerators, washing machines, ovens, hair driers etc.

- Use Sankey diagrams to represent processes in energy terms.

This representation is useful in conveying the idea that the total amount of energy is the same at the beginning and end of a process, without having to state this explicitly.

Working out money costs is important in both making it seem real, and in keeping the ideas relevant. A good aim is to send students home with information their families will find interesting or surprising.

Most important, activities such as these make it clear that energy changes are the kind of thing you have to *calculate*, not just look at or chat about. At the same time, doing sums like this gives students a feeling of definiteness and practical use of the ideas. That will probably work better than logical definitions to make them feel secure.