Costing up activities with joules

All of our everyday activities, whether driving to school, doing the washing-up, or going for a walk, have a cost. The cost we are thinking about here is not one of money, but one of energy. In fact, energy provides a common currency that allows us to count the relative cost of all of these different kinds of activity.

The comparisons are made in joule (J), which is the unit of energy. Just as we can look at the prices of new goods or services that we might want to buy, so can we check out the energy costs of different processes and activities. If we don't have access to sufficient energy, this rules out the possibility of doing whatever it is we might want to do.

When counting energy costs the numbers are often large, so we use larger chunks of the currency, grouping the joules into thousands to give kilojoule (kJ). Quantifying processes in terms of energy in one of the fundamental methods of problem solving in science.

Keeping a human alive for a day

Let's start with thinking about the energy costs of keeping a human alive and functioning for one whole day. The average daily energy food intake (carbohydrate, protein, fat and alcohol) in the UK is equivalent to 10,500 kilojoule for men and 8400 kilojoule for women. The different components of our diet are not equally good at providing this energy. The following table shows how much energy is provided by one gram of each component:

{17

component	energy/kilojoule
carbohydrate (starch or sugar)	16
protein
fat	37
alcohol	29

Over the course of a typical day, if we are not to retain this energy in a chemical store as fat, we need to be active. Different activities help with this energy balance to greater or lesser extents. Just to maintain the basic bodily functions of an adult costs about 4.6 kilojoule a minute.

This Basal Metabolic Rate (BMR) varies among individuals, and with age and population group. It is always measured at rest and usually accounts for 75% of human energy requirements.

The following figures showing how further activity increases the energy cost:

energy for each minute of activity	energy cost/kilojoule
sitting	6
standing	7
washing or dressing	15
walking slowly	13
walking moderately quickly	21
walking up and down stairs	38
light work (most domestic work, lorry driving, carpentry, bricklaying)	10-20
moderate work (gardening, tennis, dancing, jogging, cycling up to 20 km/hour, digging)	21-30
strenuous work (coal mining, cross-country running, football, swimming the crawl)	>30

Feeding up the UK population

Where do people in the UK get their energy from?

This is how people in the UK satisfy their energy needs:

food group	percentage
milk and milk products	11
meat and meat products	16
eggs and egg dishes	2
fish and fish dishes	2
fat spreads	6
sugar, confectionery and preserves	6
vegetables	12
fruit and nuts	2
cereals (including bread, cakes, pastries)	30
other foods	4
beverages	9

These days foods are marked with the energy that they provide:

food	energy provided per 100 gram / kilojoule
white rice	1450
whole milk	258
lettuce	49
margarine	3036
lamb chop	1468
white flour	1456
plain chocolate	2126
white bread	965

Energy balance in humans

Comparing the amount of energy coming in with the amount going out, over a day or a longer period, allows us to make simple predictions about whether or not particular activities will be viable. Food input limits possibilities.

For example, you might calculate whether or not your energy intake is sufficient to sustain a week long back-packing holiday in the Scottish Highlands.

If the energy balance falls short on the input side you will soon start to feel lethargic and weary, It's just the same as with cash-flow problems, if expenditure outstrips income, the enterprise soon grinds to a halt. There are choices, but these are restricted by the ultimate limiting factor: energy.

Energy for the home

Another everyday concern is the energy balance in our homes. In Northern Europe, mostly keeping the house warm enough in winter, but sometimes also keeping it cool in summer. Again, energy provides a fundamental limiting factor. If we do not have access to sufficient energy we cannot stay warm enough (or cool enough).

The quantities required are even larger, so now we measure the energy in millions of joules, or megajoules (MJ). The following UK figures for average energy consumption per household by final use in megajoules show some interesting changes in domestic energy usage over a time period of 30 years.

year	warming homes	warming water	cooking	lighting and appliances	total
1971	57 552	27 456	5808	7920	98 736
1981	60 720	25 344	4752	11 088	101 376
1991	62 832	24 288	3696	12 672	102 960
2001	63 888	23 760	2640	13 200	103 488

Comparisons across time

The general pattern is that increases due to increasing number of houses are being partially offset by more efficient use of resources, but there is also increased demand caused by changing lifestyles (about 5 % increase per household over the period shown). These patterns are broadly similar to other Northern European countries. Canada and the USA use considerably more resources.

Regional energy statistics for the whole of the UK are not currently available, although a number of regions are concerned to collect this data, to ensure enough energy is made available over the course of a year. One big advantage of having the common energy currency is that gas and electricity can be compared directly in terms of what you can do with each.

For example, the total annual demand for energy in South-East England is about 32,400 megajoule for each person, with approximately 75 % of this being met by gas. This preference for gas may be due in part to price. In 2000, in the South East, electricity cost the consumer 7.4 p for 3.6 megajoule, while the same quantity of energy delivered by gas cost only 1.6 p. Since energy is supplied in an open market, it is no surprise that there is a whole range of calculators on the Internet to help you estimate your energy needs and to work out how to best provide this energy. The lowest financial cost solution is often to use a mixture of gas and electricity. The common currency of energy allows such calculations to be made, comparing energy costs for equal periods of time.

Energy costs for travelling a kilometre

Travelling a kilometre by different means leads to different energy costs.

A range of factors are likely to affect your choice of mode of transport. These might include the weather (no cycling today…It's too wet!), or the speed at which you want to go (… but I've got to be there in ten minutes!).

Looking at the figures, it is clear that the energy cost per kilometre rises quite steeply for the bicycle as the speed rises. In fact it is quite tiring to cycle along at high speed. In such cases, it is important for the rider to be aware of how quickly their energy budget is being spent, and to consider the rate at which her store of energy is emptying (not wanting to exhaust energy supplies with half of the journey still to go). In just the same way, you may want to keep an eye on the state of your petrol tank as you drive.

Power requirements depend also on speed

How energy accumulates with time is measured in joule per second. This quantity is the power, measured in watt, where one joule per second is a power output of one watt.

1 watt = 1 joule1 second

Human power and horse power

Humans can work steadily to shift about 75 joule a second, or 75 watt. That is about 10 % of what a horse could manage, so humans work at 0.1 horse-power. Having a standard horse-power was important early on in the development of steam engines, as the engines were used largely for pumping water out of mines, replacing horse driven pumps. Any prospective buyer of these new engines needed to know how many horses the engine could replace. Consequently the horse-power of the engine became a critical selling point. In saying how much water each could lift in a fixed length of time, a common currency once again came into play. Now you would make the comparison in watts.

Later, steam locomotives came to drag trains around, and again the common currency became important, this time to inform the train operator of the ability of the locomotive engine to get a train up to speed. This would require a certain number of joules, and the operator would want this to be done within a certain time. In other words, they needed to choose a locomotive whose maximum power was greater than or equal to the power needed.

power needed = energy to get the train up to speedtime in which you want to get the job done

The key point about energy presented here is that analysing a problem in terms of energy does not tell you what will happen, but it does tell you what cannot happen. Choose a locomotive with insufficient power and you cannot get the train up to speed in time. Choose a locomotive with plenty of power and you will be able to, and you may still choose not to push the engine to its maximum power. Simply having enough power or energy available does not make an process happen. In exactly the same way, having lots of cash does not mean that you will necessarily go out to spend it on certain goods. It simply means that you have the chance to spend. If you have no cash you certainly cannot spend it, and so some courses of action are not open to you.

Power and cars

The relative power of different models of car is of interest to many, and may well be quoted in sales literature.

These are some power figures for a selection of cars available in the UK:

car	power/kilowatt
Ford Ka	44.0
Fiesta 1.4	50.0
Mondeo 2.0	106.7
Honda Accord2.0	114.1
Jaguar XJ4.2	223.8
Land Rover Freelander 1.8	85.8
Range Rover 3.0	129.8
Lotus Exige	100.0
Mini 1.6	67.1
Nissan Micra1.0	49.2
Peugot 2061.4	56.0
Renault Clio 1.4	73.1
Rolls-Royce Phantom	337.9
Toyota Corolla 2.0 D	66.4
VW Golf 1.4	55.2

Bigger power figures (as for the Rolls-Royce and the Jaguar) have two consequences: if pushed to operate at maximum power, these cars will burn petrol at a greater rate, thus costing more to run the car per hour, and they will also reach the speed limit sooner, with all other things being equal. Again the fact that you can achieve a higher acceleration does not mean that you must do so. The figures quoted are the maximum working power for each car.

Home appliances working

Let's think about making a pot of tea. Boiling enough water for a pot of tea takes 180 second with my kettle. The kettle is marked 3.0 kilowatt, which means that it costs me 3000 joule every second to run the kettle. To boil the kettle, I must therefore pay the electricity board for 3000 joule / second  ×  180 second which can be worked out to be 540,000 joule. Other domestic appliances cost me different numbers of joules, as they work at different rates for different lengths of time. Some are high power, but work only for a short time (cooker, kettle). Others are lower power, but work more or less continuously (refrigerator) or for long periods of time (lighting).

Here are some typical annual costs:

appliance	energy / megajoule
freezer	2380
cooking	2380
dishwasher	1700
lighting	1300
refrigerator	1080
tumble dryer	1010
kettle	900
television	792
washing machine	84
iron	270
vacuum cleaner	90

To find out how much energy each appliance uses, simply keep a log of how long you run it for (time in second – the duration), then multiply this quantity by the power of the appliance (power in watt).

energy = power × duration

energyjoule = powerwatt × durationsecond

Or

energykilojoule = powerkilowatt × durationsecond

Of course the averages given above vary with lifestyle and occupancy. Here are some estimates of how the annual total energy per household might vary:

household	energy / megajoule
working couple	14 820
single person	1100
family with two children (parents working, children at school)	19 730

Possibilities by country – a common currency

Globally the energy available to each individual also determines what people can or cannot do. The life-chances of people in countries around the world are significantly affected by the quantity of energy available to them. You can find up to date figures in terajoule (TJ; where 1 terajoule is 1,000,000 megajoule), demonstrating the huge variation in energy available per capita.

These figures raise lots of interesting questions. Some countries are increasing their per capita consumption, some decreasing. There are some puzzling differences between countries that in other ways might be thought to be comparable.

There are also some questions to be asked about the data. For example if the figures are exactly the same, does this reflect a failure to gather new information? You might notice that the majority of these repetitions occur for the less developed nations.

This common currency of the number of joules we have to spend affects all parts of our lives, from simply staying alive to powering iPods, laptops, domestic heating and cars. We pay for what we do in joules, as well as in monetary currency. In both cases if you don't have enough of the currency, certain activities, goods or services will be beyond your budget.

Standard and not so standard units

The standard unit for energy is the joule, but not all energies are quoted in joules. There is therefore a very real chance that you will come across data in awkward units. If you need to perform conversions, the following tables should help.

Energy conversion table

energy unit	equivalent
joule	1 J
kilojoule	1000 J
megajoule	1 000 000 J
gigajoule	1 000 000 000 J
terajoule	1 000 000 000 000 J
Btu	1055 J
therm	105 500 000 J
gallon of petrol	131 000 000 J
barrel of petrol	5 498 000 000 J
barrel of crude oil	6 119 000 000 J
ton of coal	21 896 000 000 J
million cubic feet of natural gas	1 083 000 000 000 J
calorie	4.1868 J
kilocalorie	4186.8 J
kilowatt-hour	3 600 000 J

Power conversion table

quantity	equivalent
1 Btu per hour	0.293 W
1 joule per second	1 W
1 kilowatt hour per day	41.7 W
1 food calorie per minute	69.77 W
1 horsepower	745.7 W
1 kilowatt	1000 W
1 Btu per second	1054 W
1 gallon of gasoline per hour	39 kW
1 million barrels of oil per day	73 GW

Energy is quantitative

Energy is quantitative in essence: if you are not using the idea of energy to make quantitative comparisons, then you're likely abusing the idea. The quantity of energy places a limitation on possible changes, it does not cause any of those changes.

As quantifying energy requires you to freeze the action, so looking from snapshot to snapshot, power, which enables you to analyse what is happening now, is often more useful. The accumulation of power over the duration of a process is the energy that is shifted over that process.