Power and energy

There are many occasions when you might want to know how fast energy is being transferred:

• an electric motor driving a sewing machine or a lathe
• an immersion heater in a water tank warming up the bath water
• sunlight concentrated by mirrors on a boiler of water to produce steam
• a loudspeaker emitting sound waves
• your own body lifting itself, or a weight.

You may want to know how much energy is transferred in a day so that you know how much fuel has been used, and so calculate the size of a fuel bill.

The rate that energy is being transferred is called power.

Efficiency

The efficiency of a machine is a measure of how much energy is transferred to the machine (from, for example, energy stored chemically in fuel and oxygen) and how much is then transferred to do a useful job (to, for example, energy stored gravitationally when a lift full of people is lifted up).

Efficiency = useful energy transferred from the machineenergy transferred to the machine x100%

Machines are not 100% efficient because energy is dissipated to the surroundings; warming it up. These energy ‘losses’ can be reduced but never eliminated.

‘Wasted’ energy

Cars and power stations need cooling systems; the energy dissipated needs to go somewhere. There is a tendency for energy transfers to be lopsided. Energy stored thermally in a high temperature furnace can be used to do work. Energy stored thermally in the surroundings (at a lower temperature) cannot. A kettle of boiling water can run a model steam engine; but emptied into a bath of cold water it will only provide a tepid bath which could not run a steam engine. The same amount of energy is there but it is less available, less useful.

Power range of an electric motor

Machines have a maximum power at which they operate, which is a trade-off between the load and the time they take to do the job. If a motor is spinning without any load being raised then the useful output power is zero; all the input power is being used to fan the air and warm it up a little. If the motor is stalled, by too heavy a load, its useful power is again zero. Between these two extremes the motor has a wide range of adjustable power transfer behaviour.

The watt and its origins

The SI unit of power is the watt. A watt is not just an electrical unit even though we come across it most frequently applied to electrical devices. Car engines can be rated in watts too.

Before the age of steam engines, machinery used to pump water from mines was driven by horses. The business partnership between Matthew Boulton and James Watt, in the late 18th century, has been described as follows:

“Boulton’s idea was that he would sell something that no one had ever sold before – power. He actually used those words; he wrote to Empress Catherine of Russia saying, ‘I am selling what the whole world wants: power’. And this is how he did it. He sent his people down to Cornwall to say: ‘We are offering engines on these terms. Our firm, Boulton & Watt, will set up the engines, free, gratis and for nothing, at your mine. We will service them for the first five years and all we are asking in return is one-third of the difference between the cost of coals and the cost of hay for the horses that would have to do the same amount of work.’ Well, the mine owners thought he was obviously crazy but they accepted the offer.”

“Now of course came the disputed question of how much work a horse could do. …Watt measured the amount of work a horse could do by making a horse pull something lifted over a pulley. He conceived of the idea of work being the product of force and distance and of power being the rate of doing work.” [J D Bernal (1973) The Extension of Man: A history of physics before 1900 . Paladin pp 270, 271]

In modern values, 1 horsepower = 746 watts. To give a ‘feeling’ for the size of a watt, it is about the amount of energy transferred per second by a rat. So a watt is about 1 rat-power.

The kilowatt hour

A common energy unit is used by power companies to measure the amount of energy transferred by the electrical devices that consumers use. This unit is the kilowatt hour. This means that energy is being transferred at a rate of one kilowatt for an hour. (The power unit is multiplied by time to give an energy unit.)

1 kWhour = 1,000 x 60 x 60 = 3,600,000 joules.

Humans can work steadily at a rate of about 100 W. We pay about 8p for a kilowatt hour of energy transferred to us by electrical companies. If we were paid the same amount for labouring, that would be only 0.8p for an hour.

You could not live on a wage like that in countries where push-button controlled motors are in abundance. But in the developing world, where subsistence farming depends on manual labour, then this represents a real ‘currency exchange rate’. The industrialized world has created ‘power stations’ which act like slaves working for each of its citizens. A 1GW power station provides the power of 10 million slaves working at a rate of 100 W.