Power and energy
There are many occasions when you might want to know how fast energy is being transferred from one energy store to another:
- 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 to produce steam
- a loudspeaker transferring energy into the energy carried by sound waves
- your own body transferring chemical energy stored in food into thermal energy of the body and potential energy of a raised 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.
The efficiency of a machine is a measure of how much energy is transferred from the source to the machine and how much is then transferred to do a useful job.
Machines are not 100% efficient because energy is transferred to the environment; warming it up. These energy ‘losses’ can be reduced but never eliminated.
Cars and power stations need cooling systems to transfer their ‘waste’ thermal energy to. There is a tendency for energy transfers to be lopsided with some of the thermal energy from the high temperature furnace running down to low temperature thermal energy. Low temperature thermal energy is not so useful. 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 thermal 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 used by consumers. 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.