4.Main Content
guidance
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.
Efficiency
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.
‘Wasted’ energy
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
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
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.
An older unit, the horsepower, used to be used for mechanical devices and is still in use today. Before the time of James Watt, railways and other machinery were driven by horses. When Boulton and Watt started offering their early steam engines to mine owners they met the question: ‘If I were to buy your engine, how many horses will it replace?’ So Watt experimented with a Cornish farm horse raising a load in a mineshaft and decided that 550 ft.lb per second was a reasonable estimate for 1 horse-power. That is equivalent to 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 to all our various household gadgets. 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 0.6p 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.
Energy used in the human body
Human beings are only about 25% efficient for doing mechanical jobs. For every 1,000 joules of energy which are transferred from fuel stored in muscles, only 250 joules are transferred to raising a load or doing some other kind of job. 750 joules are transferred to thermal energy in the body. Thermodynamics shows that muscles could be more than 70% efficient in transferring their chemical energy to do useful jobs, but only if the action was conducted infinitely slowly. So when estimating the useful energy transferred from chemical energy stored in food to muscles in order to climb the stairs, for an eight hour day, then the answer needs to be multiplied by four to find the demand on food.
In order to raise 1kg a height of 1m then 10 J of energy need to be transferred. This can be obtained from four grains of sugar, a mini-snack. One grain of sugar is for raising the load and three grains for transfer to thermal energy. If you raise 1 kg through a height of 1 m every second requiring 1 mini-snack per second then this is about 10 grams of sugar per hour. Not enough to allow you to eat a cream-cake or a bar of chocolate without putting on 'weight' (i.e. mass)!
Updated 3 Jul 2009