Chapter 1: Energy
The chapter problem: the hillside field centre
A field centre stands beside a stream in the hills. The stream drops steeply and turns a water wheel. The wheel drives a generator, and the generator makes electricity for the centre.
These are the facts to use all the way through the chapter.
- The stream brings 30 kg of water to the wheel each second.
- The water falls 12 m from the top of the drop to the wheel.
- The useful output power of the generator is 2.1 kW.
- Each kettle holds 1.5 kg of water, heated through 80 °C.
- The specific heat capacity of water is 4200 J/kg°C.
By the end of the chapter you will work out how much energy the falling water gives up each second. You will find the greatest power the wheel could produce, the efficiency of the generator, and the time the kettle needs. You will also decide whether the stream is a sound energy resource for the centre.
First contact: no working yet. Estimate. The water gives up about joules each second. The generator makes 2100 joules each second. Is the generator close to the energy in the falling water, or far below it?
If you are not sure where to start
The falling water gives up energy from its gravitational potential store. Some of that energy is transferred to the surroundings on the way. So the generator makes less than the water gives up.
By the end of this chapter
You will be able to:
- name the energy stores, and describe how energy is transferred between them;
- calculate the energy in an object's kinetic, gravitational potential and elastic potential stores;
- calculate the energy transferred when a substance is heated;
- calculate power, and use it to find an energy transfer or a time;
- state the principle of conservation of energy for a closed system;
- explain dissipation, and describe how to reduce unwanted energy transfer;
- calculate the efficiency of an energy transfer;
- compare renewable and non-renewable energy resources.
Where it is used
Every energy bill, every choice of appliance and every decision about insulation uses these ideas. So does the choice between a wind farm, a gas power station and a hydro scheme. The same numbers decide how much a journey costs and how much carbon dioxide it adds to the air.
Your turn to connect it
Where in your own week do you pay for energy, or try to use less of it? Write two examples. One should be about a machine, and one should be about heating.