1.2 Conservation, dissipation and energy resources — Learn

Prerequisites: Section 1.1, especially energy stores, power and the idea that energy is transferred rather than used up.

By the end of this section you can: state the principle of conservation of energy for a closed system; explain what dissipation means; describe how to reduce unwanted energy transfer; calculate the efficiency of an energy transfer; and compare the energy resources used on the Earth.

1. Conservation of energy

A closed system is a system that no energy can enter or leave. In a closed system, the total energy stored never changes. This is the principle of conservation of energy.

Energy is transferred between stores inside the system, but the total stays the same. A ball dropped in a vacuum, with no air resistance, loses gravitational potential energy at exactly the rate at which it gains kinetic energy.

Worked example 1. A ball falls from a ledge. At the ledge it has 24 J in its gravitational potential store. Air resistance is ignored. State the energy in its kinetic store just before it lands, and explain your answer.

The total energy is unchanged, so the 24 J that leaves the gravitational potential store enters the kinetic store. Just before landing,

E_k = 24\,\text{J}

In a real room there is air resistance. The ball then has a little less kinetic energy, because some energy has been transferred to the thermal store of the air.

2. Dissipation

In every real change, some energy is transferred to the surroundings in a way that is not useful. This is dissipation. Dissipated energy is often stored in the thermal store of the surroundings, and it spreads out.

Dissipated energy has not been destroyed. It is still there, but it is stored in a less useful way. Friction, air resistance and the heating of a wire are all ways in which energy is dissipated.

Worked example 2. A machine is supplied with 2000 J of energy. It transfers 800 J usefully. How much energy is dissipated, and where does it go?

\text{dissipated} = 2000 - 800 = 1200\,\text{J}

The 1200 J is transferred to the thermal store of the machine and the air. It spreads out and becomes hard to use.

3. Reducing unwanted energy transfer

You can reduce unwanted transfer in two common ways.

Lubrication. Oil between moving surfaces reduces friction, so less energy is transferred to the thermal store.
Thermal insulation. A layer of trapped air or foam slows the transfer of energy from a warm object to its cooler surroundings.

For a building, the rate at which it cools depends on its walls. A thicker wall transfers energy more slowly, so the building cools more slowly. A wall made of a material with a higher thermal conductivity transfers energy faster, so the building cools faster.

4. Efficiency

The efficiency of an energy transfer compares the useful output with the total input.

\text{efficiency} = \frac{\text{useful output energy transfer}}{\text{total input energy transfer}}

Efficiency has no unit. It can be written as a decimal or as a percentage. A transfer can never be more than 100% efficient, because the useful output cannot be larger than the total input.

Worked example 3. A motor is supplied with 500 J of energy and transfers 350 J usefully. Calculate its efficiency.

\begin{aligned} \text{efficiency} &= \frac{350}{500} \\ &= 0.70 \\ &= 70\% \end{aligned}

The other 150 J is dissipated to the thermal store of the motor and the air.

Worked example 4. A machine is 40% efficient. Its useful output is 800 J. Calculate the total input.

\begin{aligned} \text{efficiency} &= \frac{\text{useful output}}{\text{total input}} \\ 0.40 &= \frac{800}{\text{total input}} \\ \text{total input} &= \frac{800}{0.40} \\ &= 2000\,\text{J} \end{aligned}

The efficiency of a transfer can be increased by reducing the energy that is dissipated. A machine with moving parts can be lubricated. A hot pipe can be wrapped in insulation. A device can be designed so that less energy is transferred to the surroundings. Each of these makes the useful output a larger share of the same input.

Watch out. Efficiency compares the useful output with the total input, not with the waste. A transfer that gives 350 J usefully from 500 J has an efficiency of $350 \div 500 = 0.70$ , not $350 \div 150$ . As a percentage it is 70%, not 0.70%. If you work out a value above 1, or above 100%, you have divided by the wrong number. Re-check by comparing your useful output with the total input.

Try it: efficiency

An energy transfer takes in a total power and gives out a useful power. The rest is dissipated. The figure lets you set both values.

Predict first. Do not move the sliders yet. If the input is 120 W and the useful output is 60 W, what is the efficiency? Write your answer as a decimal and as a percentage.

Test. Set the input to 120 W and the useful output to 60 W. Check your prediction. Now keep the useful output at 60 W and raise the input to 200 W. Read the new efficiency and the wasted power.

Explain. Why does the efficiency fall when the input rises but the useful output stays the same? Why can the efficiency never be more than 100%? Write your answer in two or three sentences.

5. Energy resources

The main energy resources available on the Earth are:

Resource	Renewable?
Fossil fuels (coal, oil and gas)	No
Nuclear fuel	No
Bio-fuel	Yes
Wind	Yes
Hydroelectricity	Yes
Geothermal	Yes
The tides	Yes
The Sun	Yes
Water waves	Yes

A renewable resource is one that is replaced as it is used, so it will not run out. A non-renewable resource is used up faster than it is replaced.

Energy resources are used for transport, for generating electricity and for heating. Different resources suit different uses. Oil suits transport because it can be carried in a tank and stored until it is needed. The Sun and wind suit electricity generation because the fuel costs nothing.

Resources differ in reliability. Wind does not always blow, and the Sun does not always shine, so these resources are not always available. Fossil fuels and nuclear fuel can be used at any time, so they are more reliable. Resources also differ in their effect on the environment: burning fossil fuels adds carbon dioxide to the air, and wind farms change the look of a landscape.

The mix of resources used has changed over time. In many countries the share from renewable resources has grown, and the share from coal has fallen. Renewable resources do not run out, and they produce less carbon dioxide when they generate electricity.

6. Progress check

Return to the chapter problem. The water gives up 3528 J each second, and the generator gives out 2100 J each second. Work out the efficiency of the generator. Decide whether the stream on its own is a reliable energy resource for the centre, and give one reason.

You should now be able to

state the principle of conservation of energy for a closed system;
explain what dissipation is and where the dissipated energy goes;
describe how lubrication and thermal insulation reduce unwanted energy transfer;
describe how the thickness and the thermal conductivity of a wall affect the rate at which a building cools;
calculate the efficiency of an energy transfer, as a decimal or a percentage;
compare renewable and non-renewable energy resources, and explain trends in their use.