Energy and Heat · Grade 8

Why does no machine give back everything you put into it?

Because at every conversion some of the energy leaves in a form you did not want, and almost always that form is heat. Conservation still holds perfectly — not one joule was destroyed — but heat that has spread into the air is no longer useful. Efficiency is the ratio of useful output to total input, and it is always below one hundred percent.

Learning objectives

Calculating efficiency

Efficiency is the useful output divided by the total energy put in, multiplied by a hundred to give a percentage. What counts as "useful" is set by what the device is for, so the very same energy can be useful in one machine and wasted in another.

An old filament bulb takes a hundred joules of electricity and emits about five joules of light — an efficiency of five percent. An LED produces about forty joules of light from the same hundred, eight times better.

The same arithmetic applies to a car engine at around 25 percent, to an electric heater at nearly 100 percent, and to the human body, which turns roughly 20 percent of its food into mechanical work.

Where the missing part ends up

In a filament bulb the wire glows until it gives out light, but most of the energy leaves it as infrared. You can feel it by moving a hand towards a lit bulb — that is the 95 percent which did not become light.

In a car engine the missing part leaves in the hot exhaust gases, in the cooling system, and in friction between moving parts. All three routes have the same destination: warming the surroundings.

Here the wording has to be careful. The energy was not wasted in the sense of vanishing — all of it exists as heat dispersed in the air. It was wasted in the sense that it can no longer be used, because heat spread thinly at low temperature is extremely hard to collect again.

Comparing energy sources

A non-renewable source is one that runs out: coal, oil and natural gas formed over millions of years and are not replaced at anything like the rate we burn them. A renewable source replaces itself: sun, wind, water and waves.

Israel is in an unusual position here. The country is small, but solar radiation in the Negev is among the strongest in the world — roughly 2,000 hours of sunshine a year — so solar is the natural direction, while large-scale hydroelectric power is nearly impossible without rivers.

A fair comparison needs three measures rather than one: the efficiency of the conversion, the cost per kilowatt-hour, and the environmental effect across the whole life of the installation. A source that wins on one of them may well lose on the other two.

Worked examples

  1. A device takes in 500 joules and produces 120 joules of useful output. What is its efficiency?

    1. Divide useful output by total input: 120 over 500
    2. That gives 0.24
    3. Multiply by a hundred

    Answer: 24 percent

  2. An LED with 40 percent efficiency receives 10 joules. How much light does it give?

    1. 40 percent is 0.4
    2. 0.4 times 10 joules

    Answer: 4 joules of light, with 6 joules leaving as heat

  3. An advert claims a device is 130 percent efficient. What is wrong?

    1. Over a hundred percent means output greater than input
    2. That would mean energy was created from nothing
    3. Conservation of energy forbids it

    Answer: It is impossible; the advertiser has undercounted the input or mismeasured the output

Common mistakes

Thinking low efficiency contradicts conservation of energy
The two fit together exactly. The total number of joules is always conserved; efficiency only measures which fraction of them came out in the form you wanted.
Saying that wasted energy was destroyed
All of it still exists as heat spread through the surroundings. "Wasted" here means it can no longer be used, not that it stopped existing.
Comparing energy sources on efficiency alone
A source can be efficient and expensive, or cheap and polluting. Efficiency, cost and environmental effect are three separate measures, and any one of them on its own gives a biased answer.

What to remember

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