← Engines and efficiency

The impossible machine

An online ad shows an engine for sale. The seller claims it delivers 1200 J of useful work from every 1000 J of fuel energy it takes in.

Is such an engine possible?

Check the claim against the first law: the change in a system's energy equals the energy that enters it minus the energy that leaves it.

Take the engine as the system. On each run, 1000 J enters and 1200 J leaves.

the advertised engine1000 J in from fuel1200 J outas claimed useful work
The ad's claim drawn: 1200 J leaving against 1000 J entering; the balance needs 200 J from nowhere.

1000 - 1200 = -200. Run after run, the engine would need 200 J from nowhere.

More energy out than in breaks the first law. The advertised engine is impossible.

Now a second kind of claim: a device said to turn all the heat it takes in into useful work, wasting nothing.

That breaks the second law's limit: no real device converts all the heat it takes in into useful work. Some input heat always ends up in the cooler surroundings.

So run two checks on any claimed machine. Check one asks whether more energy comes out than goes in; if so, the machine is impossible by the first law. Check two asks whether all the input is claimed to become useful output; if so, the machine is impossible by the second law.
The two checkscheckquestionif yesonedoes more energy come out than goes in?impossible by the first lawtwois all the input claimed to become useful output?impossible by the second law
Run both checks on every claimed machine.

A machine that passes both checks may be possible. An engine taking in 1000 J and delivering 250 J of work while 750 J leaves as heat breaks neither law.

enginefuel energy in, 1000 Juseful work, 250 Jheat, 750 J
A machine both laws allow: 250 J carries on as work, 750 J bends away as heat, and the widths add up.

Machines claimed to run with nothing entering, or to put out more than they take in, are called perpetual motion machines. None has ever run.

Q: A crowdfunding page advertises a generator producing 2600 J of electrical output from 2000 J of fuel energy. Judge whether the generator is possible.

Energy in each run: 2000 J. Energy out: 2600 J.

2000 - 2600 = -600. The generator would need 600 J from nowhere on every run.

More energy out than in breaks the first law.

The generator is impossible: it claims more energy out than in.

Q: A video claims a camp stove fan turns all of the heat entering it into useful work, wasting none. Judge the claim.

The claim: every joule of input heat becomes useful work, nothing wasted.

No real device converts all the heat it takes in into useful work.

Some input heat always ends up in the cooler surroundings.

The claim is impossible: it breaks the second law's limit.

A seller claims a water pump delivers 880 J of useful work for every 800 J of electrical energy it takes in. Is the pump possible or impossible?

An engine takes in 600 J and delivers 150 J of useful work, with 450 J leaving as heat. Tamsin says: 'This engine breaks neither law; it is possible.' Is she correct?

Mirek watches a video of a wheel said to spin forever and light a lamp, with no energy entering it. Mirek says: 'With clever enough design, such a wheel could work.' Is he correct?

Your turn

Four machines are advertised. Which one is possible?

An ad claims an engine delivers 1500 J of useful work from 1200 J of fuel energy per run. Enter the energy the engine would need to create from nowhere on each run, in J.

A startup claims its generator converts all of the heat from its burner into electrical output, wasting nothing. Why is the claim impossible?