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Nothing is lost, it spreads out

What went in equals the useful part plus what warmed the surroundings, and why lost is the wrong word.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

You will account for every unit of energy a machine takes in, splitting it into the useful part and the part that warmed the surroundings, compare machines by their useful share, and explain why energy that has spread out is still there even though nobody can use it.

2. What you already have

You can name a transfer and follow a chain of them, and you have already seen one table where the total stayed the same from the first row to the last. This lesson says why that was not a coincidence, and what to do when the numbers look as though they do not balance.

You have also felt the evidence many times: a laptop warm on your knees, a flashlight warm in your hand, a bicycle's brakes warm after a long hill. Every one of those warm things is a place where energy went.

3. Words for this lesson

4. In equals useful plus warmth

Whenever a machine runs, the energy that goes in comes out in two parts:

$$\text{what went in} \;=\; \text{the useful part} \;+\; \text{what warmed the surroundings}$$

A hand drill takes 80 units of effort from the child turning it and gives the drill bit 20 units of turning. The other 60 warmed the drill, the wood and the child's hands.

Nothing was destroyed and nothing was lost. Every unit is somewhere; it is just that somewhere is now a very large amount of slightly warmer stuff, and there is no way to gather it back up.

That is what makes the equation a check. If your two parts do not add up to what went in, you have not found a leak in the universe — you have forgotten a place to look.

5. Which part is the useful one

The useful part is decided by what the machine is for, not by what is biggest.

Notice the kettle. Almost everything it does is warming, and almost all of that warming is useful, because warming is what a kettle is for. The same warmth from a lamp is not useful at all.

So useful is not a physics word about the energy; it is a word about what somebody wanted. The physics does not care, and the total comes out the same either way.

6. Out of every hundred units

To compare two machines fairly, ask how many of every 100 units each one turns into its useful job. That number is its useful share.

The useful share and the warmth share always add up to 100, because every unit goes one way or the other. A bigger useful share means less warming of things nobody wanted warmed, so the same job needs fewer units taken in. Engineers call this idea efficiency, and in later courses you will write it as a percent.

7. Why the warmth cannot be gathered back

If the warm units are still there, why can we not collect them and use them again? Because they are spread out. Warming a whole room by a tiny amount puts one or two units into each of billions of bits of air, walls and furniture. To use them again, you would have to collect every one of those tiny amounts back into one place, and no machine can do that.

Think of a spoonful of sugar stirred into a swimming pool. Every grain is still in the pool, but nobody can scoop the spoonful back out. Energy that has spread out as warmth is like that sugar. It counts in the total, and it is useless for the job.

This is why every machine needs a fresh supply of energy to keep running: batteries go flat, cars need fuel, and people need food.

8. How to check an energy balance

Every time you balance a machine's energy, run three checks.

1. The parts add up. Useful plus warmth must equal what went in. If they do not, something was left out.
2. No part is bigger than the total. The useful part cannot be more than what went in; a machine never gives out more than it takes.
3. Something is warm. If you found warmth in your numbers, you should be able to name what got warmer: the motor, the wire, the air.

The second check is worth remembering. Inventors have claimed for hundreds of years to have built machines that give out more than they take in. Every one has failed, because the total never grows.

9. Saving energy at home

When people talk about saving energy, they do not mean keeping energy from being destroyed; it never is. They mean taking fewer units out of stores like fuel and batteries to do the same useful jobs.

There are two ways to do that. The first is to use a machine with a bigger useful share, such as swapping an old bulb for an LED. The second is to stop warming things nobody wants warmed: turning off a light in an empty room, or closing a door so warm air does not spread outside.

Both come from the same balance. In equals useful plus warmth, so if the useful part stays the same and the warmth goes down, less has to go in.

10. Machines that are nearly all warmth, on purpose

Some machines are built to warm things, so for them the warmth is the useful part. A toaster, a hair dryer, a space heater and an oven all turn nearly every unit they take in into warming. Their useful share is close to $100$ out of every $100$, because warming is exactly the job.

Even so, the balance still holds. A space heater that takes in $1000$ units warms the room with about $990$ of them. The other $10$ or so leave as a soft glow of light and a faint hum of sound. Those are its wasted units, which is the reverse of a light bulb, where the glow is the job and the warmth is the waste.

This is why the useful part has to be decided by asking what the machine is for. The same warmth is useful in a heater and wasted in a lamp, and the same light is useful in a lamp and wasted in a heater. The physics treats every unit the same way; only our purpose decides which ones we call useful.

11. In the world: changing the bulbs in a school

A school has $500$ old filament light bulbs. Each one needs $60$ units of energy every hour to make its light, and only $6$ of those units come out as light; the other $54$ warm the classroom. Across the school, that is $500 \times 54 = 27{,}000$ units of warmth every hour that nobody asked for. In summer, the air conditioning then has to work harder to carry that warmth back outside.

The school replaces them with LED bulbs that give the same $6$ units of light from only $15$ units taken in. Each LED warms the room with $15 - 6 = 9$ units an hour instead of $54$. The school now takes in $500 \times 15 = 7{,}500$ units an hour for lighting instead of $30{,}000$.

No energy was saved from destruction; none ever is. What changed is how many units had to come out of the power plant's fuel to do the same useful job.

12. In the world: a car engine

A gasoline car engine is not a very good machine at its job. Out of every $100$ units in the fuel, only about $25$ end up pushing the car along. The other $75$ warm the engine, the exhaust gases and the air. That is why a car has a radiator and a fan: to carry the unwanted warmth away before the engine overheats.

An electric car's motor does much better, turning about $85$ of every $100$ units from its battery into motion. Its warmth share is only about $15$.

Engineers at car companies in Michigan, California and around the world spend their careers trying to raise the useful share. Every unit that goes into motion instead of warming the air means the car goes further on the same fuel or the same charge.

13. Lost means nobody looked

Textbooks say energy is lost as heat, and children reasonably conclude that some of it stopped existing. It did not. Not one unit of it, not ever, anywhere that has been measured.

What happened is that it spread out. It went into the air, the casing, the bench and your hand, warming each of them by an amount too small to notice. It is all still there, and it is all completely useless, because there is no way to collect it back up into one place.

Those two facts sit together and they are both true: nothing is lost, and you cannot have it back. Machines wear out their batteries not because energy is destroyed but because it ends up somewhere nobody can reach.

When an energy sum does not balance, the question is never where did it go. It is what did I forget to measure — and the answer is usually something that got slightly warm. Warmth is the easiest place to forget, because it is spread so thinly that you rarely notice it unless you touch the machine. So when a sum looks short, touch the machine, or picture touching it, and ask what feels warmer than before.

14. A hand drill

1. Find what went in.

   $80\ \text{units of effort}$

   From the child turning the handle.

2. Decide what it is for.

   $\text{turning the bit}$

   That is the useful part.

3. Find the useful part.

   $20\ \text{units}$

   The bit's moving store.

4. Subtract to find the warmth.

   $80 - 20 = 60\ \text{units}$

   In equals useful plus warmth.

5. Say where the warmth is.

   $\text{the drill, the wood, her hands}$

   Put your hand on the drill afterward and you can feel it.

15. An electric kettle

1. Find what went in.

   $200\ \text{units}$

   From the socket, by an electric current.

2. Decide what it is for.

   $\text{warming the water}$

   Here the useful part is itself warming.

3. Find the useful part.

   $180\ \text{units into the water}$

   Nearly all of it.

4. Subtract to find the rest.

   $200 - 180 = 20\ \text{units}$

   The kettle's body and the kitchen.

5. Find the useful share.

   $180 \text{ of } 200 = 90 \text{ of every } 100$

   Halve both numbers.

6. Compare with a filament bulb.

   $90 \text{ against } 10 \text{ of every } 100$

   Same equation, very different shares: the split is not fixed.

16. Which bulb for a reading lamp?

1. Read what is needed.

   $40\ \text{units of light}$

   The useful part is fixed by the job.

2. Count the old bulb's hundreds.

   $40 \div 10 = 4 \text{ hundreds}$

   Ten units of light from each hundred.

3. Find what the old bulb takes in.

   $4 \times 100 = 400\ \text{units}$

   Four hundreds.

4. Count the LED's hundreds.

   $40 \div 40 = 1 \text{ hundred}$

   Forty units of light from each hundred.

5. Find what the LED takes in.

   $1 \times 100 = 100\ \text{units}$

   One hundred.

6. Compare the warmth.

   $400 - 40 = 360 \text{ against } 100 - 40 = 60$

   The old bulb warms the room six times as much.

7. Choose the bulb.

   $\text{the LED}$

   The same light for a quarter of the units taken in.

17. Your turn: a toy car takes 120 units from its battery and 30 end up as movement. Where are the other 90?

1. Subtract to find the rest.

   $120 - 30 = 90$

   In equals useful plus warmth.

2. Your turn: work this step out. Its working is at the end of the packet.

   Say they did not vanish.

3. Your turn: work this step out. Its working is at the end of the packet.

   Say where they are.

18. Guided practice

a hand drill takes $80$ units out of the child's chemical store. Only $20$ of them end up as the drill bit's moving store. How many units end up warming the surroundings instead?

Answer: units

19. Guided practice

Complete the worked solution: an electric fan takes in $20$ units, and $8$ of them end up moving the air. How many warm the fan's motor and the room, and how many of every five units are useful?

1. Find the warmth.

   $20 - 8 =$ _a units

   What went in minus the useful part.

2. Share the useful part out.

   $8 \div \text{lots of five} =$ _b of every five

   There are as many lots of five as the input has fives.

3. Share the warmth out.

   $\text{warmth} \div \text{lots of five} =$ _c of every five

   The two shares add up to five.

20. Guided practice

a wind-up radio takes $50$ units and only $35$ do the job it was built for. What happened to the other $15$?

• They warmed the machine and the air around it, spread out too thinly to use
• They were lost
• They were used up doing the work
• They went back into the store

21. Guided practice

Match each machine to the one change it was built to make. Everything else it does is warmth nobody asked for.

22. Practice

a toy car's motor takes $120$ units out of the chemical store in the battery, and $30$ of them end up as the car's moving store. Account for every unit.

23. Practice

A machine holds $54$ units in its chemical store. Each run empties $27$ of them: $9$ does the useful job and $18$ warms the surroundings. Run it until the store is empty.

This task has no paper form; do it on a device.

24. Practice

A machine takes in $68$ units and $43$ of them do the useful job. Mark on the scale how many units end up warming the surroundings.

0 |——————————| 100

Mark the position with a cross, then write the value:

25. Practice

An old filament bulb turns $10$ of every $100$ units it takes in into light; the rest warms the room. An LED bulb turns $40$ of every $100$ units into light. A reading lamp needs $120$ units of light. For each bulb, fill in how many units it must take in, and how many of those warm the room.

26. Somewhere new

A phone charger is warm to the touch while it works. Over an evening it draws $50$ units from the socket and puts $18$ units into the phone's battery. How many units went into warming the charger and the air around it?

Answer: units

27. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

28. Test question

a wind-up radio takes $50$ units out of the spring's stretched store, and $35$ of them end up as sound spreading out from the speaker. Account for every unit.

29. What you can do now

You can balance what went in against the useful part and the warmth. Tell someone why a warm phone charger is evidence rather than a fault.

Working for the steps left to you

17. Your turn: a toy car takes 120 units from its battery and 30 end up as movement. Where are the other 90?, step 2

17. Your turn: a toy car takes 120 units from its battery and 30 end up as movement. Where are the other 90?, step 3