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Following a chain of transfers

Several transfers in a row, the paths between them, and why the total is the same at every stage.

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 follow an energy transfer through a chain of several stages, naming the path between each pair of stores as well as the stores themselves, and show that the total is the same at every stage.

2. What you already have

You can name one transfer: which store went down, which went up, and by what path. A chain is that same sentence written several times over, with the store that went up in one line being the store that goes down in the next.

You can also count units in two stores and check that they add up to the same total. In a chain there are more stores to count, but the check is the same: every row adds up to what you started with.

3. Words for this lesson

4. Every chain has paths in it, not only stores

A flashlight, written out properly:

1. the chemical store in the battery is full;
2. an electric current carries the transfer to the bulb;
3. the thin wire in the bulb gets hot;
4. light and warmth spread out into the room.

Stages 1, 3 and 4 are about stores — something that has more or less in it than before. Stage 2 is a path — nothing sits in it, it is how the transfer travels.

Every chain alternates like that, and the paths are the stages people leave out. Writing chemical, then light skips the current and the hot wire, and then there is no way to answer the obvious question: why does a flashlight get warm?

And at almost every stage, some units go into warming something along the way. A full chain says where those went too.

5. The total is the same at every stage

Follow a battery's store as it empties down the chain:

The right-hand column never moves. That is not a coincidence and it is not a rule about batteries — it is true of every chain anybody has ever measured.

It is also the reason the word lost is never right here. When something seems to go missing partway down a chain, it has not gone missing; it has gone somewhere that was not on your list. Usually it has warmed something up.

6. Where the warming happens

Almost every stage of a real chain warms something. The wire in a flashlight bulb gets hot; that is how it glows. A motor gets warm as it turns. Brakes get hot when they rub. Your muscles warm up when you exercise.

This warming does not break the rule about the total. It is just one more store going up: the thermal store of the surroundings. A toy car's battery with $60$ units might pass $45$ to the car's moving store and $15$ to warming the motor. $45 + 15 = 60$, so every unit is still counted.

Scientists say the warming units are dissipated: spread out thinly into the surroundings. They are still there, but spread so thin that they are hard to use again. That is why a flat battery cannot be recharged by the warmth its flashlight left in the room.

7. Writing a chain as a flow diagram

A quick way to write a chain is as a row of boxes and arrows. Each box is a store; each arrow is a path, with its name written on it.

$$\text{battery} \xrightarrow{\text{current}} \text{hot wire} \xrightarrow{\text{light, heating}} \text{room}$$

If you ever find two boxes side by side with no arrow between them, a path is missing. If you find two arrows in a row with no box between them, a store is missing. The diagram makes the gaps easy to see.

Add a small arrow leaving each box downward, labeled warming, for the units that go into the surroundings. Then the diagram shows the whole story: the main chain along the top, and the warming leaking out at each stage.

8. How long can a chain be?

Some chains are very long. Follow the energy in the electricity that lights your classroom back far enough and it goes through a power plant, a fuel, and plants that grew millions of years ago.

1. Long ago, light from the Sun reached ancient plants.
2. The plants' chemical stores filled as they grew.
3. Buried and squeezed for millions of years, they became coal.
4. At a power plant, burning the coal heats water into steam.
5. The steam pushes a turbine, and a generator makes an electric current.
6. The current reaches your classroom and lights a lamp.

Every one of those stages is one store going down and another going up, with a path between. Long chains are made of the same links as short ones.

9. How to check a chain

Run three checks on any chain you write.

1. Alternating. Does every pair of stores have a path between them? Read along the chain: store, path, store, path.
2. Starting store. Does the first stage say what was full before anything happened, and whose it was?
3. Nothing vanishes. If there are numbers, do the units at the end add up to the units at the start, warming included?

The first check catches the most common mistake, a missing path. The third catches the next most common one: forgetting the warming, so the numbers seem to shrink. When your totals do not match, look for a stage that warmed something, and put those units in.

10. Chains inside your own body

You are running energy chains all day long. At breakfast, the food you eat carries a chemical store. Your body breaks the food down and stores some of it in your muscles, ready to use. When you climb the stairs to your classroom, your muscles pull on your bones, which is a force, and your raised store fills as you get higher.

At every stage, some units warm you up. That is why you feel hot after running and why your body is warmer than the room even when you sit still: some of the food's store is always being passed on as warmth. Out of every $100$ units of food you use for climbing, only about $20$ to $25$ end up in your raised store. The rest warm your body and, through your skin and breath, the air around you.

Doctors and nutritionists count these units carefully. The Calories printed on a food label are a measure of the chemical store the food carries, before your body starts passing it down the chain.

11. In the world: an electric car

An electric car's battery might hold $1000$ units in its chemical store. When the car drives, an electric current carries the transfer to the motor, and the motor turns the wheels. Suppose $900$ units reach the car's moving store and $100$ warm the motor and the wires.

When the driver slows down, many electric cars run the chain backward. The wheels turn the motor like a generator, and a current carries some of the moving store back into the battery. This is called regenerative braking. If $300$ of the $900$ units return to the battery, only $600$ go into warming the brakes and the air.

Engineers design these cars by writing out the chain and counting every unit. Each stage where fewer units warm the surroundings means the car goes further on one charge.

12. In the world: a hydroelectric dam

The Hoover Dam on the Colorado River holds back Lake Mead. The water behind the dam is high up, so it has a huge raised store. When gates open, gravity pulls the water down through giant pipes, and its moving store fills.

The fast water pushes the blades of a turbine, a force that fills the turbine's moving store. The turbine turns a generator, which makes an electric current. The current travels along power lines to cities in Nevada, Arizona and California. There it lights homes, runs refrigerators and charges phones. At the very end, almost all of it becomes warmth in those homes.

Out of every $100$ units in the water's raised store, about $90$ reach the power lines as current. The other $10$ warm the pipes, turbines and water along the way. It is one of the longest, most carefully counted chains in the country.

13. Nothing in a chain gets used up

A flat battery feels like proof that energy gets used up, and the battery used up its energy is the sentence almost everyone writes.

What is actually true is narrower and more interesting: the battery's chemical store is empty. The energy that was in it is still in the world — it is spread thinly through the room as warmth, and it went out of the window as light. You could in principle go and find every unit of it. What you could not do is get it back into the battery, which is a different complaint and the subject of the next lesson.

So keep two sentences apart:

• this store is empty — often true, and checkable;
• the energy is gone — never true.

A second mistake is forgetting the warming when you count. If a battery had $60$ units and the car's moving store got $45$, it is tempting to say $15$ units vanished. They did not: they warmed the motor and the air. Put them in their own column and the total comes back to $60$. Every time the numbers seem to shrink down a chain, look for the stage that warmed something, and give those units a place of their own in your table, so that nothing seems to vanish.

14. A bow and arrow

1. Name the full store at the start.

   $\text{the archer's chemical store}$

   Stage one: full before she draws.

2. Name the first path.

   $\text{a force: her arms pull the string}$

   Stage two: how the transfer travels.

3. Name the middle store.

   $\text{the bow's stretched store}$

   Stage three: full while she holds it drawn.

4. Name the second path.

   $\text{a force: the string pushes the arrow}$

   Stage four: released.

5. Name the end store.

   $\text{the arrow's moving store}$

   Stage five: the arrow flies.

15. Where the chain would break

1. Read the short version.

   $\text{chemical store empties, arrow flies}$

   It leaves out the bow entirely.

2. Look for a box with no arrow.

   $\text{archer} \ \dots \ \text{arrow}$

   Two stores side by side with no path between them.

3. Put back the missing path.

   $\text{a force bends the bow}$

   The archer's arms do the pulling.

4. Put back the missing store.

   $\text{the bow's stretched store}$

   Holding a drawn bow is tiring because the bow is storing it.

5. Put back the second path.

   $\text{the string pushes the arrow}$

   How the stretched store reaches the arrow.

6. Read the mended chain.

   $\text{chemical} \to \text{stretched} \to \text{moving}$

   The skipped stage was the explanation of what the bow is for.

16. A bike ride down a hill, counted

1. Name the full store at the top.

   $\text{raised store: } 90 \text{ units}$

   The rider and bike are high up and still.

2. Name the path down.

   $\text{a force: gravity pulls down the slope}$

   How the transfer travels.

3. Fill the moving store at the bottom.

   $\text{moving: } 80 \text{ units}$

   Most of the raised store arrives here.

4. Find the warming on the way down.

   $90 - 80 = 10 \text{ units}$

   Air and tires warmed a little.

5. Follow the brakes.

   $\text{moving } 80 \to \text{brakes' thermal store}$

   Rubbing is the path; the brakes get hot.

6. Add up the warming at the end.

   $10 + 80 = 90 \text{ units}$

   All of it ended up as warmth.

7. Check the total.

   $90 \text{ at the start}, \ 90 \text{ at the end}$

   Nothing was used up.

17. Your turn: a cyclist freewheels down a hill and brakes at the bottom. Where has it all gone?

1. Name the first transfer.

   $\text{raised down, moving up}$

   Gravity pulls the bike down the slope.

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

   Name the second transfer.

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

   Say where it ends.

18. Guided practice

Here are the four stages of a kettle boiling water, jumbled. Put them in the order they happen.

Number the steps in order (write the number in the box):

• the chemical store in the power plant's fuel is full
• an electric current carries the transfer to the kettle
• the heating element passes it into the water by heating
• the water's thermal store is full and it boils

19. Guided practice

Complete the worked solution: an archer's chemical store goes down by $48$ units as she draws her bow, and $8$ of those units warm her muscles. When she lets go, $16$ units warm the string and the air. Follow the rest down the chain.

1. Fill the bow's stretched store.

   $48 - 8 =$ _a units

   What did not warm her muscles went into bending the bow.

2. Fill the arrow's moving store.

   $\text{stretched} - 16 =$ _b units

   What did not warm the string and air went into the arrow.

3. Add up all the warming.

   $8 + 16 =$ _c units

   Nothing was lost: the warming and the arrow add back to the start.

20. Guided practice

In an archer firing an arrow, each of these stages has a different job. Match them.

21. Guided practice

A student writes the chain for a flashlight as: *the battery's chemical store goes down, and light spreads out into the room.* What has been left out?

• The current along the wire, and the thin wire in the bulb heating up
• Nothing: those are the only two things that happen
• The switch being pressed
• The light energy inside the battery waiting to come out

22. Guided practice

Four sentences about a flashlight left on all night. Mark the one that says where the energy went, rather than saying it disappeared.

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

23. Practice

A battery starts with $12$ units in its chemical store, and they leave a quarter at a time. Fill in what is still in the store, what has already left it, and the total.

24. Practice

A flashlight has $54$ units in its battery's chemical store. Move all of them along the chain — battery, then wire, then out into the room — a step at a time. One button breaks the rules; do not use it.

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

25. Practice

A toy car's battery starts with $60$ units in its chemical store. The car runs until the battery is flat: the motor passes $45$ units to the car's moving store and warms up with the rest. Then the car rolls to a stop on the carpet. Fill in each store at the start, when the battery has just gone flat, and when the car has stopped.

26. Somewhere new

An old mill uses a water wheel to lift and drop a heavy hammer onto iron. Put the five stages of the chain in the order they happen.

Number the steps in order (write the number in the box):

• The water behind the dam has a full raised store.
• Gravity pulls the falling water onto the paddles and the wheel's moving store fills.
• The gearing lifts the hammer, filling its raised store.
• The hammer is released and its moving store fills as it drops.
• At the strike, the iron's thermal store fills and the hammer stops.

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 battery starts with $12$ units in its chemical store, and they leave a quarter at a time. Fill in what is still in the store, what has already left it, and the total.

29. What you can do now

You can write out a chain of transfers with its paths in it. Tell someone why the battery used up its energy is not quite right, and what to say instead.

Working for the steps left to you

17. Your turn: a cyclist freewheels down a hill and brakes at the bottom. Where has it all gone?, step 2

17. Your turn: a cyclist freewheels down a hill and brakes at the bottom. Where has it all gone?, step 3