Can You Make a Hand Warmer?: Going Further 6–8

Changes that give out heat, and changes that take it in

You already know many changes that give out heat. A gas stove burns gas and heats your pan. Your body “burns” its food slowly, and that keeps you warm. When builders put chuna (quicklime) into water to make whitewash, the water gets so hot that it can boil.

A change that gives out heat to its surroundings is exothermic (exo means “out”, thermic means “heat”). A change that takes in heat from its surroundings is endothermic (endo means “in”). You will meet these words again in Grade 9 (Exothermic reaction and Endothermic reaction).

Here is how to tell them apart. Put a thermometer in the mixture, and watch it.

If the thermometer goes up, the change is giving out heat: it is exothermic.
If the thermometer goes down, the change is taking in heat: it is endothermic. The heat it needs comes from the nearest things: the water, the container, and your hand. That is why the cold pack feels cold.

Change	Heat	What you notice
gas burning on a stove	given out	the flame is hot
quicklime (chuna) in water	given out	the water gets very hot
iron rusting	given out	usually too slowly to notice
baking soda in vinegar	taken in	the glass gets a little cooler
urea fertilizer dissolving in water	taken in	the water gets cold
water freezing	given out	(see Taking the heat away)
ice melting	taken in	your drink gets cold

Some of these are chemical reactions: new substances are made (rust from iron, carbon dioxide from gas). Others are not: when salt or urea dissolves, it is still salt or urea, only spread through the water; when water freezes, it is still water. Heat goes in or out in all of them, and all of them can be used to make a pack hot or cold.

A student dissolves a spoonful of a white powder in a glass of water. The thermometer falls from 25 °C to 17 °C. What can she say?

Pick an answer to see why.

A hand warmer must make your hands warm. Which kind of change could you use in it?

Pick an answer to see why.

Where does the heat come from?

The heat is not made from nothing. It was stored in the substances all along. To see where, think about what holds particles together.

In What Does a Molecule Look Like? you saw that atoms hold on to each other with bonds. In Where Does the Heat Go When Ice Melts? you saw that pulling particles apart against their pull takes energy, like lifting a bag of rice onto a shelf. Now put these together into two rules:

Pulling particles apart takes in energy.
Particles coming together and holding on gives out energy.

Every reaction does both. Atoms let go of their old partners (energy in), and join new ones (energy out). Which is bigger decides what you feel:

If more energy comes out when the new partners join than went in to pull the old ones apart, the extra comes out as heat. The change is exothermic.
If more energy goes in than comes out, the change takes the difference from its surroundings. It is endothermic.

Dissolving works the same way. The particles of the solid must be pulled out of their crystal (energy in). Then water molecules crowd round each one and cling to it (energy out).

Figure 4.1 Where the heat comes from. Top: in rusting, oxygen molecules must be pulled apart, which takes in energy; then the oxygen atoms join the iron, which gives out much more. Bottom: when calcium chloride dissolves, its ions (charged particles) are pulled out of the crystal, which takes in energy; then water molecules cling to each ion, which gives out energy. For calcium chloride, the energy given out wins, and the water gets hot. For urea, the energy taken in wins, and the water gets cold.

The two amounts can be very close. For calcium chloride, the energy given out when the water clings on is only a few per cent bigger than the energy needed to pull the crystal apart. But a few per cent of a large amount is still plenty to make the water hot.

In a reaction, the energy needed to pull the old particles apart is more than the energy given out when they join up in new ways. What happens to the temperature of the mixture?

Pick an answer to see why.

How much heat?

To design a pack, you need numbers. Chemists have measured how much heat each substance gives out or takes in. Here are some, for each gram dissolved in plenty of water at 25 °C, and for iron as it rusts.

Substance	Heat for each gram	Where you meet it
calcium chloride, dissolving	gives out about 730 J	hot packs; it is also spread on icy roads, and is the white powder in damp-absorbing boxes
ammonium nitrate, dissolving	takes in about 320 J	instant cold packs
urea, dissolving	takes in about 240 J	fertilizer; some cold packs
table salt, dissolving	takes in about 66 J	hardly noticed in cooking
iron, rusting	gives out about 7,400 J	air-activated hand warmers

The calcium chloride number is for the dry powder. Calcium chloride that has already soaked up water from damp air gives out less.

From Where Does the Heat Go When Ice Melts? you know that it takes 4.2 J to warm 1 g of water by 1 °C. (In Grade 10 you will meet this as water’s specific heat capacity.) So if a pack gives its heat to the water in it:

$\text{rise in temperature} = \frac{\text{heat given out}}{\text{mass of water (g)} \times 4.2}$

This is only roughly right. Some heat warms the bag and the dissolved solid, and some escapes into the air while it dissolves, so a real pack comes out a few degrees cooler. It is good enough to plan with.

That last answer is the key to designing a pack. What matters for how hot it gets is not the amount of powder alone, but how much powder there is for each gram of water: its concentration. Double the powder in the same water, and the rise doubles. Double the water as well, and the rise stays the same.

Design a hand warmer

Engineers don’t just build something and hope. They follow a loop of steps, and go round it as many times as they need.

Figure 4.2 The engineering design loop. Set the goal, then build, test and improve, round and round, until the design meets the goal.

Step 1: Set the goal

Write down exactly what “a good hand warmer” means, so that you can test it with a thermometer and a clock. The things it must do are its criteria. The limits you must work within are its constraints.

Criteria (for a pack that is held in the hand, in a room at 10 °C):

a.It must get to 40 °C or more: warm enough to feel good.
b.It must never go over 50 °C, so that it can’t burn.
c.It must stay between 40 °C and 50 °C for at least 20 minutes.

Constraints: it must fit in a hand (no more than 200 g of water); it must use a substance that is safe to handle in a sealed bag; it must be cheap.

Why stop at 50 °C? Skin can be burned by things that don’t feel very hot, if they touch it for long enough. In experiments in the 1940s, skin kept at 44 °C for six hours was burned. Each degree hotter roughly halved the time, and at 54 °C about half a minute was enough. Bought hand warmers get hotter than our target (the one in the photo below says 55–70 °C on its back), and that is why they say: keep it in a pocket or a glove, never against bare skin for long, and never on a baby.

Steps 2 and 3: Plan and build, then test

You can change four things: which substance, how much of it, how much water, and what is round the pack. A thin plastic bag lets heat escape quickly; a thick cloth pouch traps a layer of still air around the pack and slows the heat’s escape, as a sweater does for you.

Try it in the widget before you try it for real. It works out the temperature with the formula above, and lets the pack lose heat to the room as a real one does (how fast it loses heat is made up, but realistic).

Each test starts with everything at 10 °C, a cold room. Choose a substance, how much of it, how much water and a cover, and look at the graph of the pack’s temperature over an hour. The green band is the target, 40–50 °C; the dashed line is the room’s 10 °C. Add each test to the table, then change one thing and test again. Can you meet all three criteria? (A very strong urea pack stops cooling at about −11 °C, where some of its water starts to freeze.)

Substance:

Amount of calcium chloride: 20 g Water: 100 g

Cover:

Hottest: 43 °C
Minutes at 40–50 °C: 5 min
Heat given out: 14,660 J

Warm enough, but it cools below 40 °C too soon. Make it bigger, or wrap it better.

Substance	Amount	Water	Cover	Hottest or coldest	Minutes at 40–50 °C

In the widget, you test 20 g of calcium chloride in 100 g of water, in a thin bag. Then you change to 40 g of calcium chloride, keeping everything else the same. What happens?

Pick an answer to see why.

Two packs have the same concentration: 20 g of calcium chloride in 100 g of water, and 40 g in 200 g. Both are in thin bags. How do they compare?

Pick an answer to see why.

Testing fairly

When you test for real, change one thing at a time. If you change the amount of powder and the cover together, and the pack gets better, you can’t tell which change helped. Keep everything else the same: the water’s starting temperature, the kind of bag, how long you shake it, and where you put the thermometer.

Here are the results of one student’s tests, with a real pack, a thermometer and a clock. (Made up for this book, but typical of what you would get.)

Test	What she used	Highest temperature	Minutes between 40 °C and 50 °C
1	10 g calcium chloride, 100 g water, thin bag	26 °C	0
2	20 g calcium chloride, 100 g water, thin bag	43 °C	5
3	20 g calcium chloride, 100 g water, cloth pouch	44 °C	11
4	30 g calcium chloride, 150 g water, cloth pouch	44 °C	13
5	35 g calcium chloride, 150 g water, cloth pouch	50 °C	27

Test 1 was too cool. In test 2 she doubled the powder, and the pack got past 40 °C, but cooled too quickly. In test 3 she changed only the cover, and the pack stayed warm about twice as long. In test 4 she made the whole pack bigger with the same concentration: it got just as hot, and stayed warm only a little longer. In test 5 she kept the bigger pack and added a little more powder to the same water: it got hotter, up to 50 °C but not over, so it started higher and took 27 minutes to cool to 40 °C. Test 5 meets all three criteria.

Step 4: Improve

A design that passes can still be made better. Is it too heavy? Does it cost too much? Could it be used again? Each answer sends you round the loop again. That is how bought hand warmers were designed, as you will see next.

Hand warmers you can buy

The packet that rusts

The packet at the bus stop is an air-activated hand warmer. Inside is a damp mixture of iron powder, salt water, activated charcoal and vermiculite. It gets warm because the iron rusts.

You have seen iron rust: a bicycle left out in the monsoon, a nail in a puddle. Rusting gives out a lot of heat, about 7,400 J for each gram of iron, about ten times as much as calcium chloride. But a rusty nail never feels warm, because it rusts over weeks and its heat leaks away as fast as it is made. The hand warmer makes the iron rust fast:

The iron is a fine powder, so a huge surface is open to the air.
The salt water makes iron rust faster, as the salty sea air rusts cars in towns by the sea.
The activated charcoal is full of tiny holes that hold air and water close to the iron.
The vermiculite, a light mineral, soaks up the water so the powder stays damp but not wet.

It must not rust too fast, though, or it would be too hot and used up in minutes. So the mixture is sealed in an inner bag with tiny holes, which let air in slowly. The whole thing is sold in an airtight wrapper. Until you open it, no air gets in, and nothing happens. Seal a half-used warmer in an airtight bag, and it stops, to be used later.

Figure 4.3 Inside an air-activated hand warmer. The inner bag, with its tiny holes, sits in an airtight wrapper until you tear it open. Close-up: the damp mixture of iron powder, activated charcoal and vermiculite. Air comes in through the holes, the iron rusts, and heat comes out.

A disposable hand warmer in its printed plastic wrapper, front and back, lying on a wooden table — **Figure 4.4** A disposable hand warmer sold in Germany (made in Korea), front and back. The back lists what is inside (iron, water, activated charcoal, cellulose and zeolite, a mineral that holds water as vermiculite does), says it warms itself to 55–70 °C, and lasts up to 8 hours. It weighs about 30 g. Photo: Suricata, CC BY-SA 3.0

The holes control how fast the iron rusts, and so how hot the pack gets. The amount of iron controls how much heat it can give altogether, and so how long it lasts.

A hand warmer in a pocket, on a 10 °C morning. Change how many air holes its inner bag has, and how much iron powder is in it, and watch its temperature over a day (the dashed line is the pocket’s 10 °C). (The energy from each gram of iron is real; how much air each hole lets in, and how fast the pocket loses heat, are made up, chosen to behave like real packs.)

Air holes: 70

Iron:

Settles at: 48 °C
At 40 °C or more for: 8.6 hours
Heat it can give: 148,000 J

Just right: the pack stays between 40 and 50 °C until the iron is nearly used up.

In the widget, you give a hand warmer more air holes but the same iron. What happens?

Pick an answer to see why.

The pack you can use again

Another kind of hand warmer is a clear plastic pouch of liquid with a small metal disc inside. Bend the disc with a click, and white crystals spread through the liquid in a few seconds. The pack warms to about 50–55 °C, and stays warm for a while as it goes solid.

The liquid is a solution of sodium acetate (the salt you get from baking soda and vinegar). Its crystals melt at about 58 °C. Melted, and then cooled very gently, it can stay liquid far below that temperature, at room temperature, waiting. The click of the disc starts the first crystals, and then the whole pack crystallizes at once. As it goes solid, it gives out the heat it took in when it melted, just as freezing water gives out its latent heat (Taking the heat away). No new substance is made: it is a change of state, not a chemical reaction.

To use it again, put the pack in boiling water until all the crystals melt, then let it cool. It is ready for next time.

Two plastic pouches on a table: the left one full of clear liquid, the right one filled with white solid crystals — **Figure 4.5** Two reusable hand warmers. Left: ready to use, the liquid clear. Right: after the click, the liquid has crystallized into a white solid and given out its heat. Boiling the pack melts the crystals again. Photo: Suricata, CC BY-SA 3.0

Cold packs

An instant cold pack has a small inner bag of water inside a bag of dry powder, usually ammonium nitrate or urea. Squeeze the pack hard, and the inner bag bursts. The powder dissolves, taking in heat, and the pack can get close to 0 °C. It is used once, on a sprain or a bump, when there is no freezer nearby.

A flat blue plastic pack with “Instant cold pack” and Japanese writing printed on it, and the words “Do not eat” — **Figure 4.6** An instant cold pack from Japan. You hit or squeeze it to burst the inner bag of water. Like most of them, it warns: do not cut it open, and do not eat what is inside. Photo: Qurren, CC BY-SA 4.0

A story from science

From warm stones to rusting iron

For hundreds of years, people in Japan warmed themselves in winter with warm stones (onjaku): stones heated in the fire, wrapped in cloth, and tucked into their clothes until they cooled.

In 1923, a Japanese inventor, Niichi Matoba, made a pocket warmer that burned lighter fuel very slowly, without a flame, on a little pad of platinum. It stayed warm for many hours, and it is still made today.

Then, in the 1970s, Japanese companies began selling a new kind (the best known, Hokaron, went on sale across Japan in 1978): a paper packet of iron powder, salt and charcoal that warmed up when you took it out of its wrapper and shook it. It was cheap, light and safe, and it could be thrown away when it was used up. The disposable kairo, as it is called in Japan, spread across the world. When you warm your hands with one, you are using a reaction that people spend money to stop everywhere else: rust.

Investigate it yourself

Activity

A cold pack from fertilizer

Urea is the white fertilizer that many farmers in Nepal spread on their fields. Dissolving it takes in heat. Make a cold pack, then find out what makes it colder.

You need: urea fertilizer (a cup of it, from a farming family or an agrovet shop), water, a kitchen thermometer if you have one, two or three small zip-lock plastic bags, a teaspoon, a measuring cup, and an adult to help.

Take care: use only urea, nothing else, and never mix it with bleach or any other cleaner. Don’t taste it or touch your eyes or mouth after touching it; use the spoon, not your fingers, and wash your hands afterwards. Keep it away from small children and animals. When you finish, pour the solution into a bucket of water (at least ten times as much water), and use that to water the garden: it is plant food, but too strong for plants before you add the water.

Put half a cup of tap water in a zip-lock bag. Feel it, or measure its temperature.
Add 2 level teaspoons of urea. Squeeze out the air, close the bag tightly, and squash the bag gently until the urea has dissolved.
Feel the bag, or measure the temperature again.
Now test like an engineer. Change one thing: try 4 teaspoons in the same half cup, then 4 teaspoons in a whole cup. Keep everything else the same. Write down the coldest temperature each time.
Which pack got coldest? Which stayed cold longest? Wrap one in a cloth and see if it stays cold longer.

What you should see

The water gets noticeably colder as the urea dissolves, by several degrees or more. 4 teaspoons in half a cup gets colder than 2 teaspoons in half a cup: about twice the fall. 4 teaspoons in a whole cup cools about as much as 2 teaspoons in half a cup, because the concentration is the same, but it stays cold longer, because there is more of it. The cloth slows the heat flowing in from the room, so the wrapped pack stays cold longer.

Activity

Warm iron in a jar

Rust gives out heat. Here is a gentle way to feel it, without the special mixture.

You need: a pad of plain steel wool (from a hardware shop; a stainless-steel kitchen scrubber will not work, because stainless steel doesn’t rust), a cup of vinegar, a glass jar with a lid, a thermometer that fits in the jar, rubber gloves, and an adult to help.

Take care: wear the gloves, because steel wool has tiny sharp splinters. Vinegar is safe, but keep it out of your eyes.

Put the thermometer in the empty jar, close the lid, and after 5 minutes read the temperature.
Soak the steel wool in vinegar for 1 minute. (The vinegar cleans off the thin coating of oil that stops it rusting in the shop.) Squeeze out the vinegar.
Wrap the damp steel wool round the bulb of the thermometer, put both in the jar, and close the lid.
Read the temperature every minute for 10 minutes.

What you should see

The temperature slowly rises by a few degrees. The iron is rusting, using the oxygen in the jar, and giving out heat. After a day the steel wool is orange-brown. It warms much less than a hand warmer, because steel wool’s threads have far less surface than a fine powder, and there is no salt or charcoal to speed the rusting up.

In short

An exothermic change gives out heat, so the thermometer goes up. An endothermic change takes in heat from its surroundings, so the thermometer goes down.
Heat moves in chemical reactions (rusting, burning) and in other changes (dissolving, freezing, melting). Heat always flows from hotter to colder; “cold” never flows.
Pulling particles apart takes in energy; particles joining together gives out energy. If more comes out than goes in, the change is exothermic; if less, endothermic.
How hot or cold a dissolving pack gets depends on the substance and its concentration (how much for each gram of water). How long it lasts depends on how big it is and how well it is wrapped.
An engineer sets criteria and constraints, then builds, tests and improves, changing one thing at a time.
An air-activated hand warmer rusts iron powder fast, with salt water and charcoal, but lets air in slowly through tiny holes, so the heat comes out gently for hours.

Questions

Which of these is an endothermic change?

Pick an answer to see why.

A student is testing heat packs. In her second test she uses more calcium chloride and a cloth pouch instead of a thin bag. The pack stays warm much longer. What is wrong with her test?

Pick an answer to see why.

Which pack would get the hottest?

Pick an answer to see why.

a.

A pack holds 15 g of calcium chloride and 100 g of water, both at 10 °C.

a.How much heat does the calcium chloride give out as it dissolves?
b.About how hot does the water get?
c.Does it meet the criterion of reaching at least 40 °C?
d.Without changing the water, how much calcium chloride would you need to reach 45 °C?

Answer

a.Heat = 15 g × 730 J per g = 10,950 J.
b.Rise = 10,950 ÷ (100 × 4.2) = 10,950 ÷ 420 = 26.1 °C. The water gets to about 10 + 26 = 36 °C.
c.No: 36 °C is below 40 °C (and a real pack, losing some heat, would be a little cooler still).
d.A rise of 35 °C needs 100 × 4.2 × 35 = 14,700 J, and 14,700 ÷ 730 ≈ 20 g.

b.

Use the idea of pulling apart and joining up to explain why:

a.dissolving calcium chloride makes water hot;
b.dissolving urea makes water cold.

Answer

When any solid dissolves, its particles are pulled out of the crystal, which takes in energy, and then water molecules crowd round each particle and cling to it, which gives out energy.

a.For calcium chloride, the energy given out as the water clings on is more than the energy taken in to pull the crystal apart. The extra energy comes out as heat, and the water gets hotter: exothermic.
b.For urea, the energy given out is less than the energy taken in. The difference is taken from the water itself, whose molecules slow down, so the water gets colder: endothermic.

c.

A student tested three cold packs, each in a thin bag, starting at 25 °C. (Made-up results.)

Pack	Urea	Water	Coldest temperature	Minutes below 15 °C
A	15 g	100 g	17 °C	0
B	30 g	100 g	9 °C	9
C	60 g	200 g	9 °C	15

a.Which two packs show the effect of the amount of urea in the same water? What is the effect?
b.Why do packs B and C reach the same coldest temperature?
c.Why does C stay cold longer?
d.A coach wants a cold pack that stays below 15 °C for at least 20 minutes and weighs less than 300 g. Suggest a change to pack B or C, and say how you would test it.

Answer

a.A and B: both have 100 g of water, and B has twice the urea. Twice the urea took in twice the heat, so B cooled about twice as much (16 °C instead of 8 °C).
b.B and C have the same concentration: 30 g for every 100 g of water. So each gram of water gives up the same heat, and cools by the same amount.
c.C is twice as big. To warm up again it must take in twice as much heat from the room, but its surface is less than twice as big, so heat gets in more slowly compared with what it needs. It stays cold longer.
d.Good answers: put pack C (260 g, under 300 g) in a cloth pouch or a foam sleeve, to slow the heat coming in from the room; or use a little more urea for each gram of water so it starts colder. Test it by changing only that one thing from pack C, starting at the same temperature, reading the thermometer every minute, and counting the minutes below 15 °C. Repeat to make sure the result is reliable.

d.

Ramesh says, “Iron rusting can’t be used for a hand warmer: my bicycle rusts, and it never gets warm.” Explain why his bicycle doesn’t feel warm, and how a hand warmer makes the same reaction useful.

Answer

Rusting does give out a lot of heat, about 7,400 J for each gram of iron, but a bicycle rusts very slowly, over months, only on its surface. The heat comes out so slowly that it leaks into the air as fast as it is made, and the bicycle never warms up.
A hand warmer makes the iron rust much faster: the iron is a fine powder with a huge surface, it is kept damp with salt water, which speeds up rusting, and charcoal holds air and water close to it. But it is sealed in a bag with tiny holes, so air gets in only slowly, and the heat comes out gently over hours instead of all at once. It stays in an airtight wrapper until it is needed.

e.

Design a cold pack for a school’s first-aid box.

a.Write two criteria and two constraints for it.
b.Which substance would you use, and why?
c.Describe how you would test it, and what you would measure.

Answer

a.Criteria, for example: it must get to 10 °C or below within 2 minutes of squeezing; it must stay below 15 °C for at least 15 minutes. Constraints, for example: it must be safe if it leaks, cost little, weigh under 300 g, and keep for a year in the box without going off.
b.Urea is a good choice: it takes in heat as it dissolves (about 240 J for each gram), it is cheap, easy to buy in Nepal, and much safer to handle than ammonium nitrate. (Ammonium nitrate takes in more heat, but it is harder to buy and must be handled with care.)
c.Build the pack with the water in a small inner bag that bursts when squeezed. Start every test at the same room temperature. Squeeze it, put a thermometer against or inside it, and read the temperature every minute. Record the coldest temperature and how many minutes it stays below 15 °C. Then change one thing at a time (the amount of urea, the amount of water, a cloth cover), test again, and keep the change if it helps. Test each design more than once.

Where to go next

Where Does the Heat Go When Ice Melts? Melting and freezing take in and give out heat too, without any chemistry. The reusable hand warmer uses this. Where Does the Heat Go When Ice Melts?
Can You Build a Box That Keeps Ice Frozen All Day? The other half of the problem: slowing the flow of heat, with a whole design project.
What Happens to the Dal Bhat You Eat? Your body is a slow exothermic reaction: it “burns” food with oxygen to keep you warm and moving.