Which holds more energy, a cup of boiling water or a bath of warm water?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Explain the difference between heat and temperature
Read a thermometer and record temperatures in degrees Celsius
Amina touches a cup of hot tea and pulls her hand away. Then she steps into a bath that only feels warm. Which one holds more energy?
Temperature tells you how hot something is. We measure it in degrees Celsius, written °C. A thermometer is the tool that measures it.
Water freezes at 0 °C. Water boils at 100 °C at sea level. High on a mountain it boils at a lower temperature. A healthy body is about 37 °C.
Ice water, a healthy body and boiling water, on a scale from 0 to 100 °C.
To read a thermometer, look at the top of the liquid. Find the nearest number below it. Then count the small marks up from that number.
The liquid is 3 marks above 30. Mei's tea is 33 °C. Always write the unit: 33 °C.
Heat is energy moving from a hotter thing to a cooler thing. It always moves that way. It stops when both are at the same temperature.
Draw it first
Draw hot and cool water mixing
1 Draw a cup of hot water at 80 °C and a cup of cool water at 20 °C. Use the same amount in each.
2 Pour them together. Energy moves from the hot water to the cool water.
3 They end at one temperature, about halfway between: about 50 °C. Heat stopped moving.
The energy in a thermal store depends on two things. One is the temperature. The other is how much of the stuff there is. Thermal energy is the energy in a thermal store.
Tea cooling in a room at 20 °C. Heat moves out of the tea until it is as cool as the room.
Worked example
Use the graph. How many degrees did the tea cool in the first 10 minutes? How many in the next 10?
At 0 minutes the tea is 80 °C. At 10 minutes it is 63 °C.
First 10 minutes: 80 - 63 = 17 °C.
At 20 minutes it is 51 °C. Next 10 minutes: 63 - 51 = 12 °C.
The tea cools by less each time, because it is closer to the room temperature.
Answer: 17 °C, then 12 °C
See it three ways
As a picture
In words
The cup is hotter. The bath is cooler, but it holds a hundred times as much water. A bigger amount of warm water can hold more thermal energy than a small amount of hot water.
In symbols
Warming 1 cup of water (about 250 mL) by 1 °C takes about 1 kJ. Above 20 °C: the cup holds 1 × 80 kJ. The bath holds 100 × 20 kJ.
Worked example
The room is at 20 °C. Which holds more thermal energy: 1 cup of water at 100 °C, or 100 cups at 40 °C? Warming 1 cup of water (about 250 mL) by 1 °C takes about 1 kJ.
The cup is 80 °C above the room. The bath is 20 °C above the room.
Energy = number of cups × degrees above the room × 1 kJ.
Cup: 1 × 80 = 80 kJ.
Bath: 100 × 20 = 2000 kJ.
The bath holds far more thermal energy, even though it is cooler.
Answer: The bath: 2000 kJ, against 80 kJ for the cup
Try it
Fool your hands
You need: three bowls, cool water, warm water: an adult mixes a little hot water from a pot into cool water.
Be safe: An adult makes the warm water and checks that it feels comfortable on their wrist. Never use hot water.
Put cool water in the first bowl and warm water in the third bowl. Mix some of each in the middle bowl.
Put your left hand in the cool bowl and your right hand in the warm bowl. Wait 30 seconds.
Put both hands in the middle bowl. Notice how each hand feels.
What you will see: The middle bowl is at one temperature. Yet it feels warm to the hand that was cool, and cool to the hand that was warm. Your hands feel heat moving, not temperature. A thermometer is fairer.
If you cannot try it, this is what happens.
A wrong idea many people have
Heat and temperature are the same thing.
Why it feels right: People say "hot" for both a high temperature and a lot of heat.
The test that breaks it: The cup is at 100 °C and the bath at 40 °C. The cup has the higher temperature. The bath holds 2000 kJ above room temperature, against 80 kJ for the cup.
What is true: Temperature tells how hot a thing is. Heat is energy moving from hot to cool. A thing's thermal energy depends on its temperature and on how much of it there is.
Key words
temperature
how hot something is, in degrees Celsius.
thermometer
a tool that measures temperature.
heat
energy moving from a hotter thing to a cooler one.
thermal energy
the energy in a thermal store. It depends on temperature and amount.
Back to your guess
The answer is C: The bath, because there is so much more water.
The bath holds far more thermal energy. Hot is only part of the story. How much water there is matters too.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
Room temperature is 20 °C. Which holds more thermal energy? 1 cup of water at 90 °C, or a bucket of 20 cups at 50 °C?
See the answer
The bucket
Cup: 1 × 70 = 70 kJ. Bucket: 20 × 30 = 600 kJ. The bucket holds more.
If you chose B: Temperature is only half the story. The bucket has twenty times as much water. Go to S3.8.4.
If you chose C: They do not. Work out cups × degrees above the room for each one. Go to S3.8.4.
A hot spoon is put into a bowl of cool water. Which way does energy move?
See the answer
From the spoon into the cool water.
Heat always moves from the hotter thing to the cooler thing. The spoon cools and the water warms until both are at one temperature.
If you chose A: There is no flow of cold. Energy only moves from the hotter thing to the cooler thing. Go to S3.8.4.
If you chose C: Energy does move. It keeps moving until the spoon and the water are at the same temperature. Go to S3.8.4.
What temperature does this thermometer show?
See the answer
27 °C
The liquid is 2 marks above 25. Each mark is 1 °C. So the reading is 25 + 2 = 27 °C.
If you chose A: You counted two marks up from 20. The liquid is higher: count up from 25. Go to S3.8.4.
If you chose B: You counted down from 25 by two. The liquid is above 25, so count up. Go to S3.8.4.
If you chose C: You read the number above the liquid. Count the small marks up from 25. Go to S3.8.4.
The air is 24 °C in the morning and 31 °C in the afternoon. How many degrees warmer is it in the afternoon?
See the answer
7 °C
Change = 31 - 24 = 7 °C.
If you chose A: You added the two temperatures. To find how much warmer, subtract. Go to S3.8.4.
If you chose B: That is the afternoon temperature. The question asks for the change. Go to S3.8.4.
What does the thermal energy in a pot of water depend on?
See the answer
Its temperature and how much water there is.
Thermal energy depends on both. A hotter thing holds more, and a bigger amount holds more.
If you chose B: Temperature matters, but so does the amount. A big pot of warm water holds more than a small cup of hot water. Go to S3.8.4.
If you chose C: The amount matters, but so does the temperature. The same amount holds more energy when hotter. Go to S3.8.4.
From an earlier chapter
Review: a gadget takes in 70 J and gives 20 J of useful energy. How much is wasted?
See the answer
50 J
Wasted = 70 - 20 = 50 J.
If you chose A: You added. Wasted energy is what is left over, so subtract the useful energy. Go to S3.8.3.
If you chose C: That is the useful energy. The wasted energy is the rest. Go to S3.8.3.
Keep it
Copy this into your exercise book.
Temperature tells how hot a thing is, in °C. Heat is energy moving from hot to cool. Thermal energy depends on temperature and on how much there is.
Draw: A thermometer with the liquid at 27 °C. Mark 20, 25 and 30 on it.
