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Temperature in degrees Celsius

Measurement · level 3, lesson 6 of 6

A question to start

The coldest temperature ever measured in Canada was −63 °C (read "minus sixty-three degrees Celsius"), at a tiny village called Snag, in the Yukon, in February 1947. The story goes that people there heard their breath freeze into a fine powder that fell with a hiss.

The average temperature on the surface of Mars is about −60 °C. So the coldest day Canada has ever recorded was colder than an ordinary day on Mars. What do these numbers below zero mean, and how do you compare them? That is this lesson.

The idea

Temperature and the thermometer

Temperature tells us how hot or cold something is. We measure it with a thermometer. Many thermometers are a thin glass tube with a coloured liquid inside. When the liquid gets warmer, it expands (takes up a little more room), and since the tube is narrow, the only place it can go is up. When it cools, it shrinks and the line goes down. The marks beside the tube turn the height of the line into a number.

Digital thermometers work differently inside, but they show the same kind of number.

Degrees Celsius

In Canada and most of the world, temperature is measured in degrees Celsius, written °C. The scale is named after Anders Celsius, a Swedish astronomer, who made a 100-step scale in 1742. (Funny fact: he first put 0 at boiling and 100 at freezing. The scale was turned the right way up soon after.)

The scale is built on two fixed points of water:

  • 0 °C: water freezes into ice (and ice melts).
  • 100 °C: water boils (at sea level).

The gap between them is split into 100 equal steps, called degrees. That fits the metric family, which loves the number 100.

Benchmarks to carry in your head:

Temperature What it feels like
100 °C boiling water
37 °C inside your body
30 °C a hot summer day
20 °C a comfortable room
4 °C inside a fridge
0 °C water freezes
−18 °C inside a freezer
−30 °C a bitter winter day on the Prairies

Below zero

Temperatures colder than freezing are below zero, and we write them with a minus sign: −5 °C is "minus five" or "five below zero". These are negative numbers.

A thermometer is a number line standing up. Numbers go up as it gets warmer, and down past zero as it gets colder. The further down a temperature is, the colder it is. So:

  • −10 °C is colder than −2 °C, even though 10 is bigger than 2. Below zero, the bigger the number after the minus sign, the colder it is.
  • Any temperature below zero is colder than any temperature above zero.

Reading a thermometer

−30−20−100 10203040 ? 10 degrees between numbers 5 spaces between numbers each space: 10 ÷ 5 = 2 degrees top of the line: 3 spaces below −10, so −16 °C

Read it the same way as any scale (you did this for kitchen scales in lesson 2):

  1. Find what one small space is worth. From 0 to 10 there are 5 spaces, so each is \(10 \div 5 = 2\) degrees.
  2. Find the nearest numbered mark to the top of the liquid: −10.
  3. Count spaces from there, in the right direction. The line is 3 spaces below −10. Going down means colder, so the reading is \(10 + 3 \times 2 = 16\) degrees below zero: −16 °C.

The trap is in step 3. Below zero, going down makes the number after the minus sign bigger. Count "−10, −12, −14, −16", not "−10, −8, −6, −4".

How much warmer? Count through zero

To find the difference between two temperatures, picture them on the number line and count the steps between them, just as you counted on for elapsed time in lesson 3.

If one is below zero and one is above, jump to zero first.

−10−8−6−4 −2024 6810 8 up to 05 more

From −8 °C to 5 °C: 8 degrees up to zero, then 5 more. The difference is \(8 + 5 = 13\) degrees.

Why not \(8 - 5 = 3\)? Because the two temperatures are on opposite sides of zero. The gap between them includes the whole stretch below zero and the whole stretch above it, so the two parts add.

If both are below zero, say −20 °C and −5 °C, they are on the same side, and the gap is \(20 - 5 = 15\) degrees. Count it: from −20 up to −5 is 15 steps.

Places and seasons

Temperatures change with the season and with the place. Here are rough averages for the coldest and warmest months in three Canadian cities (they change a little from year to year).

City January (about) July (about)
Vancouver 4 °C 18 °C
Ottawa −10 °C 21 °C
Yellowknife −25 °C 17 °C

Vancouver is beside the ocean, which keeps winters mild. Yellowknife is far north and far from any ocean, so its winters are very cold. Its yearly swing, from about −25 °C to about 17 °C, is \(25 + 17 = 42\) degrees.

Temperatures on Mars

Mars is farther from the Sun than Earth is, and its air is very thin, like a blanket with almost no stuffing. Sunlight warms the ground in the day, but the thin air cannot hold the heat at night. So:

  • the average surface temperature on Mars is about −60 °C (on Earth it is about 15 °C);
  • on a summer afternoon near the Mars equator, the ground can warm to around 20 °C;
  • the same place can drop below −70 °C that night;
  • near the poles in winter it can fall below −120 °C, cold enough for carbon dioxide from the air to freeze into frost.

Worked examples

1. Which is colder? Put in order from coldest to warmest: 3 °C, −7 °C, 0 °C, −12 °C, 15 °C.

On the number line, the furthest down is coldest: −12, −7, 0, 3, 15.

2. Across zero. In the morning it is −8 °C. By afternoon it is 5 °C. How much did it warm up?

8 degrees up to zero, then 5 more: 13 degrees.

3. A drop. It is 3 °C at sunset and the temperature falls 7 degrees overnight. What is it in the morning?

Falling 3 degrees takes it to 0 °C. That leaves \(7 - 3 = 4\) more degrees to fall, so it ends at −4 °C.

4. Earth and Mars. How much warmer is Earth's average (15 °C) than Mars's (−60 °C)?

60 degrees up to zero, then 15 more: \(60 + 15 = 75\) degrees.

5. Snag and Mars. Which is colder, the Snag record (−63 °C) or the Mars average (−60 °C), and by how much?

Both are below zero. −63 is further down, so Snag was colder, by \(63 - 60 = 3\) degrees.

6. A Mars sol. Suppose a rover's ground sensor reads 15 °C one afternoon and −75 °C that night. How big was the swing?

75 up to zero, plus 15: 90 degrees in a single sol. Few places on Earth swing even half that much in one day.

Try it

  1. Which is warmer: −4 °C or −9 °C? By how many degrees?
  2. Order from coldest to warmest: 8 °C, −1 °C, −15 °C, 0 °C, −6 °C.
  3. On a thermometer the numbered marks go up in 10s, with 10 spaces between each pair. What is each space worth?
  4. It is −3 °C. It warms up 10 degrees. What is the new temperature?
  5. It is 6 °C. It gets 9 degrees colder. What is the new temperature?
  6. Use the table: how much warmer is Ottawa in July than in January? And Vancouver?
  7. Water boils at 100 °C and freezes at 0 °C. What temperature is exactly halfway between?
  8. A freezer is at −18 °C and a fridge at 4 °C. How many degrees apart are they?
Answers
  1. −4 °C is warmer (it is higher on the number line), by \(9 - 4 = 5\) degrees.
  2. −15, −6, −1, 0, 8.
  3. 10 degrees split into 10 spaces: \(10 \div 10 = 1\) degree each.
  4. 3 degrees takes it to 0 °C, and \(10 - 3 = 7\) more takes it to 7 °C.
  5. 6 degrees takes it to 0 °C, and \(9 - 6 = 3\) more takes it to −3 °C.
  6. Ottawa: from −10 to 21 is \(10 + 21 = 31\) degrees. Vancouver: from 4 to 18 is \(18 - 4 = 14\) degrees.
  7. Half of 100 is 50: 50 °C.
  8. 18 up to zero, plus 4: \(18 + 4 = 22\) degrees.

Common mistake

Thinking −10 is warmer than −2 because 10 is bigger. Below zero, a bigger number after the minus sign means colder: −10 °C is 8 degrees colder than −2 °C. Picture the thermometer: −10 is lower down.

Subtracting across zero. From −8 °C to 5 °C is not \(8 - 5 = 3\) degrees. When one temperature is below zero and the other above, add the two distances from zero: \(8 + 5 = 13\).

Where it leads