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Section 3.6 Temperature

Why Temperature?
Uwera wakes up in the morning and checks the weather, it’s cold and foggy with temperatures around 9Β°C.
What does that mean? Will he wear a light dress or a warm jacket?
Understanding temperature in math helps us make these decisions! It teaches us how to read thermometers, work with negative numbers, and even convert between Degrees Celsius and kelvins.
Have you ever wondered why some countries use different temperature units? Or why water freezes at 0Β°C but boils at 100Β°C? Learning about temperature isn’t just about numbersβ€”it helps us understand the world around us. So, next time you check the weather, think about how math is helping you plan your day!

Subsection 3.6.1 Comparing temperatures

Activity 3.6.1.

Why do we say it’s β€˜as cold as ice’ but never β€˜as hot as fire’? Maybe because no one wants to compare themselves to burnt toast!
Make observation in the following pictures and tell me something about temperature.
(Temperature)
Figure 3.6.1. A
(Temperature-1)
Figure 3.6.2. B

Activity 3.6.2. Multiple-Choice, Not Randomized, One Answer.

Magdalene is cooking porridge, the temperature of the porridge is likely to be?

Checkpoint 3.6.3. True/False.

    If the statement correct choose true and if its wrong choose false. \({\color{blue}\text{Boiling water is colder.}}\)
  • True.

  • False! Cold water is hotter.
  • False.

  • False! Cold water is hotter.
Hint.
When anything is exposed to heat it becomes hot.

Checkpoint 3.6.4.

    If the statement correct choose true and if its wrong choose false. \({\color{blue}\text{Wet clothes are colder.}}\)
  • True.

  • True!
  • False.

  • True!
Hint.
When anything is placed in cool temperatures it becomes colder.

Activity 3.6.3.

    1. If the statement correct choose true and if its wrong choose false. \({\color{blue}\text{When it is raining it is usually hotter than a sunny day.}}\)
  • True.

  • False!A sunny day is hotter than a rainy day.
  • False.

  • False!A sunny day is hotter than a rainy day.
Hint.
Whenever it rains the temperatures becomes cool than when it’s sunny..

Activity 3.6.4.

    1. If the statement correct choose true and if its wrong choose false. \({\color{blue}\text{Water in a refrigerator is colder than boiling milk.}}\)
  • True.

  • True!
  • False.

  • True!
Hint.
Whenever an item is exposed to cool temperatures it becomes cool tand when boiling any substance it becomes hotter.

Subsection 3.6.2 Units of measuring temperatures.

Activity 3.6.5.

Hezron Samson, A grade 7 student visited a health facility centre and came across the equipment shown below.
  • What is the \(\textbf{name}\) of the equipment?
  • State \(\textbf{two functions}\) of the equipment.
  • List \(\textbf{five areas}\) where it can be used.
  • Identify the symbol\({\color{blue}(Β°C)} \)in the instrument above. What does the symbol \({\color{blue}(Β°C)} \) stand for?
  • Identify the symbol\({\color{blue}(K)} \) in the instrument. What does the symbol \({\color{blue}(K)} \) represent?

Explanation.

  1. Temperature is measured using a \({\color{blue}\text {thermometer}}.\)
  2. The most common scales used are the \({\color{blue}\text {Celcious scale}(^\circ C )}.\) and the \({\color{blue}\text {Kelvin (K) scale}}.\)
  3. The boiling point of water at sea level is \({\color{blue}\text {100} ^\circ C}\) or \({\color{blue}\text {373 Kelvin}}.\)
  4. The freezing point of water at sea level is \({\color{blue}\text {0} ^\circ C}\) or \({\color{blue}\text {273 Kelvin}}.\)
  5. The normal temperature of a human body is about \({\color{blue}\text {37} ^\circ C}\) or \({\color{blue}\text {310 Kelvin}}\)

Activity 3.6.6. Clickable β€œinteractive” Activity.

You will need; A sufuria , a thermometer, gas(source of heat) and water.
  1. Measure the initial temperature of water using a thermometer, and record in the table alongside.
  2. Put the water in a sufuria to heat.
  3. Record the temperature of the water after every minute as it heats.
Time Before
Heating
After
1 minute
After
2 minutes
After
3 minutes
After
4 minutes
Time in
degrees celsius
\((^\circ C)\)
Time in
Kelvins \((K) \)
Table 3.6.5.
\({\color{blue}\text{Identify (by clicking) all units of measuring temperatures that are correct.}}\)
β€œThe temperature before water boiling was\((37^\circ C)\) which is equal to\((308) \) Kelvins. The highest temperature by boiling is\((100) ^\circ C\) which is equal to \((383)\)Kelvins whose difference{highest temperature recorded \(- \)lowest temperature recorded} in kelvins is equivalent to \((100) \text{kelvins} \)”

Subsection 3.6.3 Converting temperature in degrees Celsius to Kelvin.

Explanation.

To convert temperature from degree celsius to Kelvin, add 273 to the temperature in degree Celsius.

Example 3.6.6.

Convert \(47^\circ C\) to Kelvin.
Solution.
\begin{align*} K =\amp ^\circ C + 273 \\ =\amp47^\circ C +273 \\ =\amp320 K \\ 47^\circ C = \amp 320 K \end{align*}
The temperature in Kelvin is \({\color{magenta}320\text{K}}\)

Example 3.6.7.

The temperature of a room was \(25^\circ C.\) What was the temperature of the room to Kelvin?
Solution.
\begin{align*} K =\amp ^ \circ +273 \\ =\amp 25^\circ C + 273\\ =\amp 298K \end{align*}
The temperature of the room was \({\color{magenta}298\text{K}}\)

Example 3.6.8.

When Daven fell sick ,her temperature rose to \(39.5 ^\circ C\text{.}\) What was her temperaturein Kelvin?
Solution.
\begin{align*} K = \amp ^\circ C \\ = \amp (273 + 39.5)\\ = \amp 311.5K \end{align*}
The temperature Daven was\({\color{magenta}311.5\text{K}}\)
\({\color{magenta}\text{Converting temperature in Kelvin to degrees Celsius.}}\)

Activity 3.6.7. Matching Problem, Temperature.

\({\color{magenta}\text{To convert temperature from Kelvin to Degrees celsius, subtract 273 from the temperature in Kelvin.} }\)

Example 3.6.9.

Convert 472 Kelvin to degree Celsius.
Solution.
\begin{align*} ^\circ C = \amp K - 273 , where K is 472 in our question.\\ = \amp (472 - 273)^\circ C\\ 472K = \amp 199 ^\circ C \end{align*}
The temperature in degrees celsius is \({\color{magenta}199 ^\circ C}\)

Example 3.6.10.

The temperature of Tana River town was \(292\text{K}\) on Saturday .What was the temperature in degrees Celsius?
Solution.
\begin{align*} ^\circ C = \amp K - 273 , where K is 292 in our question.\\ = \amp (292 - 273)^\circ C\\ 292K = \amp 19 ^\circ C \end{align*}
The temperature of Tana River was \({\color{magenta}19 ^\circ C}\)
\({\color{magenta}\text {Temperature in degrees Celsius and Kelvin.}}\)

Exploration 3.6.8.

\begin{equation*} \mathbf{\text{Now let us play with colours.}} \end{equation*}
\begin{equation*} \text{When the } {\color{blue}\text{ temperature rises}}, \text{it’s} {\color{blue}\text{like the sun}} \text{ giving the Earth a big,} {\color{blue}\text{warm } \text{ hug!} β˜€οΈ} \end{equation*}
πŸ”₯
\begin{equation*} \text{When the }{\color{purple}\text{temperature falls}}, \text{ it’s like the Earth wrapping } {\color{purple}\text{ itself in a cold}}, \text{cozy blanket of air.} ❄️ \end{equation*}
🧊
\begin{equation*} \text{On a } {\color{blue}\text{hot day}}, \text{the} {\color{blue}\text{ground} \text{feels like a heated pan}}, \text{but on a} {\color{purple}\text{cold day}}, \text{it feels like } {\color{purple}\text{stepping on ice! }} \end{equation*}
\begin{equation*} \text{If the } {\color{blue}\text{temperature rises}} \text{too much}, {\color{blue}\text{ice cream melts }}\text{into a puddle. }\text{ If it } {\color{purple}\text{drops too much}}, {\color{purple}\text{water turns into ice!}} \end{equation*}
🍦🧊
\begin{equation*} \text{In the} {\color{blue}\text{ summer}}, \text{it’s like the } {\color{blue}\text{sun turns up the heat in nature’s oven}}. \text{In the} {\color{purple}\text{ winter}}, \text{it dials the } {\color{purple}\text{temperature way down! }} \end{equation*}
πŸ”₯❄️
\begin{equation*} \text{Think of the temperature like a roller coaster}β€” {\color{blue}\text{it goes up when it’s hot }} \text{and } {\color{purple}\text{down when it’s cold! }}🎒 \end{equation*}
\(\mathbf{\text{Which colour represents temperature rise or fall in temperatures?}}\) \({\color{blue}\text{Blue}}\) or \({\color{purple}\text{purple}}\text{.}\) Click on the correct response.
Which colour represents temperature rise? \({\color{blue}\text{Blue}}\) or \({\color{purple}\text{purple}}\)
Thus colour \({\color{blue}\text{Blue}}\) \({\color{purple}\text{purple}}\)also represents all statements indicating falling of temperature or rather very low temperatures.

Example 3.6.11.

The temperature of milk in a container was \(26 ^\circ C\text{.}\) The milk was heated to \(98 ^\circ C\text{.}\) What was the rise in temperature?
Solution.
\begin{align*} \text {Initial temperature} =\amp 26 ^\circ C. \\ \text{Final temperature} =\amp 98 ^\circ C.\\ \text{Temperature increase}=\amp 72 ^\circ C. \end{align*}
The rise in the temperature of milk was \({\color{magenta}72 ^\circ C}\)

Example 3.6.12.

The highest temperature reading on a thermometer was \(27 ^\circ C\) and the lowest was \(6 ^\circ C\text{.}\) By how many degrees was the highest temperature was ahead of the lowest degree reading?
Solution.
\begin{align*} \text {Highest temperature reading} =\amp 27 ^\circ C. \\ \text{Lowest temperature reading } =\amp 6 ^\circ C.\\ \text{Temperature difference}=\amp 21 ^\circ C. \end{align*}
The highest temperature reading of the thermometer was \({\color{magenta}21 ^\circ C}\) ahead of the lowest temperature reading.