Cool Times with Heat
In this unit we use thermometers to investigate questions about temperature. We explore questions relating to cooling patterns, the effect of location on temperature, and the results of mixing of water with different temperatures
use thermometers to measure temperature in degrees Celsius
investigate factors that influence temperatures
In fact mathematics originated because of needs in other areas. We needed positive integers to enable us to know how many sheep we had. We needed negative numbers to tell us how much in debt we were and to solve simple linear equations. We needed decimals because whole numbers weren’t sufficient to describe out height.
Mathematics goes round in a loop that starts with a real need. From there the mathematics often develops by itself and generates skills and ideas that are totally useless but fascinating to the people who produce them. Then these very ‘pure’ results suddenly have an application to a new problem and the whole loop starts again.
A recent example of this is that after number had developed for quite some time, some mathematicians found some nice patterns that were of no use to anyone but were of interest in their own right. Some 200 years later, someone saw how to use these patterns to make up a code that seems to be very hard to break. Now other people are working on the mathematics to see how far they can push it and to see if, in fact, the code can be broken easily.
Getting Started
- Ask the students how a thermometer works. Use the overhead projection transparency (copymaster) of a thermometer as a focus for the discussion. To confirm the student’s ideas a simple thermometer can be created from a conical flash, a rubber bung and a glass tube. Colour the water with food colouring and gently heat the flask on an element. The water level in the tube will rise as the water expands.
- Use a water soluble overhead projector transparency pen to draw spirit levels on the thermometer transparency. Ask the students to read the temperature shown in degrees Celsius (° C).
- Tell them that they are going to investigate how quickly a thermometer reaches the correct temperature. Provide each group with two thermometers and two cups of water. One cup should contain tap water with many ice cubes in it, the other should have warm water (no more than 50° C). Invite ideas about what will happen when a thermometer is placed in each cup. (The level of the spirit will rise or sink until the correct temperature is found.)
- Tell the students to take the temperature reading every five seconds once the thermometer is immersed. The results should be recorded in a table like this:
Time (sec) 0 5 10 15 20 25 30 » Hot Water 16 31 38 41 43 44 44 » Cold Water 16 10 7 5 4 3 3 » - Ask the students to record the results on a line graph showing time in seconds (horizontal axis) and the temperature readings in degrees Celsius.
- Encourage them to explain what patterns they can see in the data and why they believe it occurs. Look for ideas about the thermometer spirit taking a short time to "heat up" or "cool down" to the temperature of the water and therefore taking a short time to close in on the correct level.
- The next challenge requires students to gain an appreciation of the feel of water temperatures. Each group needs to be provided with plastic cups, thermometers, hot tap water, cold tap water, and some ice cubes. Pose the following problem:
The average temperature of sea water in the Earth’s oceans is four degrees Celsius (4° C). The water in a bathing pool in Rotorua is at a temperature of 32° C. Using the materials you have, can you mix two containers of water, one at each of these temperatures? - Allow the students time to solve the problem. Note that the 32° C cup of water may be hard to sustain at that temperature and may need to be topped up with hot tap water which is about 50-55° C. Similarly the 4° C water will need regular addition of ice.
- Ask the students: If both cups were left for two hours, what temperature would each cup of water be then? (Both will approximate to room temperature.)
Exploring
- For the next 3 days the students will use thermometers to investigate questions about temperature. The first questions relate to cooling patterns.
Does a large amount of water cool faster or slower than a smaller amount?
Does wrapping a container of water in paper result in it cooling faster or slower? - Invite the students to form conjectures about these questions, encouraging them to explain why they believe things will occur. Set up the following experiments to test the conjectures.
- Two plastic cups are set up with different amounts of the same hot water. It is important to warm both cups in the same hot water before the test is started. The thermometers are read every two minutes.
- Three cups are filled with the same amount of water and covered with gladwrap. Leave one jar as is and choose different materials to insulate the other two with, ideas could be tinfoil, bubble wrap, fabric or paper. Poke the thermometers through the gladwarp and rad the thermometers every two minutes.
- Encourage the students to show their findings using graphs and/or tables and to report what the data shows. Ask: How is the idea of wrapping containers of hot water useful in daily life? (Hot water cylinder cladding; lagging of pipes in cold climates.)
- The second day involves explaining what factors influence the temperatures of cities around the world. Get the weather page from your daily newspaper and discuss the section that relates to world temperatures. Usually the report shows highs and lows for the previous day of capital cities from a range of countries. Ask: Why do you think that some cities may be hotter or colder than others?
Their ideas may include:
- Summer/Winter or other season (i.e. Hemisphere)
- Closeness to the Equator
- By the sea or inland
- Altitude above sea level
- Get the students to locate each of the cities in the weather report using their atlas. They can investigate any of the temperature factors raised. For example, some students might analyse the data for Southern Hemisphere and Northern Hemisphere cities and present their findings in appropriate displays.
- Similarly the students may study the effect of location on the temperatures for cities around New Zealand.
- The third investigation concerns the mixing of water with different temperatures. Ocean temperatures, in particular those in the main currents, have a significant effect on world climate. This is the result of the mixing of air at different temperatures near to the ocean and higher above the ocean.
Pose this problem: I have two cups with the same amount of water in each. The water has a temperature of 30° C in one cup and 10° C in the other. If I mix these two cups of water together, what temperature will the mixture be?
- Invite students’ ideas about the possible solution then allow groups to investigate. They will need cups, thermometer, hot and cold water, and ice cubes for cooling.
- While some inaccuracies may occur due to the room temperature, in general the temperature of the mixture should be the mean (average) of the waters being mixed, i.e. 30° C + 10° C = 40° C, 40° C ÷ 2 = 20° C.
- Allow the students to investigate other mixtures such as 200mL at 40° C and 100mL at 10° C so they can establish the idea of a "weighted" mean. That is twice as much water is at 40° C than 10° C so the mean is worked out by 40° C + 40° C + 10° C = 90° C, 90° C ÷ 3 = 30° C.
Reflecting
- In order to bring together the main ideas from this unit the students can be asked to solve a number of problems.
- Problem One: Are we good at estimating water temperature?
Make up several labelled cups of water at different temperatures up to about 55° C. Ensure each cup is wrapped in newspaper or cloth inside a tin can to limit the loss of temperature. Put an ice cream container beside each cup. The students go to each container and estimate the temperature of the water. Their estimate is written on a small piece of paper that is put into the ice cream container. After all the estimates have been done the cups and containers are distributed among the groups.
Students are asked to:
- Find the temperature of the water using a thermometer
- Display the estimates on a dot plot or stem and leaf graph - Problem Two: Why do people wear light coloured clothing in the summer and dark clothing in the winter?
Allow the students to give their reasons and record these on a board or chart.
Tell the students that they are going to check the effect of different colours on temperature. Each group makes up the same shallow containers of water (delicatessen or take away containers are ideal) at tap water temperature. Cover each container with plastic wrap to prevent water loss and wrap it with paper or fabric. The papers or fabrics (varying only in colour) used should reflect a range of colours from black to white.
Leave the containers in a hot sunny location for a few hours. Record the temperature of the water in each container by poking a thermometer through the plastic wrap. Record the results. Ask: What does this tell us about light and dark clothing?
- Problem Three: What times of the day are the hottest? What times are the coldest?
Tell them that they are going to take the air temperature at half-hour intervals during the day. Do this in four different locations, direct sunlight (sheltered), direct sunlight (breeze), shade (sheltered), shade (breeze). Ask them what patterns they expect to see in the temperatures. Record their ideas. Carry out the experiments standing the thermometers up. A wine cask with one face cut out makes an ideal thermometer holder for many groups. The open face is placed on the ‘sunny side’.
Every thirty minutes the students need to check the readings. A period from 9.00 am to 2.00 pm is ideal as it allows time to process the data and suggests that students might like to extrapolate their results for times after 2.00 pm. (E.g. I think the temperature will be 24° C at 3.00 pm.)
Ask the students to display their data on a multiple line graph:
Graph
Invite the students to make statements about what the data shows. They should be encouraged to support their statements by referring to the line graphs.
Dear Family
This week we have been looking at temperatures. We’d like you to do an experiment at home that can be reported to the class.
Temperature Problem
Take three ice blocks that are as close to being the same as possible.
Put one on a plate, one in a glass of cold water from the tap and one in a glass of hot water from a kettle.
Guess:
-
which ice block will melt first and which will melt last
-
guess how long they will take to melt
-
record the times that the three ice blocks actually take to melt.
Bring your results to school by Thursday and we’ll put all the data together to produce a class graph.
| Attachment | Size |
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| Cooltimeswithheatcm1.pdf | 64.9 KB |
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