Introduction
In this investigation, students will explore the concept of energy transfer and temperature
changes. By using a temperature sensor attached to a computer, students will be able to
investigate mixing water of various volumes and develop a model for predicting mixing
results.
Students will gain experience with both inquiry skills and content, including:
 understanding that heat moves in predictable ways, flowing from warmer objects
to cooler ones, until both reach the same temperature.
 using technology to gather data and make accurate measurements
 identifying and controlling variables
 developing descriptions, explanations, predictions, and models using evidence
 communicating experimental methods
 using mathematics to answer questions about the natural world
 creating appropriate graphical representations of data
 applying and adapting a variety of appropriate strategies to solve problems
 using the language of mathematics to express mathematical ideas precisely
 Communicating mathematical thinking coherently and clearly to peers, teachers,
and others
 applying mathematics in contexts outside of mathematics
Discussion Guide (TBD)
As one of the Inquiry units, Unit 6 stresses aspects of scientific inquiry – how can
students investigate various situations occurring around them. In order to have a
framework for this, the Unit focuses on the energy transfer and temperature changes in
water and in air.
The general flow of Investigation 1 is meant to help students go through a process of
scientific inquiry. As scientists, we often look at a complicated situation and try to
“break it down” to a simpler situation that can be more easily investigated. Then, using
insights from this simpler situation, the principles learned can be used in more
challenging situations. In investigation 1, students are asked to look at two situations: a
cold river flowing into a large warm lake; and a pet store manager pouring a liter of cold
water into a warm fish tank. Both situations are related, since water of two temperatures
is mixing, but the fish tank scenario is more easily investigated. Once principles from the
fish tank scenario are understood, they can then be applied to more complicated situations
to gain a better understanding of what is occurring.
Why are the temperature effects of mixing water important? In the river example, the
aquatic life in an area is affected by this mixing. For example, different types of fish
prefer different temperature environments. In colder water, you may find lake trout and
walleye. In warmer water, you may find bass or if the water is still warmer, catfish.
Temperature is not the only factor, but it is an important one.
In mixing situations created by man, these temperature changes can cause environmental
problems. An example is a steam-electric power plant using lake or river water for
cooling during the production of electricity. Water is brought into the plant and used for
cooling which in turn heats the water. This warmer water is then returned to the lake or
river, causing temperature changes which affect the aquatic life in the area. By better
understanding the nature of this mixing and the effects on temperature, we can better
understand the impact on the environment.
In Investigation 1, students look at a simplified version of the fish tank example: mixing
two cups of water. In Trial 1, experiments are qualitative – students get a feel for what
happens to temperature when two different samples of water mix. The Investigation
becomes more scientific in Trial 2. Students begin to measure both the volume and the
temperature of the initial samples and try to figure out what the resulting temperature will
be. In the Analysis of the investigation, students analyze their data to see if they can
come up with a predictive model that can help them accurately predict future mixing
possibilities.
The flow of the Investigation and the Unit is a general pattern for scientific inquiry. First,
we often look at situations qualitatively - we observe a situation of interest, and try to
figure out what is going in. In this process, we make decisions about what are the
important influences or factors in a given situation, and how can these factors be
measured more carefully. Finally, it is common to try to draw some conclusions that
solidify our understanding of what is occurring. Perhaps these conclusions can also be
applied to other similar situations to gain a better understanding of related phenomena.
Students may need practice making an accurate measurement with the sensor. Usually a
temperature sensor will reach a fairly steady temperature in water quickly. If students
wait for the sensor to be absolutely settled, they may never take a measurement, since the
water will always be slowly tending towards room temperature. One way to check
accuracy of student measurements is to look at their measured value for ice-cold water.
Ice-cold water will approach 0ºC if the ice is left in the water for a few minutes. Note
that when students are mixing ice-cold water, they should not include ice-cubes, only the
water.
This investigation is written using Celsius (°C) temperature units. In the Celsius system,
water freezes at 0 °C and boils at 100 °C. This scale may be difficult for students who
are used to the Fahrenheit (°F) system, for which water freezes at 32 °F and boils at 212
°F. You may spend some time comparing these scales if you wish, but it’s not necessary.
For the investigation, which uses bar graphs as well as numerical values to display
temperature.
Additional Teacher Background
The content of Unit 6 has to do with heat energy flow in both water and air. Heat energy
flows from hot to cold. In the process, hot objects or substances cool, and cold objects or
substances warm. Heat energy continues to flow until both objects or substances are the
same temperature. When this happens, no further heat energy flows. Unfortunately,
there is no direct way of measuring heat energy. All we can do is measure the effect of
that heat energy flowing, which is a resultant change in temperature. When no heat
energy is flowing, the temperature remains constant.
If two cups of water of the same temperature are mixed, the resulting cup will contain
water of this same temperature, since there was no difference in the heat energy of the
initial two cups. If two different temperature cups of water are mixed, the resulting water
temperature will be between the two initial temperatures. The final temperature is related
to the initial temperatures of the cups of water, and the amounts of water being mixed.
In any given mixing situation, energy must be conserved. In other words, whatever heat
energy there was before mixing will be the same after mixing. Also, when dealing with
cups of water, the mixing will be nearly complete, meaning the resulting water will all be
at a uniform temperature. As an example, if you have two cups of the same amount of
water, and one cup is 20 degrees and one cup is 40 degrees, the mixture will be 2 cups at
30 degrees. It holds that if you add all the temperatures of each cup of water and divide
by the number of cups, you will get a good estimate of the final mixture temperature.
In a perfect situation, the result would be exact. However, several energy losses occur
which affect results. The temperature of the water in any cup will change towards room
temperature as energy transfer takes place between the water and the air. If the water is
hotter than room temperature, the heat energy from the water is heating surrounding air,
resulting in a slow cooling of the water. For colder water, the reverse is true, and the
water will slowly warm. This will not play a large role in the experiment if students
proceed through measurements at a steady pace. If, however, students get distracted or
take breaks, this will affect results more.
The water will also heat or cool the Styrofoam cup it is in, and the film canisters used to
measure volume. Again, these changes are relatively minor, but will affect results.
Aside from energy losses, measurement precision will be another factor. If students do
not measure carefully, it will be more difficult to see the effect of volume on final
temperature.
Suggested Timeline
The amount of time you spend on introductory discussions, data collection and analysis
will determine your overall timeline. The following represents a possible timeline
 One half class period – “Setting Up” discussion
 One class period – Trial I: Temperature of mixing water
 One class period – Trial II: Accurately predicting water temperature
 One class period – Analysis and “Wrap Up” discussion