In this activity, you will investigate how to predict the temperature when two cups of water at different temperatures are mixed.

How do I mix water in a fish tank to adjust the temperature?

A cold mountain stream flows into a large, warm lake. What effect does the cold mountain stream have on the temperature of the lake?

A pet store manager adds a liter of cold water to a warm 50-liter fish tank to replenish the water supply. What effect does the added water have on the temperature of the tank water?

Try to write a rule for predicting the resulting temperature when two quantities of water at different temperatures are mixed.

• 3 large foam cups (500 ml or 16 oz)
• 1 small foam cup (250 ml or 8 oz)
• 2 empty 35 mm film canisters — or some other measuring unit
• cold water
• warm water, 30-40 degrees Celsius (80-100 degrees Fahrenheit)
• large pitchers or jugs

1. Obtain 1 small and 1 large foam cup.
2. Fill the small cup half full with cold water (no ice cubes).
3. Put about the same amount of the warm water in the large cup.
4. Connect the temperature sensor to the computer.

What do you think the temperature will be when you mix cold water with about the same amount of warm water? How did you come up with your prediction?

1. Place the temperature sensor in the small cup. Measure the temperature. When recording the temperature, wait until the temperature read by the sensor stops changing. Then record your result.

2. Create a new dataset, using the “new” button on the left.

3. Repeat the process for the large cup of water, and record your results.

Now that you know the temperatures of the hot and cold water, predict the following on the prediction graph. Draw what you think the temperature graph will look like if you:

a. measure the cold water for 10 seconds;
b. measure the warm water for 10 seconds;
c. mix the two and measure the mixture.

4. Test your prediction:

a. Measure the cold water for 10 seconds.
b. Measure the warm water for 10 seconds.
c. Pour the small cup of water into the large cup. Measure and record the temperature of the mixture.

How good was your prediction?

5. Repeat this entire experiment, but more precisely:

a. Measure and record the temperatures of the cold and hot water.
b. Scoop exactly one film canister of cold water and one film canister of hot water into another foam cup. Note: you can use any method available to measure equal amounts of hot and cold water.
c. Measure and record the temperature of the mixed water.

6. Create a new dataset. Try this experiment:

a. Measure and record the temperatures of the cold and hot water.
b. Scoop exactly two film canisters of cold and one of hot water into another foam cup.
c. Measure and record the temperature of the mixed water.

1. Is the temperature of your first mixture (two quantities that are about equal) close to what you expected? Explain.
2. Is the temperature of your second mixture (two quantities that are not equal) close to what you expected? Explain.
3. Can you come up with an equation that could help someone else accurately predict the final temperature for mixing two equal volumes of water, knowing only the initial temperatures? Compare this with your measured result.
4. Using the same reasoning, can you write an equation for the final temperature for mixing two parts cold with one part warm water? Compare this with your measured result.
5. Can you come up with an equation that could help someone else accurately predict the final temperature of a mixture of two different volumes of water, if they know the initial temperatures and volumes?

Suppose that a pet store manager had a 50-liter tank that he wanted to raise one degree Celsius. Propose a way he could do this without adding more than 5 liters to the tank. How much water would he use, at what temperature?

Try an experiment to test your understanding:
1. Prepare a large volume of cold water, say 1 liter.
2. Prepare a smaller volume of very hot tap water.
3. Measure the temperature of both volumes.
4. Measure the volume of hot water that must be added to the cold water to warm it one degree C.
5. Calculate how much this volume should be.
6. Compare your measurement with your calculation.