## Temperature and Volume

Comparing Temperature and Volume
The temperature and volume of a gas are closely related. In this task, you’ll observe how changing the air temperature inside an empty water bottle affects its volume. To do this, you’ll immerse the water bottle in hot water and cold water and compare the volume of hot air to the volume of cold air inside the bottle.

Estimated time to complete: 2 hours

If you’ve purchased an Edmentum lab kit, remove the thermometer and graduated cylinder from the bag labeled Common Materials. These materials are italicized in the following equipment list. Then gather any additional items shown in the list. If you’re not using an Edmentum lab kit, alternatives are suggested in parentheses.

You’ll need these materials:

thermometer, readable from 0°C to 100°C (32°F to 212°F)
graduated cylinder (may also use kitchen measures: cup, tablespoon, teaspoon, ½ teaspoon)
disposable plastic water bottle with cap (10-ounce capacity preferred), or similar transparent bottle with a tight-fitting cap
two large bowls or pots, large enough to completely contain the water bottle
hot and cold tap water
ice
stopwatch (may also use a timer or a clock)
Stay safe! Be careful when handling hot water to avoid burns.
Part A
Write a hypothesis about what will happen to the air in the plastic bottle when its temperature is decreased. What relationship do you expect to find between temperature and volume?

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Part B
It’s time to get started. Fill the plastic bottle to the brim with water. Then pour the water into a graduated cylinder or other measuring tool to measure the total capacity of the bottle. Note that you may need to fill the measuring tool multiple times. To recall how to use a graduated cylinder, watch this video on measuring volume before continuing.

If you are using household measuring tools, use these conversions to record the exact capacity of the bottle in milliliters (mL). Visit the math review for help with converting units:

1 cup = 240 mL
1 tablespoon = 15 mL
1 teaspoon = 5 mL
What is the capacity of the bottle in milliliters?

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Part C
In this experiment, you’ll perform three trials. Follow these steps to proceed with the first trial:

Fill one of the two bowls with very warm water, between 45°C and 49°C (113°F and 120°F). Use the thermometer to measure the temperature of the water in degrees Celsius, and record it in the provided table.
Stay safe! To avoid burns, do not use water hotter than 49°C.
Fill the other bowl with ice water. The temperature of the water in this bowl should be between 5°C and 10°C (41°F and 50°F). Use the thermometer to measure the temperature of the water in degrees Celsius, and record it in the table.
With the bottle uncapped, hold the bottle in the bowl of warm water. The bottle should be mostly under water, but the mouth of the bottle should be above the water so that water doesn’t enter the bottle. Hold the bottle in this position for three minutes, using the stopwatch to track the time. The air inside the bottle will come to the same temperature as the water in the bowl. Cap the bottle tightly, and then remove it from the warm water.

a bottle placed inside a vessel of warm water with the mouth of the bottle just above the level of the water in the vessel; after 3 minutes, the bottle is removed from the water and capped
Hold the bottle by the neck to avoid prolonged skin contact with the warm water.

Quickly transfer the bottle to the bowl of cold water as shown in the image. Turn the bottle upside down, and immerse it in the bowl (left). Now remove the cap (right). Notice that some water will enter the bottle. Hold the bottle in the upside-down position in the cold water for three minutes. Time yourself using a stopwatch, like before. The air inside the bottle will now come to the same temperature as the water. Take care that the bottle remains vertical in the upside-down position. If it tips far enough that air bubbles start to escape, you’ll need to restart the procedure.

two images of an inverted bottle immersed in a vessel containing water: the bottle is shown capped bottle (left) and without a cap, partially filled with water, with empty air space above the water level in the bottle (right)
Try to minimize prolonged skin contact with the cold water.

After three minutes, move the bottle up in the water until the level of the water inside the bottle is precisely even with the level of the water outside the bottle. This position ensures that the pressure of the air in the bottle equals the pressure of the atmospheric air. Be sure to keep the mouth of the bottle in the water (image on left). After the water levels are aligned, cap the bottle tightly while holding the bottle still (image on right), and then remove it from the water.

two images of an inverted bottle in a vessel containing water with the water inside the bottle even with the water line; the bottle shown uncapped (left) and then capped (right)
Set the bottle upright on a flat surface, and then remove the cap. Pour the water from the bottle into a graduated cylinder or other measuring tool to measure its volume. Record this measurement in the table below for trial 1.
Repeat steps 1–6 two more times to complete trials 2 and 3. Try to keep the temperature of the hot water constant across the trials as much as possible. Record your data in the table.

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Part D
Repeat the procedure from part C to complete three more trials. The temperature of the hot water in each trial should be the same as the temperature of the hot water in part C. But the cold water should be at a different temperature than in part C. Use any three temperature points between 15°C and 35°C (59°F and 95°F). Record your data in the table.

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Part E
Transfer your results from parts C and D to the first three rows of the provided table. Then calculate the volume of air in the bottle for each of the six trials. To do so, subtract the volume of water in the bottle recorded at the end of each trial from the total volume of the bottle you recorded in part B.

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Part F
Question
Plot air volume versus cold temperature from your six trials in part E. Add a seventh data point for the volume of the air in the bottle at high temperature. (Hint: The volume corresponding to the high temperature is the total volume of the bottle from part B.) In the relationship menu, select Linear to graph a straight line. Then check the best fit box to graph the line of best fit for your data.
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Part G
Look at the data that you graphed in part F. What can you conclude about the relationship between the temperature and the volume of a gas? Do your results agree with your hypothesis? If not, why do you think that is?

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Part H
What happened to the bottle after you placed it in cold water and before you took the cap off? Why did it happen?

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Part I
Absolute zero is the lowest possible temperature. If the relationship between the volume and the temperature of a gas were consistent all the way down to absolute zero, then a gas at absolute zero would have zero volume. According to the line of best fit produced by graphing your data, what is the temperature (in °C) of absolute zero? For better accuracy, you may use the equation of the function below the graph, plugging in 0 for V and solving for T.

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Part J
Liquid nitrogen is cold and can be used to cool objects to -196°C. If you put the bottle of warm air in liquid nitrogen at this temperature, what would the volume (mL) of air in the bottle be?

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Part K
The accepted value of absolute zero is -273.15°C. Was your result from part I close to this value? What might have caused your result to differ from the accepted value?

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