Cooling in a Cup

Materials:

• foam cups (8 oz)
• plastic or paper cups (8 oz)
• Aluminum foil
• Hot water (80-99) °C
• syringe or graduated cylinder
• thermometer or digital temperature sensor + computer with sensor control and analysis software

Observation

We observe that the cooling of hot liquid in a cup is affected by the cup material (foam, paper, plastic, metal) and by using a lid.

Question

Which raises the question: Among a metal lining, an insulating cup material, or a lid, which features are most important to keeping a hot beverage from cooling too quickly?

Search Existing Knowledge

Find information about how different mechanisms of heat transfer would be affected by using a lid and various combinations of materials. Record what you learn below.

Hypotheses

Use the information you found above to fill in the blank for each hypothesis below.

Starting with a plastic cup as our baseline,

If ______________  does not contribute much heat loss, then changing to a foam cup will not significantly decrease the cooling rate.

If ______________  does not contribute much heat loss, then adding a lid to the foam cup will not significantly decrease the cooling rate.

If ______________ does not contribute much heat loss, then adding a foil lining to the foam cup and lid will not significantly decrease the cooling rate.

Test

We will test the rate at which a liquid cools in each of the situations above.

We will use the following procedure to control for the amount of water used in each test well as for possible differences temperature of the water and the room:

1. Set up a thermometer to continuously measure the room temperature.
2. Use a high precision instrument, such as a syringe or graduated cylinder, to measure the water volume for each test. Measure out enough hot water to fill the plastic cup about 1/2 way.
3. Place a thermometer in the water and wait ten seconds.
4. Start a timer and record the temperature of the room and the water simultaneously, leave the thermometers in place.
5. Calculate the initial difference between the water temperature and the room temperature.
6. Calculate half of the initial temperature difference.
7. Calculate the temperature the water will be when the temperature difference has dropped to half of its initial value.
8. Record the time when water temperature reached the value you calculated in the previous step. This is the half-life of the temperature difference.
9. Repeat the experiment to determine the half-life when foam cup is used.
10. Repeat the experiment to determine the half-life when a lid is used on the foam cup.
11. Repeat the experiment to determine the half-life when a foil lining is added to the foam cup and lid.

Analysis

Compared to the plastic cup, by what factor did changing to a foam cup increase the half-life of the temperature difference?

Compared to the foam cup, by what factor did adding a lid increase the half-life of the temperature difference?

Compared to the foam with a lid, by what factor did adding foil lining increase the half-life of the temperature difference?

Which feature increased the half-life by the largest factor?

Which feature decreased the half-life by the largest factor?

Conclusions

Which feature is most important to preventing hot liquids from cooling: quality insulation, metal lining, or lid? Explain.

Does radiation contribute much heat loss to hot water in a cup?

Does conduction contribute much heat loss to hot water in a cup?

Do convection and evaporation contribute much heat loss to hot water in a cup?