Passage VI

Students studied the rates at which various heated, solid aluminum spheres cooled in air.

Experiment 1

The students tested 3 solid aluminum spheres, A,B, and C, having different radii. The volume, V, in cm³, and the ratio of surface area to volume, , in cm^-1, for each sphere are shown in Table 1.

Each of the spheres was fitted with a thermocouple to measure the central temperature (the temperature at the center) of the sphere. Then the 3 spheres were simultaneously heated. Once the temperature throughout each sphere was 100°C, the 3 spheres were immediately suspended at time = 0 min in air that was at a temperature of 20℃ (see Figure 1).

The spheres were allowed to cool over the next 30 min while the temperature of the air was kept constant at 20°C. A graph of the central temperature of each sphere versus time over the 30 min cooling period is shown in Figure 2. For each sphere, the cooling rate at a given time equals the graph's slope at that time.

Experiment 2

The students tested 2 solid aluminum spheres, X and Y, that were identical in size. Sphere X was painted with Coating X, and Sphere Y was painted with Coating Y. Each of the spheres was fitted with a thermocouple as in Experiment 1, and then the 2 spheres were simultaneously heated. Once the temperature throughout each sphere was 120°C, the 2 spheres were immediately suspended at time = 0 min in air that was at a temperature of 20°C. The spheres were allowed to cool over the next 55 min while the temperature of the air was kept constant at 20°C. A plot of the central temperature of each sphere versus time over the 55 min cooling.period is shown in Figure 3.