In this experiment, you will carri out a full investigation into how the colour of a surface and the volume of water together affect the rate of cooling by ...
Question 1 Report
In this experiment, you will carri out a full investigation into how the colour of a surface and the volume of water together affect the rate of cooling by radiation. You uses aluminium cans in three colours (matt black, white, and shiny silver) and two volumes of hot water (100 ml and 300 ml). You fills each can to the appropriate volume with water at 85 °C, places a cardboard lid with a thermometer through it, and records the temperature every 5 minutes for 20 minutes. You carries out all six combinations. The room temperature is 21 °C. Fig. 70.1 shows the arrangement for one can. Table 70.1 shows your results.
| Time /min | 100 ml / °C | 300 ml / °C | ||||
|---|---|---|---|---|---|---|
| Black | White | Silver | Black | White | Silver | |
| 0 | 85 | 85 | 85 | 85 | 85 | 85 |
| 5 | 68 | 73 | 76 | 78 | 80 | 82 |
| 10 | 55 | 63 | 69 | 72 | 76 | 79 |
| 15 | 45 | 55 | 63 | 67 | 72 | 77 |
| 20 | 38 | 49 | 59 | 63 | 69 | 75 |
Table 70.1
(a) Record the temperature of the 100 ml black can at 10 minutes. [1]
(b) Record the temperature of the 300 ml silver can at 20 minutes. [1]
(c) Calculate the total temperature drop for the 100 ml black can and the 300 ml black can over 20 minutes. [2]
(d) Calculate the average rate of cooling in °C per minute for the 100 ml white can over 20 minutes. [1]
(e) State which combination cools the fastest. [1]
(f) State which combination cools the slowest. [1]
(g) Describe the effect of surface colour on the rate of cooling. Use data from the table to support your answer. [2]
(h) Describe the effect of volume on the rate of cooling. Use data from the table to support your answer. [2]
(i) Explain why the 100 ml cans cool faster than the 300 ml cans. [2]
(j) Describe two precautions you should take to make this a fair test. [2]
Answer Details
(a) The temperature of the 100 ml black can at 10 minutes is 55 °C. [1]
(b) The temperature of the 300 ml silver can at 20 minutes is 75 °C. [1]
(c) Total temperature drop over 20 minutes:
\[ \text{100 ml black: } 85 - 38 = 47\,{}^{\circ}\text{C} \quad [1] \]
\[ \text{300 ml black: } 85 - 63 = 22\,{}^{\circ}\text{C} \quad [1] \]
(d) Average rate of cooling for the 100 ml white can:
\[ \text{Rate} = \frac{\text{temperature drop}}{\text{time}} = \frac{85 - 49}{20} = \frac{36}{20} = 1.8\,{}^{\circ}\text{C/min} \quad [1] \]
(e) The combination that cools the fastest is 100 ml black. [1] It has the greatest temperature drop: from 85 °C to 38 °C, a total drop of 47 °C in 20 minutes.
(f) The combination that cools the slowest is 300 ml silver. [1] It has the smallest temperature drop: from 85 °C to 75 °C, a total drop of only 10 °C in 20 minutes.
(g) Darker surfaces cool faster than lighter or shinier surfaces. [1] For example, at 100 ml volume, the black can drops 47 °C while the silver can drops only \( 85 - 59 = 26\,{}^{\circ}\text{C} \). This is because dark, matt surfaces are better emitters of infrared radiation, so they radiate thermal energy more quickly. [1]
(h) Smaller volumes cool faster than larger volumes. [1] For example, the 100 ml black can drops 47 °C while the 300 ml black can drops only 22 °C. The smaller volume stores less total thermal energy, and the surface-area-to-volume ratio is larger, meaning heat can escape more quickly relative to the energy stored. [1]
(i) 100 ml of water stores less thermal energy than 300 ml at the same starting temperature (since \( E = mc\Delta T \) and the mass is smaller). [1] Additionally, smaller volumes have a larger surface-area-to-volume ratio, meaning a greater proportion of the water is close to the surface where heat can escape, so the rate of cooling relative to the stored energy is higher. [1]
(j) Any two precautions from: [1 each, max 2]
- Use cans of the same size and shape for all six tests
- Start all tests at the same temperature (85 °C)
- Use identical cardboard lids on all cans
- Carry out all tests in the same location at the same room temperature
- Allow each can to cool fully between tests if reusing cans
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