An astrophysics experiment models the thermal emission of two small planetary probes, P and Q, inside a vacuum test chamber.
The probes are made of identical materials and have the same dimensions, but different surface finishes:
- Probe P is coated with a high-emissivity matte black layer.
- Probe Q is coated with a low-emissivity polished metallic layer.
Each probe is initially heated to a different starting temperature. The heating elements are turned off, and the probes are left to cool by radiating energy into the cold vacuum chamber.
The graph in Figure 1 shows how the temperature of each probe changes over a 50-minute period.
Some recorded measurements are shown in the table below:
| Time (minutes) | Temperature of Probe P (°C) | Temperature of Probe Q (°C) |
|---|---|---|
| 0 | 85 | 65 |
| 5 | 67 | 57 |
| 10 | 53 | 50 |
| 15 | 44 | 44 |
| 20 | 37 | 39 |
| 30 | 27 | 31 |
| 40 | 21 | 25 |
| 50 | 18 | 21 |
Use Figure 1 to determine the time when Probe P and Probe Q were at the exact same temperature.
Show your working on the graph.