Final answer:
When the absolute temperature of an object is tripled, the thermal power radiated per unit surface area increases by a factor of 81, in accordance with the Stefan-Boltzmann law, which states the power radiated is proportional to the fourth power of the temperature.
Step-by-step explanation:
If the absolute temperature of an object is tripled, we can determine the change in the thermal power radiated per unit surface area by using the Stefan-Boltzmann law, which states that the radiated heat is proportional to the fourth power of the absolute temperature. This is a key relationship in understanding how thermal radiation works.
According to the Stefan-Boltzmann law,
F ≈ T⁴
where F is the energy flux and T is the absolute temperature in kelvins. Therefore, if the temperature is tripled (T becomes 3T), the radiated power changes by a factor of (3T)⁴ or 3⁴, which equals 81. Thus, the thermal power radiated per unit surface area will increase by a factor of 81. The correct answer to the student's question is option A) increase by a factor of 81.
This means that a seemingly moderate increase in the absolute temperature can lead to a dramatic increase in the power radiated due to the fourth power relationship.