87.7k views
5 votes
If the absolute temperature of an object is tripled, the thermal power radiated per unit surface area of this object will (assuming that its emissivity is not affected by the temperature change)

A) increase by a factor of 81.
B) increase by a factor of 27.
C) increase by a factor of 18.
D) increase by a factor of 9.
E) increase by a factor of 3.

User CCJ
by
8.4k points

1 Answer

3 votes

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.

User Giladrv
by
7.2k points