Question

Two black bodies emit the same amount of radiation per second. The radius of the first is \( R_1 = 2 \, \text{m} \) and its temperature is \( T_1 = 400 \, \text{K} \). If the second body has a radius \( R_2 = 4 \, \text{m} \), what is its temperature \( T_2 \) in Kelvin?

• A. \( 200 \, \text{K} \)
• B. \( 300 \, \text{K} \)
• C. \( 250 \, \text{K} \)
• D. \( 400 \, \text{K} \)

Hint:

The Stefan-Boltzmann law relates the power emitted by a body to its temperature and surface area. For bodies emitting the same power, the temperature ratio depends on the radius ratio raised to the fourth power.