A solid at temperature T₁ is placed in an evacuated chamber that is at a temperature T₂ > T₁ . The rate of increase of the solid's temperature is proportional to

Step-by-step solution

Since the chamber is evacuated, heat transfer between the solid and the chamber occurs exclusively through radiation. According to the Stefan-Boltzmann law, the rate at which the solid absorbs heat from the chamber is P_ abs = e A T₂^4 , and the rate at which it emits heat is P_ emit = e A T₁^4 . The net rate of heat gained by the solid is given by: dQ dt = P_ abs - P_ emit = e A (T₂^4 - T₁^4) The rate of increase of the solid's temperature is related to the net heat gained by: dT₁ dt = 1 ms dQ dt = e A ms (T₂^4 -