A body's temperature is increased from 900K to 1900K. By what factor does the total power radiated per unit area increase?
To determine the factor by which the total power radiated per unit area increases, we need to compare the power radiated at the initial temperature (900K) to the power radiated at the final temperature (1900K).
The total power radiated per unit area is given by the Stefan-Boltzmann law, which states that the power radiated is proportional to the fourth power of the temperature:
P ∝ T^4
where P is the power radiated per unit area and T is the absolute temperature.
Let's denote the initial power as P1 and the final power as P2. According to the Stefan-Boltzmann law, we can write the following proportion:
P2/P1 = (T2/T1)^4
Substituting the given temperatures, we have:
P2/P1 = (1900K/900K)^4
P2/P1 = (2.11)^4
P2/P1 = 44.87
Therefore, the total power radiated per unit area increases by a factor of approximately 44.87 when the body's temperature is increased from 900K to 1900K.