Final answer:
To calculate the temperature the entire sky would have to be in order to transfer energy by radiation at 1000 W/m², we can use the Stefan-Boltzmann Law. Using the given values, the temperature is approximately 305 K.
Step-by-step explanation:
To calculate the temperature the entire sky would have to be in order to transfer energy by radiation at 1000 W/m², we can use the Stefan-Boltzmann Law, which states that the power radiated by a black body is proportional to the fourth power of its temperature. In this case, we have the power (P) and the temperature of the body receiving the energy (T). The formula is:
P/A = σ * T^4
Where P is the power, A is the surface area, σ is the Stefan-Boltzmann constant, and T is the temperature. Rearranging the equation, we have:
T = (P / A / σ)^0.25
Using the given values, P = 1000 W/m², T = 27.0°C = 300.15 K, and σ = 5.67 x 10^-8 W/m²K^4, we can calculate the temperature:
T = (1000 / σ)^0.25 = 305 K
Therefore, the temperature the entire sky would have to be in order to transfer energy by radiation at 1000 W/m² is approximately 305 K.