Chapter 14, Problem 64PE

Calculate the temperature the entire sky would have to be in order to transfer energy by radiation at $\text{1}000\text{ W}/{\text{m}}^{\text{2}}$ —about the rate at which the Sun radiates when it is directly overhead on a clear day. This value is the effective temperature of the sky, a kind of average that takes account of the fact that the Sun occupies only a small part of the sky but is much hotter than the rest. Assume that the body receiving the energy has a temperature of $\text{27}.0°\text{C}$.