An evaporative ice maker, consider a circular shallow dish of water 0.5 m in diameter and filled to the brim, resting on an insulating layer, such as loose straw, and in a windless area. At what air temperature can the water be cooled to freezing if the relative humidity of the air is 30%? Make the following assumptions:

(a) Neglect radiation,

(b) Consider radiation to a night sky of effective temperature 150K,

(c) Assume that the dish has a lip around the edge 2 mm high.