It is known that on clear nights the air temperature need not drop below \(0^{\circ} \mathrm{C}\) before a thin layer of water on the ground will freeze. Consider such a layer of water on a clear night for which the effective sky temperature is \(-30^{\circ} \mathrm{C}\) and the convection heat transfer coefficient due to wind motion is \(h=20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The water may be assumed to have an emissivity of 0.96 and to be insulated from the ground as far as conduction is concerned.

(a) Neglecting evaporation, determine the lowest temperature the air can have without the water freezing.

(b) For the conditions given, estimate the mass transfer coefficient for water evaporation \(h_{m}(\mathrm{~m} / \mathrm{s})\).

(c) Accounting now for the effect of evaporation, what is the lowest temperature the air can have without the water freezing? Assume the air to be dry.