Chapter 12, Problem 12.142P

It is known that on clear nights a thin layer of water on the ground will freeze before the air temperature drops below $0^{\circ }C$ . Consider such a layer of water on a clear night for which the effective sky temperature is $-{30}^{\circ }C$ and the convection heat transfer coefficient due to wind motion is $h={\text{ 25 W/m}}^2\cdot K$ . The water may be assumed to have an emissivity of 1.0 and to be insulated from the ground as far as conduction is concerned. Neglecting evaporation, determine the lowest temperature that the air can have without the water freezing. Accounting now for the effect of evaporation, what is the lowest temperature that the air can have without the water freezing? Assume the air to be dry.