Radiative cooling can be used to freeze water in the desert at night. Consider a shallow pan of water is placed outdoors at night, well insulated from the ground below. The surface of the water has an emissivity of 0.8. The effective night sky temperature on this clear day is 260 K. Air blows very gently over the pan, creating a convective heat transfer coefficient of 10 W/m2 -K. a. Write an expression for the rate of heat loss from the pan to the sky.
b. Write an expression for the rate of heat gain to the pan from the air.
c. What is the maximum air temperature for which the water will freeze? (Hint: Assume the water temperature is at freezing, and perform a steady state energy balance on the pan).
d. If the pan were not well insulated from the ground, would the maximum air temperature for freezing be higher or lower? Explain your answer (Hint: think about the energy balance on the pan of water).