Farmers usually concern that grapes may freeze during the night time when the effective sky temperature is low. The grape can be modeled as a small object with uniform temperature. During the night time, the grape receives irradiation from two sources, one is the cold sky on the top half of its surface (T_sky = 235 K) and the other is the ground surface of the earth on the other half of its surface (T_earth = 273 K). The total hemispherical irradiation G from the sky or the earth on the grape is equivalent to sigma T^4, where T is the temperature of the sky or the earth. The grape surface has a total hemispherical emissivity equal to 0.7. The total hemispherical absorptivity from the sky to the grape is equal to 0.9, while the total hemispherical absorptivity from the earth to the grape is equal to 0.7. Required:
a. Neglect convection heat transfer to the environment. Apply energy balance to the grape during steady state. Determine the steady state temperature of the grape. Do you think that the temperature of the grape is below the freeze temperature of -5°C?

b. One way to elevate the temperature of grapes is to use giant fan. The temperature of the surrounding air is also equal to 273 K. Explain why this method works. You can re-apply the energy balance (including the convection heat transfer) to back up your arguments. (C) You can also verify question B by actually calculate how high the convection coefficient h should be to ensure that the steady state grape temperature is equal to -5C.