Freeze drying is superior to straight drying for maintaining the structure of the vegetable/fruit being dried. The key to freeze drying is that the water is removed by sublimation (not evaporation from liquid). Hence, freeze drying occurs at low pressure conditions for water sublimation (typically identified as 200223K, well below freezing). Freeze drying involves 3 steps: (1) freezing at 1atm and 220K; (2) drying by sublimation at 220K and 40Pa; (3) warming the dry material at 300K and 1 atm. This problem only addresses the first step - freezing. Assume that freezing occurs during free fall of the pea through the freezing zone. Assume for all of the problem that the pea is sufficiently close to water in its behavior that you can use the properties of water (even when the pea is frozen). Also assume that the pea does not change size (not a perfect assumption but acceptable). Some useful properties of water/pea: Spherical pea with diameter of 6mm Latent heat of fusion 334J/g Heat capacity - 1cal/gK Thermal conductivity of pea (liquid water) 0.56W/mK Thermal conductivity of air at 1atm and 220K=20mW/mK Kinematic viscosity of air at 1atm and 220K=9106m2/s Density of air at 1atm and 220K=1.6kg/m3 Prandtl number of air at 1atm and 220K=0.7 (a) How much energy needs to be extracted to take a room temperature (300K) pea to a frozen pea at 240K ? (b) What is the terminal velocity of the pea in the freezing zone? (c) What is the convective heat transfer coefficient in the freezing zone (assuming terminal velocity) (d) How tall must the freezing zone be to ensure frozen peas at the exit? (e) The goal is to remove the water from a 6mm diameter pea. How much energy is required to dry a frozen pea by sublimation as compared to heat drying a wet pea by evaporation? Only include the energy required for the phase change (not the sensible heat involved)