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Chicken eggs possess a hard, porous shell of calcite mineral. Cylindrical pores of 10micron diameter running through the 0.5mm thickness of the shell permit the exchange of gasses to the inner membrane and egg yolk. A typical egg has 20,000 of these pores, which are not interconnected, and run parallel to each other. Each pores extends from the outer surface of the egg shell down to the egg membrane, which contains the egg yolk. The egg is approximately spherical in shape, with an outer diameter of 5.0cm. We are interested in predicting the loss of water from one egg by diffusion of water vapor through the egg shell. The source of the water vapor is the egg yolk, which is mostly water. The eggs are stored at the "hen house" with controlled temperature of 30 °C. At this temperature, the vapor pressure of water is 0.04 atm. The relative humidity of the ambient air surrounding the egg is 50% of saturation, corresponding to a H2O partial pressure of 0.022 atm.
a. What is the molecular diffusion coefficient of water vapor in air at 30 °C and 1.0 atm inside the pore? Can the diffusion be considered as a pure Knudsen diffusion? Knudsen diffusion can be assumed negligible when Kn < 0.1
b. Determine the water loss from a single egg in units of grams of water per day. State all relevant assumptions used in the calculation.
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