Chicken eggs possess a hard, porous shell of calcite mineral. Cylindrical pores of 10 micron (µm) diameter running through the 0.5 mm thickness of the shell permit the exchange of gases to the within the egg, as shown in the figure in the next column for a given single pore. A typical egg has 20,000 of these pores, which are not interconnected and which run parallel to each other. Each pore 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 5.0 cm. 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 itself, which is mostly water. The eggs are stored at the €œhen house€ temperature of 30^oC, and at this temperature the vapor pressure of water is 0.044 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^oC and 1.0 atm inside the pore? Is Knudsen diffusion very important in this diffusion process? 

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. 

c. Propose two changes in process conditions within the hen house that would reduce water loss by at least 50%. 

Transcribed Image Text:

Humidified air, 50% of saturation 10 µm diameter straight cylindrical pore (30°C, 1.0 atm) Calcite eggshell (0.5 mm thick) Membrane and egg yolk (mostly water)