Chicken eggs possess a hard, porous shell of calcite mineral. Cylindrical pores of 10 micron diameter running through the 0.5mm thickness of the shell permit the exchange of gases 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 itself, which is mostly water (you can assume it is pure water). Consider a hen house in Riverside in July with the air temperature and humidity inside the enclosure the same as that outside and the temperature in the egg and egg shell pores the same as that in the surrounding air. The air pressure surrounding the egg and in the pores is 0.95 atm.
a. What is the molecular diffusion coefficient of water vapor at the specified temperature and pressure? Should you use the binary gas diffusion coefficient, DAB, or the effective diffusion coefficient, Dae, and why?
b. How rapidly will water be lost from the eggs at the hottest time of the day (97 °F, 20% relative humidity)?
C. Assuming the eggs are initially filled with water (=yolk), how long (in days) would it take at that loss rate for 25% of the water to evaporate?