Hatching eggs need to lose weight during the incubation process, approximately 11% of their initial weight at setting.
Eggs also uptake oxygen and release carbon dioxide. Although there is a difference in weight between these molecules, the RQ value (the ratio between oxygen uptake and carbondioxide release) is of such magnitude that the weight loss will be completely correlated with the moisture loss of the eggs.
The moisture loss of eggs is a function of the water vapor pressure inside and outside the egg, and the resistance of the shell and the membranes against moisture loss (the conductance). These functions are not influenced by the fact if an egg is infertile or fertile. This means that theoretically the moisture loss of an infertile and a fertile egg will be identical, if placed in the same conditions.
In theory this is true, but in practice we often see that fertile eggs have a slightly higher moisture loss than infertile eggs. This is not due to any change in conductance of the egg, but because the development of the embryo has an influence on the water vapor pressure inside the egg.
The water vapor pressure (expressed as Pa) is a function of temperature and relative humidity. When the embryo is developing, it will produce heat and as a result the egg will be slightly warmer than its environment. Due to this increased temperature inside the egg, the water vapor pressure inside the egg will go up as well. As moisture loss if a function of water vapor pressure inside and outside of the egg over the barrier of the egg shell, a higher temperature and therefore a higher water vapor pressure inside the egg will result in a sligthly increased moisture loss.