Saturday, August 19, 2006

Salt water and eggs

On Shabbos 108a-b, the Mishnah brings down a machlokes regarding whether one is allowed to prepare small amounts of salt water on Shabbos for use as a condiment. In a b'raissa taught by Rav Yehudah bar Chaviva, it says that one is not allowed to make "strong" salt water. Rabbah and R' Yosef bar Abba state that strong salt water is defined as that of a concentration such that an egg floats in it. A quick-and-dirty kitchen laboratory experiment indicated that 2 teaspoons of salt in half a cup of water did not reach this concentration, but 3 teaspoons did; the concentration of this solution was therefore very roughly 15 mL salt/120 mL water, or an 11% solution by volume (4.7 M). I can attest that this solution was, indeed, quite strong.

The gemara, not wanting to force its readers to leave the Beis Medrash to go find an egg, asked the question of how concentrated this solution was. Abbayei answered 2/3 salt and 1/3 water. By volume, this would be 240 mL salt/120 mL water (my chavrusa pointed out that foods are rarely, if ever, measured by mass in Shas) - a much greater concentration than that which is required for the egg to simply float.

As the concentration of the salt water increases, its density would also increase, thereby causing more of the egg to protrude above the surface of the water, which introduces a different possible definition for flotation. However, the saturation concentration of salt in water is 36 mL salt/100 mL water - 1/6 that stated by Abbayei. In other words, almost all of the salt in Abbayei's solution would settle to the bottom of the solution within some short time span. When the egg is placed into this solution in which there is a salty precipitate, the presence of the additional salt would have no impact on the buoyancy of the egg, as the egg would merely contribute to the force driving the salt downwards to the bottom, leaving the concentration of the salt solution at 36mL/100mL, and with no different properties that one which was formulated with that strength to begin with.

I suppose that one can respond with the stock answer of nishtana ha-teva, that not only was the Talmudic egg twice the volume of one of our eggs, but it was also 32 times its weight (with a density greater than all but a handful of metals, such as gold, osmium, and a bunch of others that only chem nerds would be familiar with), but this is sort of the nuclear option when it comes to trying to understand a sugya. This being the case, it seems clear to me that I'm misunderstanding Abbayei (since it does not seem possible that anyone could have observed what I think that Abbayei is stating to be the case), but I don't know where my mistake is.

It may be assumed that any deviations from normal conditions (temperature, air pressure) that Abbayei may have been working under would have a minimal effect on his final results.



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