Regarding the prohibition to reheat liquid foods on Shabbat (in cases where there is not a problem due to returning food to a heat source), what constitutes a liquid? Answer:
It is noteworthy that your premise of a prohibition is not obvious. The mishna (Shabbat 145b) teaches us that ein bishul achar bishul (=ebab – once a food has been (fully?) cooked, there is no further prohibition of cooking), and no gemara clearly distinguishes between solid and liquid. The distinction begins with Rashi (Shabbat 34a) on the topic of hatmana (insulating food) on Shabbat, who raises a concern one might heat up the food before insulating and thus violate bishul. The Rosh (Shabbat 3:11) in reconciling the two sources above posits that Rashi’s problem refers to food with liquid. Many poskim have offered suggestions why liquid is worse. Perhaps the most accepted is that the change in the food from the first cooking is less noticeable regarding liquids that have cooled off (see Chazon Ish, Orach Chayim 37:13).
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356 - Reheating Liquids on Shabbat
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Several Rishonim, including the Rambam, Rashba, and Ran, apply ebab even to liquids (see Beit Yosef, OC 318). Yet, the Shulchan Aruch (OC 318:4) is stringent on the matter. The Rama (ad loc. 15) cites those who are lenient on reheating liquid and concludes that it is permitted unless the food cooled off totally. The more accepted explanation of this compromise is that the Rama fundamentally accepts the lenient position, but is stringent Rabbinically when it is cooled off because it is unnoticeable that it was already cooked. Even for Sephardim, Rav Ovadia Yosef (Yabia Omer X, OC 26) posits that the Shulchan Aruch did not totally discount the lenient position. This leads the way for various leniencies. For example, he ruled that if one did reheat a liquid on Shabbat, it does not become forbidden to eat and that it is permitted to ask a non-Jew to reheat a liquid on his behalf.
There are broad differences between opinions on the parameters of a liquid. The Beit Yosef (OC 318) cites Rabbeinu Yona as saying that it depends on the majority of the food. This seems surprisingly lenient; after all, even if the prohibition does not apply to the solid part, how can one ignore the cooking occurring to the liquid? There are a few approaches to explain. One is that we find elsewhere regarding the laws of Shabbat that an object is defined by its majority. Also, the food was already cooked, just that we say that the process was "lost" when it cooled down. Therefore, if regarding the object’s majority the cooking is not lost, we can apply the rule of ebab. Also, whether the cooking is positive or negative may depend on majority. Yabia Omer (VII, OC 42) follows this lenient position, and Igrot Moshe (OC IV, 74 Bishul 7) allows it in a case of great need.
The Chatam Sofer (Shut OC 74) says that any amount of (external?) surface liquid makes reheating forbidden. Most classical sources (see Rosh, Shulchan Aruch ibid.) seem to take an in-between approach, referring to "have liquid in it". Unfortunately, few poskim go into detail of what that entails.
Orchot Shabbat (1:22) distinguishes between liquid sitting on the solid and that which accumulates separately. How would cholent with a little liquid that accumulates mainly near the bottom be considered? It seems logical on this matter of machloket to forbid only cases in which the liquid part has significance (see similar language with a different understanding in The 39 Melochos, p. 594). This can be when one will purposely eat the gravy, or when he wants it there to make it easier to heat up the whole food. Many cholents would be considered to have a significant liquid element, especially at night (at night, there is usually not a problem because one returns it when it is still hot). However, when reheating chicken, meat, or an oily kugel, one would not have to worry about a small pool of gravy that inadvertently appears next to meat. (We are not getting involved now in the discussion of the status of congealed gravy that becomes liquid after being heated).