The Gemara declares emphatically that anything that was cooked on the eve of Shabbat can be re-cooked on Shabbat itself. There is tremendous discussion amongst the commentators as to whether this applies only to solids or as to whether the ruling also applies to liquids.

Rishonim: Rashi implies that the leniency applies primarily to solids and that one who reheats liquids would be transgressing the prohibition of the Sabbath. The Rosh concurs with this point of view. On the other hand, the Rambam concludes that the ruling applies both to solids and to liquids. According to him, I can reheat my chicken soup on Shabbat morning to boiling point. The Yemenite custom is indeed to follow this opinion. According to all views, liquids which have not descended from the temperature known as “Yad Soledet Bo,” (Codifiers argue as to what this temperature is but to some it may be even as high as 75 degrees Celsius) can be reheated to boiling point.

Halachic Codifiers: The Shulchan Aruch (318; 4), poskins stringently and therefore maintains that one may only reheat solid foods. The Ashkenazi custom according to the Rema is to be lenient on condition that the food has not cooled sown completely and is still at a temperature that one would feel comfortable serving as a hot meal (Igrot Moshe, Or Hachayim, 474). There is however, dispute as to what the Rema means. What is the nature of the prohibition of heating up chicken soup that has cooled down in its entirety? The Eglei Tal claims that this would be scripturally prohibited even according to the Rema. However, Rav Moshe Feinstein (ibid) posits that one would just be transgressing a rabbinic injunction.

A Practical Application: Could one; for example, pour boiling water into a cup that has cold-water droplets in it?

The Igrot Moshe is lenient only if the residue of water is previously boiled water that has just cooled down. He argues that one can be lenient in this regard since cooled down boiled water according to the Rema is at most a rabbinic prohibition. Droplets of cold tap water that was never previously boiled that are found in a cup would prohibit one from poring boiling water into it, as “their cooking” would represent with intention a scriptural injunction.

It should be however be noted that there are poskim who are lenient in this question even according to the stringent opinion of the Shulchan Aruch for reasons that go beyond the scope of this article (Rav Ovadya Yosef)

In all these issues, a competent halachic authority should always be consulted.