The Acharonim indeed debate this point.  The Magen Avraham (318:35) writes, "It seems to me that it is forbidden to place a piece of boiling meat into cold broth, for since it does not mix, it cooks a layer's-worth."  According to the Magen Avraham, pouring liquid onto liquid does not accomplish bishul at all, and is therefore permissible, whereas pouring a solid into a liquid has the capacity to cook kedei kelipa, since the solid does not mix with the liquid.  Other Acharonim take issue with this position, claiming that the Gemara's discussion in Pesachim deals only with the issue of beli'a, and has no bearing on the question of bishul.  In their view, then, one is permitted to place hot meat into cold gravy on Shabbat.

            The Chavat Da'at (Y.D. 91, Bei'urim 5) objects to the Magen Avraham's view and writes the following:

This is very difficult.  After all, it is permissible even to place large quantities of water into a boiling kettle for it to be warmed, for the reason that the water is a substance that mixes, and it is impossible for only some of it to be cooked, and so long as all the water has not reached the point of yad soledet no bishul occurs at all.

The Chavat Da'at's argument runs consistent with the aforementioned comments of Tosefot in Pesachim 40b, that if the cold substance is a davar ha-mit'arev, it does not undergo bishul when a hot substance is poured into it.

            In practice, however, one should follow the stringent ruling of the Magen Avraham, given that even the Chavat Da'at suggests that we should perhaps be concerned that some liquid will be absorbed into the meat and then cooked inside the boiling meat.

            We might distinguish, however, between cold liquid that had never been cooked, and liquid that was previously cooked and subsequently cooled.  In the case of previously cooked liquids, we can take into account the view that previously cooked liquid is not subject to subsequent bishul (ein bishul achar bishul be-davar lach).  We may thus rely on those who argue with the Magen Avraham and permit placing hot meat into a cold liquid that had been previously cooked.  This is reminiscent of Rav Moshe Feinstein's ruling (in Iggerot Moshe O.C. 4:74:5), which we cited in a previous shiur, that one may add ketchup (since it had been previously cooked) to hot meat in a keli sheni.

2.         The Rashba suggests an entirely different reason why one may pour water from a keli rishon into other water: "Because it cools as it is poured and completely mixes with the cold water, such that it lacks the capacity to cook."  The basic principle underlying his view is that pouring has the status of a keli rishon only when one pours over spices and the like.  When one pours water into other water, they mix together completely, and thus the poured water has the status of a keli sheni, which is incapable of accomplishing bishul.  According to the Rashba, this situation does not involve at all the issue of ila'a gavar or tata'a gavar, because, practically speaking, this is not a case of "upper" and "lower" items.  The two items mix together in the keli sheni, and therefore no bishul can occur.

3. Tosefot in our sugya advance a different approach.  In their view, when discussing a davar ha-mit'arev we can speak of neither tata'a gavar nor of a keli sheni.  Rather, this involves an entirely different issue; here, the criterion is quantity.  If the hot water that is poured from the keli rishon is of a larger quantity than the water into which it is poured, then bishul occurs and this is forbidden.  If, however, the amount of cold water exceeds that of the hot water, one may pour the hot water into the cold water.  The Berayta which allowed pouring hot water into cold water speaks of the latter case, when the cold water constitutes the majority, as more often than not one pours the smaller quantity into the larger quantity, and not vice versa.

Pouring Cold Water into Hot Water

            Both Beit Hillel and Beit Shammai agree that one may not pour cold water into hot water in a keli rishon.  Beit Shammai appear to forbid pouring even into a keli sheni, as a safeguard against the possibility that one may pour into a keli rishon, whereas Beit Hillel permit pouring cold water into hot water in a keli sheni.

            The reason for the prohibition against pouring water into a keli rishon seems fairly simple: a keli rishon has the capacity to cook, and thus one may not pour cold water into a keli rishon.  However, according to Tosefot's theory, that when the two substances mix together the occurrence of bishul depends on which constitutes the majority, this prohibition should apply only when the hot water in the keli rishon is of a larger quantity than the cold water poured into it.

            According to the other Rishonim, who did not draw Tosefot's distinction regarding quantity, the question arises whether we should forbid pouring large quantities of cold water into a very small amount of hot water.  The halakha in such a case can be inferred from the Gemara's discussion concerning the Mishna's ambiguous comment (41a), "A kettle that was removed – one may not place in it cold water to be heated, but he may place in it or in a cup so that it will be warmed."  The Gemara records two opinions in explaining this Mishna.  Rav Ada Bar Matna explained that the Mishna forbids placing small amounts of water to be heated in the empty kettle, but permits placing large amounts of water in the kettle, because the water will only be warmed, but not heated.  Abayei, by contrast, explained that the Mishna refers to a full kettle that was taken off the fire.  According to his explanation, the Mishna forbids adding a small amount of cold water to be heated in the kettle, but allows adding large amounts of water, which will only be warmed through contact with the water in the kettle.  If the kettle is emptied, Abayei claims, one may not add water to it at all, because this solidifies the utensil, which constitutes a violation of Shabbat (gemar melakha).  As the Gemara notes, Abayei's reading follows the position of Rabbi Yehuda, who forbids performing on Shabbat a davar she-eino mitkavein – an action that will, without the individual's intent, result in a forbidden activity.  Halakha follows Rabbi Shimon's view, allowing a davar she-eino mitkavein on Shabbat, and therefore one may warm cold water by placing it in an empty kettle.

            It emerges from this discussion that one may place cold water in an empty kettle, or in a kettle off the fire containing hot water, if the cold water is of a large enough quantity that it would only be warmed, but not heated to the point of yad soledet.  One must ensure, however, to place the water in the kettle all at once, rather than gradually, so as to avoid the cooking of the first drops of water poured into the kettle.

            Surprisingly, the Rambam rules differently: "A kettle was that was emptied of its water – one may place in it cold water to warm, and one may pour hot water into the cold water or cold water into the hot water, provided that it [the hot water] is not in a keli rishon, because this would heat it considerably."

It appears from the Rambam that one may place cold water in an empty kettle, but it is forbidden to place cold water in a kettle containing water, for he writes, "provided that it [the hot water] is not in a keli rishon, because this would heat it considerably." 

             The Kesef Mishneh suggests two approaches to reconcile the Rambam's ruling with the Gemara:

1. The Rambam in fact does allow placing cold water into a kettle containing hot water, so long as in the kettle it could only be warmed, and not heated.  According to the Kesef Mishneh, the Rambam alludes to this ruling when he writes, "…because this would heat it considerably," suggesting that if this would only warm the water, it is permissible to place it in the kettle.  However, the Kesef Mishneh acknowledges the difficulty of this reading, as it assumes an ambiguous and misleading formulation on the Rambam's part.
2. The Rambam did not follow Abayei's reading of the Mishna, because it presumes the position of Rabbi Yehuda regarding davar she-eino mitkavein, which is not accepted as the final halakha.  And according to Rabbi Ada Bar Matna, the Mishna permits placing water only in an empty kettle, but not in a kettle containing water, since one might place less than the amount necessary to ensure that bishul will not occur.

The Ran (on the Rif in Shabbat) distinguishes between a standard keli rishon, into which one may place large quantities of cold water to be warmed, and an ambati (see next section).  Since the water in an ambati is exceptionally hot, one may not add even large amounts of cold water, since bishul might take place given the high temperature of the water in the ambati.

            The Kesef Mishneh suggests that this may be the source for the Rambam's ruling, only the Rambam drew no distinction between a keli rishon and an ambati, and forbade adding water to a keli rishon under any circumstances.

The Status of an Ambati

            The Berayta cited at the beginning of the shiur records a debate concerning the status of an ambati with regard to bishul.  An ambati is a tub used for bathing, and in those days the water in the ambati was generally hotter than hot water used for drinking.  The Tanna Kama (first recorded view) in the Mishna allows placing hot water into cold water in an ambati, whereas Rabbi Shimon Ben Menasya forbids doing so.  The Gemara later brings a discussion concerning the precise position taken by Rabbi Shimon Ben Menasya, and the Rishonim likewise disagree in identifying the kind of ambati of which the Gemara speaks, and in determining the final halakha from the sugya.  So as to spare the reader the intricacies of this sugya[4], we will discuss here only the issues that directly impact upon the final halakha.

1. Tosefot understood that the Gemara refers to a keli sheni, and treats it more stringently than a standard keli sheni because of its exceptionally high temperature, which might mislead people into thinking it is a keli rishon.  According to the Tur (318), this stringency is not merely a safeguard against misunderstanding, but rather evolves from the bishul prohibition itself: although bishul generally cannot occur in a keli sheni, an ambati is nevertheless subject to bishul because of its particularly intense heat.

           The Tur's position is followed by the Rashba, as well, who writes:

But in an ambati, which is intended for bathing purposes, one heats [the water] considerably, and therefore one may never add cold water into hot water [in an ambati], for it is impossible to reach the point of lukewarm; it will undoubtedly reach the point of bishul, even if one filled the ambati to capacity.  And although it is a keli sheni, which generally cannot effectuate cooking, this case is different because they [tubs in the bathhouse] are generally heated excessively.

According to this view, even if the ambati is but a keli sheni, one may not pour cold water into hot water or hot water into cold water in the ambati, in accordance with Rabbi Shimon Ben Menasya's view.

2. The Rif and Rambam (Hilkhot Shabbat 22:5; see Kesef Mishneh) rule against the position of Rabbi Shimon Ben Menasya, and allow adding hot water into cold water in an ambati, but not cold water into hot water.  They understood "ambati" as referring to a keli rishon, and thus one may add hot water to cold water, just as in any other keli rishon, as discussed earlier.

            However, the Ramban and the Ran assert that there indeed exists a distinction between an ambati and a standard keli rishon even according to the view of the Tanna Kama.  In a keli rishon, one may place large quantities of cold water to be warmed, whereas in an ambati this would be forbidden.  The Ran writes (20a in the Rif):

Meaning, [it is forbidden] even to place a large amount of cold water, which would only make it lukewarm, for although the Mishna states regarding a kettle that one may place [water] into it to warm it, in an ambati they forbade even warming [water], because people are very insistent regarding its heat.

The Rambam, as mentioned, draws no distinction between an ambati and a standard keli rishon.[5]

The Final Halakha

            The Shulchan Arukh writes (318:11-12):

An ambati (Rama: meaning, a tub used for bathing) of a bathhouse, which is filled with hot water, (Rama: even though it is a keli sheni) one may not add cold water to it because it is heated considerably.  But one may place some hot water from one ambati into another ambati containing cold water.  A kettle that was emptied of its hot water – one may place into it (Rama: a large quantity of) cold water to be warmed; one may pour hot water into cold water or cold water into hot water, provided that he does not do so in a keli rishon, because this heats it considerably.

Rama: If there is so much water that it cannot be cooked, but it will only be thawed, this is permissible even in a keli rishon, so long as it is not over a fire.

In the interest of simplification, let us summarize the various halakhot as they emerge from the rulings of the Shulchan Arukh, the Rama, and later Acharonim.

1. The straightforward reading of the Shulchan Arukh suggests that he followed the Rambam's view.  In light of his comments in the Beit Yosef, we may summarize his view as follows:

            One may not pour a large quantity of water into hot water in a keli rishon, regardless of whether the water is intended for drinking or for bathing.

            One may pour hot water into cold water under all circumstances, even from a keli rishon.

            One may pour hot water from a keli sheni onto cold water or cold water into hot water in a keli sheni, even if the keli sheni is an ambati used for bathing.

            One may pour a large quantity if cold water all at once into a kettle that had been emptied of its water, so long as the water will only be warmed, but not heated.

2. The Rama's view (his points of disagreement with the Shulchan Arukh):

            The Rama forbids adding cold water to an ambati even if it is a keli sheni; the Mishna Berura explained based on the reasons given by the Tur and the Rashba (as cited earlier).  One may add a large amount of cold water to an ambati that is a keli sheni, but not a keli rishon (out of concern for the Ran's position).  This would be permissible in a keli rishon containing hot water for drinking (as opposed to bathing).

3. Halakhot discussed by later Poskim

A.     The Mishna Berura rules in accordance with Tosefot's position, that one may pour hot water from a keli rishon into cold water only if the cold water is of a larger amount than the hot water.  He adds, however, that be-di'avad, if one poured an amount of hot water that exceeded the cold water, one may drink the water, relying on the views of Rashi, the Rashba, the Tur and the Rambam, all of whom are lenient in this regard, despite the uncertainties surrounding their positions.

B.     If one pours a large amount of hot water into liquid that had been previously cooked and then cooled, such as tea essence, we may take into account the view that previously cooked liquid is no longer subject to bishul.  Therefore, even though one should preferably pour the water from the kettle into an empty utensil and then add the essence, one should not object to those who are lenient and pour the hot water directly onto the essence (Bei'ur Halakha, citing the Beit Meir).

Practically speaking, even those who generally follow the Shulchan Arukh's rulings should refrain from pouring large amounts of hot water into small amounts of cold water, in accordance with Tosefot's position.  Be-di'avad, however, one may rely on the lenient views, and thus drink water that had been prepared in this fashion.

Preparing Tea

            In this context we will briefly mention the preferred method for preparing tea on Shabbat, in light of the principles discussed in this shiur:

1. Preferably, one should prepare tea essence and keep it hot in a kettle.  When preparing tea, one should pour some essence into a cup and then pour hot water from the kettle.
2. If the essence is not hot, one should pour hot water into a cup and then add the essence.  There is no concern that one thereby colors the water, because strictly speaking, Halakha follows the view that ein tzevi'a be-okhelin – the prohibition against dyeing materials does not apply to foods.
3. If one did not prepare tea essence before Shabbat, he can prepare tea in a keli shelishi; we will discuss this further in the next shiur.

Miscellaneous Laws

            In conclusion, we will make several additional points concerning the issues addressed in this shiur:

1. If one pours hot water from a kettle into a wet cup, the drops of cold water on the cup will be "cooked" by the hot water.  Therefore, some poskim require drying the cup before pouring the hot water.  Rav Moshe Feinstein (Iggerot Moshe, O.C. 1:93) writes:

We should forbid pouring boiling water from a keli rishon into a utensil that was rinsed with cold water that had not been cooked, and drops remain on it, because the drops are cooked.  And even though one has no interest [in cooking these drops], this should be forbidden, and one must dry it [before pouring the hot water].  However, since they do not comprise the prerequisite quantity for [Shabbat] violation, then even though it is forbidden from the Torah because chatzi shiur [a violation of less than the prerequisite amount] is forbidden by Torah law, one might perhaps be lenient if he rinsed with cold water that had been cooked and then cooled, since there are those who hold that even liquids that were cooked and then cooled are not subject to bishul, and this is also a situation of pesik reisha de-lo nicha lei [where one performs an action that automatically results in the occurrence of a melakha in which he has no interest].  But if the [water] had never been boiled, this is forbidden.

Some poskim, however, ruled leniently on this issue because it is a situation of pesik reisha de-lo nicha lei, and because the Rashba and others allow adding a large amount of hot water into a small amount of cold water.  As far as practical Halakha is concerned, one should preferably dry the cup.  If, however, the drops in the cup had been cooked and then cooled, there is more room to be lenient, taking into account the views that bishul does not apply to liquids that had been previously cooked, as we cited from the Iggerot Moshe.

2. Earlier, we allowed pouring a large amount of cold water into a small amount of hot water, but we noted that the water must be poured all at once, for if one pours gradually, the first drops will be cooked by the comparatively large amount of hot water.  The Chayei Adam (20:3) indeed makes this point.  Others, however, disagreed, and allowed pouring gradually.  The Penei Yehoshua (Shabbat 41a) writes:

It would appear regarding this matter that whenever one pours the water continuously without any interruption, and he expresses his intention that he has no interest in heating [the water], but only in warming [the water] – it is therefore permissible, since no melakha of bishul can occur in this manner, and it thus does not resemble cooking at all.

One should preferably follow the stringent view and pour the water all together at the same time, rather than gradually.

3. The sugyot and poskim distinguished between hot water prepared for drinking and hot water intended for bathing, because water prepared for bathing is at a higher temperature.  Apparently, the practice was to prepare hot water for drinking only to the point of yad soledet bo, whereas water for bathing was heated beyond this temperature.  Indeed, the Rashba (Shabbat 42a s.v. notein) writes, "It is customary to add a lot of cold water to the cup and even to the kettle to be warmed, because they are prepared for drinking, and a person does not drink very hot liquids, but rather lukewarm liquids."  Accordingly, the question arises as to whether this principle would apply nowadays, when people generally prepare hot drinks by boiling the water, but bathe in water at a temperature of only 60-70 degrees Centigrade.  Should we therefore apply to hot drinks all the stringencies mentioned by the poskim concerning bathing water, such as the Rama's ruling forbidding adding cold water to an ambati even if it is a keli sheni?