(Beraisa): "Asher Tevushal Bo" teaches about a pot in which Chatas was cooked (it must be broken if it is earthenware, or Merikah u'Shtifah (scouring and rinsing, to Kasher it) if it is of metal.

Question: What is the source for a pot into which boiling Chatas was poured?

Answer: We learn from "Asher... Bo Yishaver" - if it absorbed Chatas (in any way).

(Rava): The latter law shows that Kashering is required for absorptions without cooking.

Question (Rami bar Chama): If Kodesh meat was suspended in an oven and roasted, what is the law? Is Merikah u'Shtifah required only when Kodshim were cooked inside and the Keli absorbed, but not here, for the meat did not touch the oven, so there were no absorptions?

Or, perhaps it is required whenever Kodshim were cooked inside, even without absorptions!

Shabbos 42a (Beraisa - Beis Hillel): One may pour hot water into cold water, or vice-versa.

This refers to a cup. However, in a bath, one may put only hot into cold.

R. Shimon ben Menasiyah forbids.

(Mishnah): On Shabbos, if one removed a frying pan or pot from the fire, one may not put spices into it. One may put spices into a bowl (a Keli Sheni).

R. Yehudah says, one may put into any (food), except for one with vinegar or brine.

(Beraisa - R. Yehudah): One may put into any simmering pot or pan, except for one with vinegar or brine.

This shows that R. Yehudah discusses the Reisha (putting spices in a Keli Rishon off the fire. (Compared to the first Tana,) he is lenient.

Chulin 111b (Rav Kahana, brother of Rav Yehudah): One may not put hot food in a basin in which meat was salted. A radish cut with a knife (used for meat) may be eaten with milk.

(Abaye): The basin is forbidden, for it absorbed forbidden taste. The radish is permitted, for it absorbed permitted taste.

Avodah Zarah 74b (Rava): We use boiling water to Kasher a Gas (in which a Nochri stomped grapes).

Rif and Rosh (Pesachim 8b and 2:7): Kelim used for Chametz in a Keli Sheni, e.g. bowls, it suffices to pour boiling water on them in a Keli Sheni and wait until the Isur is purged. We learn from pots of Nochrim. Everything is Kashered the way it is used.

Rambam (Hilchos Chametz 5:24): If Kelim of metal, stone or wood were used with Chametz in a Keli Sheni, e.g. cups and bowls, he puts them in a big Keli and pours boiling water over them and leaves them there until they emit (all absorbed taste). Then he rinses them, and he may use them for Matzah.

Rosh (Shabbos 3:16): The Rashbam learns from our Gemara (42b) that Iruy Keli Rishon is like a Keli Sheni. If it were like a Keli Rishon, why did the Mishnah distinguish between putting in a pot and a bowl? It should have permitted putting in a bowl, and forbidden pouring over it (from a Keli Rishon)! Also, we hold like Shmuel, who says that Tata'ah Gavar (the bottom food overpowers. I.e. when one food is put on another, the tastes mix only if the bottom is hot). If Iruy Keli Rishon cooks, this shows that the top food overpowers! The Rashbam permitted Meligah (pouring boiling water over a chicken to cook it). R. Tam said that one may infer oppositely from the Seifa. The Mishnah permits putting in a bowl, but not to pour over it! Also, if the Rashbam's inference were valid, this is difficult for Rav, who says that Ila'ah (the top food) Gavar! Rather, the Mishnah discusses a pot and bowl for parallel structure to the Reisha, which discusses putting water in a kettle or cup. R. Tam learns from Zevachim that Iruy Keli Rishon is like a Keli Rishon. Even though the Gemara said that pouring into a pot shows that absorptions without cooking forbid, it means absorptions without cooking from the heat of this pot, rather, from the heat of another pot. Also the Yerushalmi says that Iruy Keli Rishon is like a Keli Rishon. Even though we hold like Shmuel, that Tata'ah Gavar, he agrees that Iruy cooks Kedei Klipah (the thickness of a layer that can be peeled off). We challenged Shmuel from a Beraisa, and answered that Kedei Klipah must be removed. Also, in Pesachim (37b) we say that if flour put in boiling water is exempt from Chalah because it was kneaded in boiling water (because Tata'ah Gavar), also boiling water poured over flour is exempt. I.e. it cooks Kedei Klipah of the flour, and there does not remain a Shi'ur of uncooked flour to obligate Chalah. In Avodah Zarah (74b) Rava taught that boiling water is needed to Kasher a Gas in which a Nochri stomped grapes. One cannot fit the Gas in a Keli. Rather, boiling water was poured over it. Based on this, R. Tam permitted to Kasher a Keli used in a Keli Rishon through Iruy Keli Rishon. This is no proof. Yayin Nesech is different, for it is used cold, therefore we are more lenient than for other Isurim (which are heated in Kelim). If a Keli totally absorbed Isur, not all will come out through Iruy, which cooks only Kedei Klipah and purges (makes a Keli emit) only Kedei Klipah. Therefore, one who wants to cook an (unsalted) chicken through Meligah must do so in a Keli Sheni. If he does Iruy, this cooks Kedei Klipah (and the blood will not come out), so he must peel off the skin and the meat is permitted.

Shulchan Aruch (YD 68:13): Some say not to do Meligah even in a Keli Sheni. If he did, it is permitted.

Shach (33): R. Yerucham says that if one poured from a meat pot into a copper dairy pot, it need not be Kashered, for copper absorbs only if it is on the fire. The Poskim agree, and the Beis Yosef (Sof Siman 93) and Rema (Toras Chatas 33:3) rule like them. That is different. It is clear from the Bavli, Yerushalmi, and Poskim that a copper Keli absorbs through Iruy! In Zevachim we obligate Merikah u'Shtifah for a pot into which boiling Chatas was poured. This must refer to a copper Keli, for a Keli Cheres must be broken! It is difficult to say that the Gemara discusses a wooden Keli, for Stam Kelim in the Mikdash are of metal (Terumas ha'Deshen Sof 132. Also, the Gemara was discussing Kashering copper Kelim.) The Gemara was explaining the verse, which discusses cpper Kelim. The Sifra says so.

Gra (32): Zevachim 95b connotes that only Iruy Keli Rishon causes absorptions (but not a Keli Sheni).

Prishah (8): It is clear from the Rosh that R. Tam considers Iruy totally like a Keli Rishon. He brought several proofs, and concluded that a Keli used like a Keli Rishon may be Kashered through Iruy. The Rosh said that there is no proof from Avodah Zarah, since Yayin Nesech is used cold, and it cooks only Kedei Klipah. This shows that he understand that R. Tam holds that Iruy is like a full Keli Rishon (and cooks totally).

Shulchan Aruch (91:4): If boiling milk fell on meat, one peels the meat, and the rest of the meat is permitted.

Shach (7): Even if the flow was not interrupted, Kedei Klipah suffices. Even if the flow was interrupted, Kedei Klipah is needed.

Shulchan Aruch (105:2): The heat of a Keli Rishon that is Yad Soledes Bo cooks and totally forbids. The heat of a Keli Sheni does not cook. Some say that also, it does not emit (what is absorbed in the Keli), and it does not absorb (from its contents). Some say that it emits and absorbs, and forbids Kedei Klipah. It is proper to be concerned for this l'Chatchilah, but b'Di'eved it is permitted without a Klipah. It suffices to rinse.

Tur (citing the Rashba): Some say that only heat of a Keli Rishon, which cooks, emits. A Keli Sheni, and Iruy (pouring from a Keli Rishon), which is like a Keli Sheni, does not emit. This is wrong. The heat of Beis ha'Shechitah (the neck at the time of Shechitah) and of Chelev of the flanks, emits, and this is less than a Keli Sheni. Rather, every heat through fire emits, even if it is not Yad Soledes Bo.

Beis Yosef (DH Kosav ha'Rashba): How can the Tur say that the Rashba means that when hot falls into hot, it forbids only Kedei Klipah? Later in this Siman, he infers from the Rashba that the heat of salting (which is less) forbids everything! Also, in Pesachim (76a) we say that when hot falls into hot, it forbids; when hot falls into cold, one must remove Kedei Klipah. We cannot say that also hot into hot forbids only Kedei Klipah!

Shach (5): R. Tam holds that Iruy cooks Kedei Klipah, like a Keli Rishon. The Rashbam agrees that Iruy (of an Isur, or milk over meat) is absorbed in Kedei Klipah, just it does not emit and absorb at the same time. Therefore, one may do Iruy over a chicken (if it causes blood to be emitted, it will not be reabsorbed). He holds that a Keli Sheni does not absorb at all. R. Tam holds that Iruy is absorbed only Kedei Klipah. This is unlike Maharshal (Teshuvah 62), who say that it is totally absorbed. The Prishah says that R. Tam holds that it cooks totally. This is astounding. R. Tam and all who hold like him, including Semag, hold that a Keli Sheni does not cause absorptions Kedei Klipah. The Bach is stringent to say that a Keli Sheni emits and absorbs at once, and totally forbids. This is astounding. We are stringent to say that Iruy Keli Rishon forbids Kedei Klipah! Therefore, regarding Shabbos and meat and milk it is forbidden. Even if the flow was interrupted, Kedei Klipah is forbidden (Pesachim 76a). Even though the Rema (76:10) does not require Kedei Klipah for Iruy Keli Rishon over a chicken, that is because it does not emit and absorb at the same time. However, it absorbs. Tosfos in Zevachim, the Mordechai, Hagahos Ashri and the Ran say so. Kedei Klipah suffices. This is clear from the Poskim, Tur and Shulchan Aruch (91:4).

Gra (13): In the Yerushalmi, R. Yonah forbids Iruy like a Keli Rishon. R. Yosi rejects this; a Keli Cheres, even a Keli Sheni, absorbs, but the spices do not get cooked. Regarding Shabbos, we are concerned only for cooking. It says that Iruy cooks regarding Shabbos and regarding meat and milk.

Gra (14): Chulin 111b proved that absorption occurs even without cooking. The Ramban learn from Kodshim. We require Merikah u'Shtifah. Hag'alah in a Keli Sheni is not enough, even for a copper Kelim.

Shulchan Aruch (OC 451:1): One cannot Kasher for Pesach any Keli Cheres used for hot Chametz through heating it, even if it was not on the fire, only hot Chametz was poured into it.

Rema: Some forbid even in a Keli Sheni.

Magen Avraham (3): The stringent opinion forbids even a Keli that was put into a Keli Sheni. I say that even the Rambam forbids only through Iruy. Regarding metal Kelim, he says 'if they were used for a Keli Sheni, e.g. bowls and cups, he pours boiling water over them.' One does Iruy into bowls. Also, he allows Kashering through Iruy, so we must say that they were used for Chametz through Iruy. He calls it a Keli Sheni because after pouring into it, it is a Keli Sheni. The Rif says similarly. The Rambam (Halachah 25) said the same about Keli Cheres. The Beis Yosef agrees, for he omitted the law of Keli Cheres.

Shulchan Aruch (5): If one did Iruy over Kelim from a Keli Rishon, he Kashers them through Iruy Keli Rishon. It is not enough to Kasher them in a Keli Sheni.

Gra (DH Ela): Something used in a Keli Rishon cannot be Kashered through Iruy, which emits and absorbs only Kedei Klipah.

Mishnah Berurah (41): When Kashering through Iruy, he must ensure that they flow from the Keli Rishon not be interrupted.

Shulchan Aruch (6): The law of Kelim depends on the primary usage. Even if bowls are sometimes used on the fire, since they are used mostly through Iruy, they are Kashered in this way.

Rema: Some are stringent to do Hag'alah in a Keli Rishon. This is the custom. The same applies to anything for which there is concern lest it was used in a Keli Rishon, e.g. spoons.